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class="vector-toc-link" href="#Stări_și_transformări"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Stări și transformări</span> </div> </a> <button aria-controls="toc-Stări_și_transformări-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Stări și transformări subsection</span> </button> <ul id="toc-Stări_și_transformări-sublist" class="vector-toc-list"> <li id="toc-Principiul_zero_al_termodinamicii" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Principiul_zero_al_termodinamicii"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Principiul zero al termodinamicii</span> </div> </a> <ul id="toc-Principiul_zero_al_termodinamicii-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lucru_mecanic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lucru_mecanic"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Lucru mecanic</span> </div> </a> <ul id="toc-Lucru_mecanic-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Principiul_întâi_al_termodinamicii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Principiul_întâi_al_termodinamicii"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Principiul întâi al termodinamicii</span> </div> </a> <button aria-controls="toc-Principiul_întâi_al_termodinamicii-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Principiul întâi al termodinamicii subsection</span> </button> <ul id="toc-Principiul_întâi_al_termodinamicii-sublist" class="vector-toc-list"> <li id="toc-Energie_internă" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energie_internă"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Energie internă</span> </div> </a> <ul id="toc-Energie_internă-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cantitate_de_căldură" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cantitate_de_căldură"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Cantitate de căldură</span> </div> </a> <ul id="toc-Cantitate_de_căldură-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temperatură_empirică" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temperatură_empirică"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Temperatură empirică</span> </div> </a> <ul id="toc-Temperatură_empirică-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ecuații_de_stare" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ecuații_de_stare"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Ecuații de stare</span> </div> </a> <ul id="toc-Ecuații_de_stare-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Principiul_al_doilea_al_termodinamicii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Principiul_al_doilea_al_termodinamicii"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Principiul al doilea al termodinamicii</span> </div> </a> <button aria-controls="toc-Principiul_al_doilea_al_termodinamicii-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Principiul al doilea al termodinamicii subsection</span> </button> <ul id="toc-Principiul_al_doilea_al_termodinamicii-sublist" class="vector-toc-list"> <li id="toc-Temperatură_termodinamică" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temperatură_termodinamică"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Temperatură termodinamică</span> </div> </a> <ul id="toc-Temperatură_termodinamică-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Entropie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Entropie"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Entropie</span> </div> </a> <ul id="toc-Entropie-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Stări_de_echilibru" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stări_de_echilibru"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Stări de echilibru</span> </div> </a> <button aria-controls="toc-Stări_de_echilibru-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Stări de echilibru subsection</span> </button> <ul id="toc-Stări_de_echilibru-sublist" class="vector-toc-list"> <li id="toc-Potențiale_termodinamice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Potențiale_termodinamice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Potențiale termodinamice</span> </div> </a> <ul id="toc-Potențiale_termodinamice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Schimb_de_căldură" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schimb_de_căldură"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Schimb de căldură</span> </div> </a> <ul id="toc-Schimb_de_căldură-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Schimb_de_substanță" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schimb_de_substanță"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Schimb de substanță</span> </div> </a> <ul id="toc-Schimb_de_substanță-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Transformări_ireversibile" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Transformări_ireversibile"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Transformări ireversibile</span> </div> </a> <ul id="toc-Transformări_ireversibile-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Principiul_al_treilea_al_termodinamicii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Principiul_al_treilea_al_termodinamicii"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Principiul al treilea al termodinamicii</span> </div> </a> <ul id="toc-Principiul_al_treilea_al_termodinamicii-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lectură_suplimentară" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lectură_suplimentară"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Lectură suplimentară</span> </div> </a> <ul id="toc-Lectură_suplimentară-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vezi_și" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vezi_și"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Vezi și</span> </div> </a> <ul id="toc-Vezi_și-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Cuprins" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Comută cuprinsul" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Comută cuprinsul</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Termodinamică</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Mergeți la un articol în altă limbă. Disponibil în 125 limbi" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-125" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">125 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Termodinamika" title="Termodinamika – afrikaans" lang="af" hreflang="af" data-title="Termodinamika" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – germană (Elveția)" lang="gsw" hreflang="gsw" data-title="Thermodynamik" data-language-autonym="Alemannisch" data-language-local-name="germană (Elveția)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Termodinamica" title="Termodinamica – aragoneză" lang="an" hreflang="an" data-title="Termodinamica" data-language-autonym="Aragonés" data-language-local-name="aragoneză" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – angika" lang="anp" hreflang="anp" data-title="उष्मागतिकी" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A%D8%A9" title="ديناميكا حرارية – arabă" lang="ar" hreflang="ar" data-title="ديناميكا حرارية" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B7%D9%8A%D8%B1%D9%85%D9%88%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83" title="طيرموديناميك – Moroccan Arabic" lang="ary" hreflang="ary" data-title="طيرموديناميك" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF_%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="তাপগতি বিজ্ঞান – asameză" lang="as" hreflang="as" data-title="তাপগতি বিজ্ঞান" data-language-autonym="অসমীয়া" data-language-local-name="asameză" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – asturiană" lang="ast" hreflang="ast" data-title="Termodinámica" data-language-autonym="Asturianu" data-language-local-name="asturiană" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Termodinamika" title="Termodinamika – azeră" lang="az" hreflang="az" data-title="Termodinamika" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترمودینامیک – South Azerbaijani" lang="azb" hreflang="azb" data-title="ترمودینامیک" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – bașkiră" lang="ba" hreflang="ba" data-title="Термодинамика" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – Bavarian" lang="bar" hreflang="bar" data-title="Thermodynamik" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Termuodinam%C4%97ka" title="Termuodinamėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Termuodinamėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Termodinamika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Тэрмадынаміка – belarusă" lang="be" hreflang="be" data-title="Тэрмадынаміка" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Тэрмадынаміка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэрмадынаміка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – bulgară" lang="bg" hreflang="bg" data-title="Термодинамика" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="তাপগতিবিজ্ঞান – bengaleză" lang="bn" hreflang="bn" data-title="তাপগতিবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Termodinamika" title="Termodinamika – bosniacă" lang="bs" hreflang="bs" data-title="Termodinamika" data-language-autonym="Bosanski" data-language-local-name="bosniacă" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – catalană" lang="ca" hreflang="ca" data-title="Termodinàmica" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8E%D8%B1%D9%85%DB%86%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="تێرمۆدینامیک – kurdă centrală" lang="ckb" hreflang="ckb" data-title="تێرمۆدینامیک" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Termodynamika" title="Termodynamika – cehă" lang="cs" hreflang="cs" data-title="Termodynamika" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – ciuvașă" lang="cv" hreflang="cv" data-title="Термодинамика" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Thermodynameg" title="Thermodynameg – galeză" lang="cy" hreflang="cy" data-title="Thermodynameg" data-language-autonym="Cymraeg" data-language-local-name="galeză" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Termodynamik" title="Termodynamik – daneză" lang="da" hreflang="da" data-title="Termodynamik" data-language-autonym="Dansk" data-language-local-name="daneză" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – germană" lang="de" hreflang="de" data-title="Thermodynamik" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%81%CE%BC%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE" title="Θερμοδυναμική – greacă" lang="el" hreflang="el" data-title="Θερμοδυναμική" data-language-autonym="Ελληνικά" data-language-local-name="greacă" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – engleză" lang="en" hreflang="en" data-title="Thermodynamics" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Termodinamiko" title="Termodinamiko – esperanto" lang="eo" hreflang="eo" data-title="Termodinamiko" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – spaniolă" lang="es" hreflang="es" data-title="Termodinámica" data-language-autonym="Español" data-language-local-name="spaniolă" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Termod%C3%BCnaamika" title="Termodünaamika – estonă" lang="et" hreflang="et" data-title="Termodünaamika" data-language-autonym="Eesti" data-language-local-name="estonă" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Termodinamika" title="Termodinamika – bască" lang="eu" hreflang="eu" data-title="Termodinamika" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – Extremaduran" lang="ext" hreflang="ext" data-title="Termodinámica" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترمودینامیک – persană" lang="fa" hreflang="fa" data-title="ترمودینامیک" data-language-autonym="فارسی" data-language-local-name="persană" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Termodynamiikka" title="Termodynamiikka – finlandeză" lang="fi" hreflang="fi" data-title="Termodynamiikka" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/L%C3%A4mm%C3%A4oppus" title="Lämmäoppus – Võro" lang="vro" hreflang="vro" data-title="Lämmäoppus" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Thermodynamique" title="Thermodynamique – franceză" lang="fr" hreflang="fr" data-title="Thermodynamique" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Termod%C3%BCnaamik" title="Termodünaamik – frizonă nordică" lang="frr" hreflang="frr" data-title="Termodünaamik" data-language-autonym="Nordfriisk" data-language-local-name="frizonă nordică" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Termodynamika" title="Termodynamika – frizonă occidentală" lang="fy" hreflang="fy" data-title="Termodynamika" data-language-autonym="Frysk" data-language-local-name="frizonă occidentală" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teirmidinimic" title="Teirmidinimic – irlandeză" lang="ga" hreflang="ga" data-title="Teirmidinimic" data-language-autonym="Gaeilge" data-language-local-name="irlandeză" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Termodinamik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – galiciană" lang="gl" hreflang="gl" data-title="Termodinámica" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – guarani" lang="gn" hreflang="gn" data-title="Termodinámica" data-language-autonym="Avañe'ẽ" data-language-local-name="guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%A8%D7%9E%D7%95%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94" title="תרמודינמיקה – ebraică" lang="he" hreflang="he" data-title="תרמודינמיקה" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – hindi" lang="hi" hreflang="hi" data-title="उष्मागतिकी" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – Fiji Hindi" lang="hif" hreflang="hif" data-title="Thermodynamics" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Termodinamika" title="Termodinamika – croată" lang="hr" hreflang="hr" data-title="Termodinamika" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/T%C3%A8modinamik" title="Tèmodinamik – haitiană" lang="ht" hreflang="ht" data-title="Tèmodinamik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiană" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Termodinamika" title="Termodinamika – maghiară" lang="hu" hreflang="hu" data-title="Termodinamika" data-language-autonym="Magyar" data-language-local-name="maghiară" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1" title="Ջերմադինամիկա – armeană" lang="hy" hreflang="hy" data-title="Ջերմադինամիկա" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Thermodynamica" title="Thermodynamica – interlingua" lang="ia" hreflang="ia" data-title="Thermodynamica" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Termodinamika" title="Termodinamika – indoneziană" lang="id" hreflang="id" data-title="Termodinamika" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Termodinamika" title="Termodinamika – iloko" lang="ilo" hreflang="ilo" data-title="Termodinamika" data-language-autonym="Ilokano" data-language-local-name="iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Termodinamiko" title="Termodinamiko – ido" lang="io" hreflang="io" data-title="Termodinamiko" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Varmafr%C3%A6%C3%B0i" title="Varmafræði – islandeză" lang="is" hreflang="is" data-title="Varmafræði" data-language-autonym="Íslenska" data-language-local-name="islandeză" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Termodinamica" title="Termodinamica – italiană" lang="it" hreflang="it" data-title="Termodinamica" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%A6" title="熱力学 – japoneză" lang="ja" hreflang="ja" data-title="熱力学" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Toermodainamix" title="Toermodainamix – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Toermodainamix" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="თერმოდინამიკა – georgiană" lang="ka" hreflang="ka" data-title="თერმოდინამიკა" data-language-autonym="ქართული" data-language-local-name="georgiană" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/So%C5%8Bga%C9%A3_n%C9%9B_%C9%96o%C5%8B_kp%C9%9Bl%C9%9Bk%CA%8B%CA%8B_t%C9%9B" title="Soŋgaɣ nɛ ɖoŋ kpɛlɛkʋʋ tɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Soŋgaɣ nɛ ɖoŋ kpɛlɛkʋʋ tɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – kazahă" lang="kk" hreflang="kk" data-title="Термодинамика" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B4%EC%97%AD%ED%95%99" title="열역학 – coreeană" lang="ko" hreflang="ko" data-title="열역학" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Termod%C3%AEnam%C3%AEk" title="Termodînamîk – kurdă" lang="ku" hreflang="ku" data-title="Termodînamîk" data-language-autonym="Kurdî" data-language-local-name="kurdă" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – kârgâză" lang="ky" hreflang="ky" data-title="Термодинамика" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Thermodynamica" title="Thermodynamica – latină" lang="la" hreflang="la" data-title="Thermodynamica" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – luxemburgheză" lang="lb" hreflang="lb" data-title="Thermodynamik" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgheză" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Termudinamica" title="Termudinamica – Lombard" lang="lmo" hreflang="lmo" data-title="Termudinamica" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Termodinamika" title="Termodinamika – lituaniană" lang="lt" hreflang="lt" data-title="Termodinamika" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Termodinamika" title="Termodinamika – letonă" lang="lv" hreflang="lv" data-title="Termodinamika" data-language-autonym="Latviešu" data-language-local-name="letonă" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – macedoneană" lang="mk" hreflang="mk" data-title="Термодинамика" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A4%E0%B4%BE%E0%B4%AA%E0%B4%97%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B4%82" title="താപഗതികം – malayalam" lang="ml" hreflang="ml" data-title="താപഗതികം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA" title="Термодинамик – mongolă" lang="mn" hreflang="mn" data-title="Термодинамик" data-language-autonym="Монгол" data-language-local-name="mongolă" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="ऊष्मागतिकी – marathi" lang="mr" hreflang="mr" data-title="ऊष्मागतिकी" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Termodinamik" title="Termodinamik – malaeză" lang="ms" hreflang="ms" data-title="Termodinamik" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%AC%E1%80%99%E1%80%AD%E1%80%AF%E1%80%92%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%94%E1%80%99%E1%80%85%E1%80%BA" title="သာမိုဒိုင်းနမစ် – birmană" lang="my" hreflang="my" data-title="သာမိုဒိုင်းနမစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmană" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – germana de jos" lang="nds" hreflang="nds" data-title="Thermodynamik" data-language-autonym="Plattdüütsch" data-language-local-name="germana de jos" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – nepaleză" lang="ne" hreflang="ne" data-title="उष्मागतिकी" data-language-autonym="नेपाली" data-language-local-name="nepaleză" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Thermodynamica" title="Thermodynamica – neerlandeză" lang="nl" hreflang="nl" data-title="Thermodynamica" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Termodynamikk" title="Termodynamikk – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Termodynamikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Termodynamikk" title="Termodynamikk – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Termodynamikk" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Termodinamica" title="Termodinamica – occitană" lang="oc" hreflang="oc" data-title="Termodinamica" data-language-autonym="Occitan" data-language-local-name="occitană" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Daayinaamiksii_Ho%E2%80%99aa" title="Daayinaamiksii Ho’aa – oromo" lang="om" hreflang="om" data-title="Daayinaamiksii Ho’aa" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%BE%E0%A8%AA_%E0%A8%97%E0%A8%A4%E0%A9%80_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਤਾਪ ਗਤੀ ਵਿਗਿਆਨ – punjabi" lang="pa" hreflang="pa" data-title="ਤਾਪ ਗਤੀ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Termodynamika" title="Termodynamika – poloneză" lang="pl" hreflang="pl" data-title="Termodynamika" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – Piedmontese" lang="pms" hreflang="pms" data-title="Termodinàmica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%DA%BE%D8%B1%D9%85%D9%88%DA%88%D8%A7%D8%A6%DB%8C%D9%86%D8%A7%D9%85%DA%A9%D8%B3" title="تھرموڈائینامکس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="تھرموڈائینامکس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%DA%89%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترموډینامیک – paștună" lang="ps" hreflang="ps" data-title="ترموډینامیک" data-language-autonym="پښتو" data-language-local-name="paștună" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Termodin%C3%A2mica" title="Termodinâmica – portugheză" lang="pt" hreflang="pt" data-title="Termodinâmica" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – rusă" lang="ru" hreflang="ru" data-title="Термодинамика" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D1%96%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Термодінаміка – Rusyn" lang="rue" hreflang="rue" data-title="Термодінаміка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – sakha" lang="sah" hreflang="sah" data-title="Термодинамика" data-language-autonym="Саха тыла" data-language-local-name="sakha" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – sardiniană" lang="sc" hreflang="sc" data-title="Termodinàmica" data-language-autonym="Sardu" data-language-local-name="sardiniană" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Termudin%C3%A0mica" title="Termudinàmica – siciliană" lang="scn" hreflang="scn" data-title="Termudinàmica" data-language-autonym="Sicilianu" data-language-local-name="siciliană" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – scots" lang="sco" hreflang="sco" data-title="Thermodynamics" data-language-autonym="Scots" data-language-local-name="scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%BF%D8%B1%D9%85%D9%88%DA%8A%D8%A7%D8%A6%D9%86%D8%A7%D9%85%DA%AA%D8%B3" title="ٿرموڊائنامڪس – sindhi" lang="sd" hreflang="sd" data-title="ٿرموڊائنامڪس" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Termodinamika" title="Termodinamika – sârbo-croată" lang="sh" hreflang="sh" data-title="Termodinamika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Ta%E1%BA%93%C9%A3lasmussut" title="Taẓɣlasmussut – tachelhit" lang="shi" hreflang="shi" data-title="Taẓɣlasmussut" data-language-autonym="Taclḥit" data-language-local-name="tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8F%E0%B6%B4_%E0%B6%9C%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80" title="තාප ගති විද්‍යාව – singhaleză" lang="si" hreflang="si" data-title="තාප ගති විද්‍යාව" data-language-autonym="සිංහල" data-language-local-name="singhaleză" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Thermodynamics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Termodynamika" title="Termodynamika – slovacă" lang="sk" hreflang="sk" data-title="Termodynamika" data-language-autonym="Slovenčina" data-language-local-name="slovacă" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – slovenă" lang="sl" hreflang="sl" data-title="Termodinamika" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Termodinamika" title="Termodinamika – albaneză" lang="sq" hreflang="sq" data-title="Termodinamika" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – sârbă" lang="sr" hreflang="sr" data-title="Термодинамика" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://sv.wikipedia.org/wiki/Termodynamik" title="Termodynamik – suedeză" lang="sv" hreflang="sv" data-title="Termodynamik" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mwendojoto" title="Mwendojoto – swahili" lang="sw" hreflang="sw" data-title="Mwendojoto" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA_%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="வெப்ப இயக்கவியல் – tamilă" lang="ta" hreflang="ta" data-title="வெப்ப இயக்கவியல்" data-language-autonym="தமிழ்" data-language-local-name="tamilă" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%89%E0%B0%B7%E0%B1%8D%E0%B0%A3%E0%B0%97%E0%B0%A4%E0%B0%BF%E0%B0%95%E0%B0%B6%E0%B0%BE%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%82" title="ఉష్ణగతికశాస్త్రం – telugu" lang="te" hreflang="te" data-title="ఉష్ణగతికశాస్త్రం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – tadjică" lang="tg" hreflang="tg" data-title="Термодинамика" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjică" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B8%E0%B8%93%E0%B8%AB%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="อุณหพลศาสตร์ – thailandeză" lang="th" hreflang="th" data-title="อุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – tagalog" lang="tl" hreflang="tl" data-title="Termodinamika" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Termodinamik" title="Termodinamik – turcă" lang="tr" hreflang="tr" data-title="Termodinamik" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – tătară" lang="tt" hreflang="tt" data-title="Термодинамика" data-language-autonym="Татарча / tatarça" data-language-local-name="tătară" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Термодинаміка – ucraineană" lang="uk" hreflang="uk" data-title="Термодинаміка" data-language-autonym="Українська" data-language-local-name="ucraineană" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%B1_%D8%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA" title="حر حرکیات – urdu" lang="ur" hreflang="ur" data-title="حر حرکیات" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Termodinamika" title="Termodinamika – uzbecă" lang="uz" hreflang="uz" data-title="Termodinamika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Veps" lang="vep" hreflang="vep" data-title="Termodinamik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nhi%E1%BB%87t_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Nhiệt động lực học – vietnameză" lang="vi" hreflang="vi" data-title="Nhiệt động lực học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Termodinamika" title="Termodinamika – waray" lang="war" hreflang="war" data-title="Termodinamika" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6" title="热力学 – chineză wu" lang="wuu" hreflang="wuu" data-title="热力学" data-language-autonym="吴语" data-language-local-name="chineză wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="თერმოდინამიკა – Mingrelian" lang="xmf" hreflang="xmf" data-title="თერმოდინამიკა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%98%D7%A2%D7%A8%D7%9E%D7%90%D7%93%D7%99%D7%A0%D7%90%D7%9E%D7%99%D7%A7" title="טערמאדינאמיק – idiș" lang="yi" hreflang="yi" data-title="טערמאדינאמיק" data-language-autonym="ייִדיש" data-language-local-name="idiș" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6" title="热力学 – chineză" lang="zh" hreflang="zh" data-title="热力学" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8" title="熱力學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="熱力學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Jia%CC%8Dt-le%CC%8Dk-ha%CC%8Dk" title="Jia̍t-le̍k-ha̍k – chineză min nan" lang="nan" hreflang="nan" data-title="Jia̍t-le̍k-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chineză min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8" title="熱力學 – cantoneză" lang="yue" hreflang="yue" data-title="熱力學" data-language-autonym="粵語" data-language-local-name="cantoneză" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11473#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Spații de nume"> <div 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class="mw-list-item"><a href="/wiki/Special:Ce_se_leag%C4%83_aici/Termodinamic%C4%83" title="Lista tuturor paginilor wiki care conduc spre această pagină [j]" accesskey="j"><span>Ce trimite aici</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:Modific%C4%83ri_corelate/Termodinamic%C4%83" rel="nofollow" title="Schimbări recente în legătură cu această pagină [k]" accesskey="k"><span>Schimbări corelate</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:Trimite_fi%C8%99ier" title="Încărcare fișiere [u]" accesskey="u"><span>Trimite fișier</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:Pagini_speciale" title="Lista tuturor paginilor speciale [q]" accesskey="q"><span>Pagini speciale</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Termodinamic%C4%83&oldid=16410186" title="Legătură permanentă către această versiune a acestei pagini"><span>Legătură permanentă</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Termodinamic%C4%83&action=info" title="Mai multe informații despre această pagină"><span>Informații despre pagină</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:Citeaz%C4%83&page=Termodinamic%C4%83&id=16410186&wpFormIdentifier=titleform" title="Informații cu privire la modul de citare a acestei pagini"><span>Citează acest articol</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fro.wikipedia.org%2Fwiki%2FTermodinamic%25C4%2583"><span>Obține URL scurtat</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fro.wikipedia.org%2Fwiki%2FTermodinamic%25C4%2583"><span>Descărcați codul QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tipărire/exportare </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Carte&bookcmd=book_creator&referer=Termodinamic%C4%83"><span>Creare carte</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Termodinamic%C4%83&action=show-download-screen"><span>Descărcare ca PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Termodinamic%C4%83&printable=yes" title="Versiunea de tipărit a acestei pagini [p]" accesskey="p"><span>Versiune de tipărit</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> În alte proiecte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Thermodynamics" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11473" title="Legătură către elementul asociat din depozitul de date [g]" accesskey="g"><span>Element Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspect"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspect</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mută în bara laterală</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ascunde</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De la Wikipedia, enciclopedia liberă</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><table class="vertical-navbox nowraplinks plainlist" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tbody><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em;padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a class="mw-selflink selflink">Termodinamică</a></th></tr><tr><td style="padding:0.2em 0 0.4em;display:block;margin:0.3em 0 0.4em;"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/w/index.php?title=Fi%C8%99ier:Carnot_heat_engine_2.svg&lang=ro" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/langro-220px-Carnot_heat_engine_2.svg.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/langro-330px-Carnot_heat_engine_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/langro-440px-Carnot_heat_engine_2.svg.png 2x" data-file-width="840" data-file-height="370" /></a></span><div style="padding-top:0.2em;line-height:1.2em">Schema unei mașini termice Carnot</div></td></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;">Ramuri</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="hlist"> <ul><li><a class="mw-selflink selflink">Clasică</a></li> <li><a href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">Statistică</a></li> <li><a href="/wiki/Termodinamic%C4%83_chimic%C4%83" title="Termodinamică chimică">Chimică</a></li> <li><a href="/w/index.php?title=Termodinamic%C4%83_cuantic%C4%83&action=edit&redlink=1" class="new" title="Termodinamică cuantică — pagină inexistentă">Cuantică</a></li></ul> </div> <ul><li><a href="/w/index.php?title=Termodinamica_echilibrului&action=edit&redlink=1" class="new" title="Termodinamica echilibrului — pagină inexistentă">la echilibru</a> / <a href="/wiki/Termodinamica_neechilibrului" title="Termodinamica neechilibrului">nu la echilibru</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/wiki/Principiile_termodinamicii" title="Principiile termodinamicii">Principii</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="hlist"> <ul><li><a href="/wiki/Principiul_zero_al_termodinamicii" title="Principiul zero al termodinamicii">Zero</a></li> <li><a href="/wiki/Principiul_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii">Primul</a></li> <li><a href="/wiki/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii">Al doilea</a></li> <li><a href="/wiki/Principiul_al_treilea_al_termodinamicii" title="Principiul al treilea al termodinamicii">Al treilea</a></li></ul> </div></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/wiki/Sistem_termodinamic" title="Sistem termodinamic">Sisteme</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="hlist"> <ul><li><a href="/wiki/Sistem_izolat" title="Sistem izolat">Izolat</a></li> <li><a href="/wiki/Sistem_%C3%AEnchis" title="Sistem închis">Închis</a></li> <li><a href="/wiki/Sistem_deschis" title="Sistem deschis">Deschis</a></li> <li><a href="/wiki/Sistem_termodinamic#Sisteme_termodinamice" title="Sistem termodinamic">Adiabatic</a></li></ul> </div> <table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Stare_termodinamic%C4%83" title="Stare termodinamică">Stare</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li><a href="/wiki/Ecua%C8%9Bie_de_stare" title="Ecuație de stare">Ecuație de stare</a></li> <li><a href="/wiki/Gaz_ideal" title="Gaz ideal">Gaz ideal</a></li> <li><a href="/wiki/Gaz_real" title="Gaz real">Gaz real</a></li> <li><a href="/wiki/Stare_de_agregare" title="Stare de agregare">Stare de agregare</a></li> <li><a href="/wiki/Faz%C4%83_(termodinamic%C4%83)" title="Fază (termodinamică)">Fază</a></li> <li><a href="/wiki/Echilibru_termodinamic" title="Echilibru termodinamic">Echilibru</a></li> <li><a href="/wiki/Volum_de_control" title="Volum de control">Volum de control</a></li> <li><a href="/wiki/Instrument_pentru_termodinamic%C4%83" title="Instrument pentru termodinamică">Instrumente</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Transformare_termodinamic%C4%83" title="Transformare termodinamică">Procese</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li><a href="/wiki/Destindere_Joule" title="Destindere Joule">Destindere liberă</a></li> <li><a href="/wiki/Proces_izobar" title="Proces izobar">Izobar</a></li> <li><a href="/wiki/Proces_izocor" title="Proces izocor">Izocor</a></li> <li><a href="/wiki/Proces_izotermic" title="Proces izotermic">Izotermic</a></li> <li><a href="/wiki/Proces_adiabatic" title="Proces adiabatic">Adiabatic</a> <ul><li><a href="/wiki/Coeficient_de_transformare_adiabatic%C4%83" title="Coeficient de transformare adiabatică">exponent</a></li></ul></li> <li><a href="/wiki/Proces_izentropic" title="Proces izentropic">Izentropic</a></li> <li><a href="/wiki/Proces_izentalpic" title="Proces izentalpic">Izentalpic</a></li> <li><a href="/wiki/Proces_politropic" title="Proces politropic">Politropic</a></li> <li><a href="/wiki/Proces_cvasistatic" title="Proces cvasistatic">Cvasistatic</a></li> <li><a href="/wiki/Proces_reversibil" title="Proces reversibil">Reversibil</a></li> <li><a href="/wiki/Proces_ireversibil" title="Proces ireversibil">Ireversibil</a> <ul><li><a href="/wiki/Disipare" title="Disipare">disipare</a></li></ul></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Ciclu_termodinamic" title="Ciclu termodinamic">Cicluri</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li><a href="/wiki/Ciclul_Carnot" title="Ciclul Carnot">Carnot</a></li> <li><a href="/wiki/Ma%C8%99in%C4%83_termic%C4%83" title="Mașină termică">Direct</a></li> <li><a href="/wiki/Ciclu_termodinamic_inversat" class="mw-redirect" title="Ciclu termodinamic inversat">Inversat</a></li> <li><a href="/wiki/Randament_termic" title="Randament termic">Randament și eficiență</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Diagram%C4%83_termodinamic%C4%83" title="Diagramă termodinamică">Diagrame termodinamice</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li><a href="/wiki/Diagrama_presiune%E2%80%93volum" title="Diagrama presiune–volum">p-V</a></li> <li><a href="/wiki/Diagrama_temperatur%C4%83%E2%80%93entropie" title="Diagrama temperatură–entropie">T-s</a></li> <li><a href="/wiki/Diagrama_entalpie%E2%80%93entropie" title="Diagrama entalpie–entropie">h-s</a></li> <li><a href="/wiki/Diagrama_presiune%E2%80%93entalpie" title="Diagrama presiune–entalpie">p-h</a></li> <li><a href="/w/index.php?title=Diagrama_psihrometric%C4%83&action=edit&redlink=1" class="new" title="Diagrama psihrometrică — pagină inexistentă">Psihro</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/wiki/Lista_propriet%C4%83%C8%9Bilor_termodinamice" title="Lista proprietăților termodinamice">Propertăți ale sistemelor</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Notă: <a href="/wiki/Poten%C8%9Bial_termodinamic#Parametri_conjugați" title="Potențial termodinamic">Parametri conjugați</a> cu <i>italice</i></div> <table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;margin-top:0.4em;"><tbody><tr><td style="padding:0 0.1em 0.4em;padding-bottom:0.7em;"> <ul><li><a href="/wiki/Propriet%C4%83%C8%9Bi_intensive_%C8%99i_extensive" title="Proprietăți intensive și extensive">Proprietăți intensive și extensive</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Func%C8%9Bie_de_proces" title="Funcție de proces">Funcții de proces</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding-bottom:0.7em;;padding-bottom:0.4em;"> <div class="hlist"> <ul><li><a href="/wiki/Lucru_mecanic" title="Lucru mecanic">Lucru mecanic</a></li> <li><a href="/wiki/C%C4%83ldur%C4%83" title="Căldură">Căldură</a></li></ul> </div></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Func%C8%9Bie_de_stare" title="Funcție de stare">Funcții de stare</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding-bottom:0.7em;"> <ul><li><a href="/wiki/Temperatur%C4%83" title="Temperatură">Temperatură</a> / <i><a href="/wiki/Entropie" title="Entropie">Entropie</a></i></li> <li><a href="/wiki/Presiune" title="Presiune">Presiune</a> <small>(<a href="/wiki/Presiune_intern%C4%83" title="Presiune internă">internă</a>, <a href="/wiki/Presiune_par%C8%9Bial%C4%83" title="Presiune parțială">parțială</a>)</small> / <i><a href="/wiki/Volum_(termodinamic%C4%83)" title="Volum (termodinamică)">Volum</a></i></li> <li><a href="/wiki/Poten%C8%9Bial_chimic" title="Potențial chimic">Potențial chimic</a> / <i><a href="/wiki/Num%C4%83r_de_particule" title="Număr de particule">Număr de particule</a></i></li> <li><a href="/wiki/Titlul_vaporilor" title="Titlul vaporilor">Titlul vaporilor</a></li> <li><a href="/wiki/Propriet%C4%83%C8%9Bi_reduse" title="Proprietăți reduse">Proprietăți reduse</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/wiki/Propriet%C4%83%C8%9Bi_ale_materialelor_(termodinamic%C4%83)" title="Proprietăți ale materialelor (termodinamică)">Proprietăți ale materialelor</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Baze_de_date_termodinamice_pentru_substan%C8%9Be_pure&action=edit&redlink=1" class="new" title="Baze de date termodinamice pentru substanțe pure — pagină inexistentă">Baze de date cu proprietăți</a></li></ul> <div style="font-size:90%;margin-top:0.4em;border-top:1px solid #aaa;text-align:center;"> <table> <tbody><tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Capacitate_termic%C4%83_masic%C4%83" title="Capacitate termică masică">Capacitate termică masică</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891d40a9b18752b04065caee655d008b3ec11428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:1.676ex;" alt="{\displaystyle c=}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c609f4d3c5692ea4495479ef47594dc67f9fa464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.817ex; height:2.176ex;" alt="{\displaystyle \partial S}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Compresibilitate" title="Compresibilitate">Coeficient de compresibilitate</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.239ex; height:2.509ex;" alt="{\displaystyle \beta =-}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc4a48eb2412f08b54fe438b5139c88f9cfa372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.487ex; height:2.509ex;" alt="{\displaystyle \partial p}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Dilatare_termic%C4%83" title="Dilatare termică">Coeficient de dilatare volumică</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92d4583d351f08c1c70985f0c843b2fff1b01e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.941ex; height:1.676ex;" alt="{\displaystyle \alpha =}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> </tbody></table></div></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/w/index.php?title=Ecua%C8%9Bii_termodinamice&action=edit&redlink=1" class="new" title="Ecuații termodinamice — pagină inexistentă">Ecuații</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="hlist"> <ul><li><a href="/w/index.php?title=Teorema_lui_Carnot_(termodinamic%C4%83)&action=edit&redlink=1" class="new" title="Teorema lui Carnot (termodinamică) — pagină inexistentă">Teorema lui Carnot</a></li> <li><a href="/wiki/Teorema_lui_Clausius" title="Teorema lui Clausius">Teorema lui Clausius</a></li> <li><a href="/w/index.php?title=Rela%C8%9Bia_fundamental%C4%83_a_termodinamicii&action=edit&redlink=1" class="new" title="Relația fundamentală a termodinamicii — pagină inexistentă">Relația fundamentală</a></li> <li><a href="/wiki/Legea_gazelor_ideale" title="Legea gazelor ideale">Legea gazelor ideale</a></li> <li><a href="/wiki/Teorema_st%C4%83rilor_corespondente" title="Teorema stărilor corespondente">Stări corespondente</a></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Poten%C8%9Bial_termodinamic#Relațiile_Maxwell" title="Potențial termodinamic">Relațiile Maxwell</a></li> <li><a href="/w/index.php?title=Rela%C8%9Biile_reciproce_Onsager&action=edit&redlink=1" class="new" title="Relațiile reciproce Onsager — pagină inexistentă">Relațiile Onsager</a></li> <li><a href="/w/index.php?title=Ecua%C8%9Biile_termodinamice_ale_lui_Bridgman&action=edit&redlink=1" class="new" title="Ecuațiile termodinamice ale lui Bridgman — pagină inexistentă">Ecuațiile Bridgman</a></li></ul> </div> <ul><li><i><a href="/w/index.php?title=Tabel_cu_ecua%C8%9Bii_termodinamice&action=edit&redlink=1" class="new" title="Tabel cu ecuații termodinamice — pagină inexistentă">Tabel cu ecuații termodinamice</a></i></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">Potențiale</a></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="plainlist"><ul><li style="line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Energie_intern%C4%83" title="Energie internă">Energie internă</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(S,V)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/921f33f9c6551562ec836007b035c2de6323d2d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.912ex; height:2.843ex;" alt="{\displaystyle U(S,V)}"></span></li><li style="line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Energie_liber%C4%83" title="Energie liberă">Energie liberă</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(T,V)=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e93692f031ba6484d82731c54db83a69daed3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}"></span></li><li style="line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Entalpie" title="Entalpie">Entalpie</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(S,p)=U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6407d78e5f39d07f70e2414a92e08e2e068519f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}"></span></li><li style="line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Entalpie_liber%C4%83" title="Entalpie liberă">Entalpie liberă</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(T,p)=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd7a8f0b8ae04963da133e3b202432e1b6caed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}"></span></li></ul></div> <div class="hlist"> <ul><li><a href="/wiki/Entropie_liber%C4%83" title="Entropie liberă">Entropie liberă</a></li></ul> </div></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;"><div class="hlist" style="margin-left:0em;"><div class="plainlist"><ul style=""><li style="">Istorie </li><li style="">Cultură</li></ul></div></div></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th style="padding:0.1em;font-style:italic;"> Istorie</th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li><a href="/wiki/Istoria_termodinamicii" title="Istoria termodinamicii">Generală</a></li> <li><a href="/w/index.php?title=Istoria_entropiei&action=edit&redlink=1" class="new" title="Istoria entropiei — pagină inexistentă">Istoria entropiei</a></li> <li><a href="/wiki/Legile_gazelor" title="Legile gazelor">Legile gazelor</a></li></ul> </div> <ul><li><a href="/w/index.php?title=Istoria_perpetuum_mobilelor&action=edit&redlink=1" class="new" title="Istoria perpetuum mobilelor — pagină inexistentă">Istoria perpetuum mobilelor</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <a href="/wiki/Filozofia_fizicii" title="Filozofia fizicii">Filozofie</a></th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li><a href="/w/index.php?title=Entropie_%C8%99i_timp&action=edit&redlink=1" class="new" title="Entropie și timp — pagină inexistentă">Entropie și timp</a></li> <li><a href="/w/index.php?title=Entropie_%C8%99i_via%C8%9B%C4%83&action=edit&redlink=1" class="new" title="Entropie și viață — pagină inexistentă">Entropie și viață</a></li> <li><a href="/w/index.php?title=Clichetul_brownian&action=edit&redlink=1" class="new" title="Clichetul brownian — pagină inexistentă">Clichetul brownian</a></li> <li><a href="/wiki/Demonul_lui_Maxwell" title="Demonul lui Maxwell">Demonul lui Maxwell</a></li> <li><a href="/w/index.php?title=Paradoxul_mor%C8%9Bii_termice&action=edit&redlink=1" class="new" title="Paradoxul morții termice — pagină inexistentă">Paradoxul morții termice</a></li> <li><a href="/w/index.php?title=Paradoxul_lui_Loschmidt&action=edit&redlink=1" class="new" title="Paradoxul lui Loschmidt — pagină inexistentă">Paradoxul lui Loschmidt</a></li> <li><a href="/w/index.php?title=Sinergetic%C4%83_(Haken)&action=edit&redlink=1" class="new" title="Sinergetică (Haken) — pagină inexistentă">Sinergetică</a></li></ul> </div></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> Teorii</th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li><a href="/wiki/Teoria_caloricului" title="Teoria caloricului">Teoria caloricului</a></li></ul> </div> <ul><li><i><a href="/wiki/Vis_viva" title="Vis viva">Forța vie</a></i></li> <li><a href="/wiki/Echivalentul_mecanic_al_caloriei" title="Echivalentul mecanic al caloriei">Echivalentul mecanic al caloriei</a></li> <li><i><a href="/wiki/Putere" title="Putere">Putere motrice</a></i></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> Lucrări fundamentale</th></tr><tr><td style="padding:0 0.1em 0.4em"> <ul><li><div style="padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/w/index.php?title=An_Experimental_Enquiry_Concerning_the_Source_of_the_Heat_which_is_Excited_by_Friction&action=edit&redlink=1" class="new" title="An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction — pagină inexistentă">An Experimental Enquiry<br />Concerning ... Heat</a></i></div></li> <li><div style="padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br />Heterogeneous Substances</a></i></div></li> <li><div style="padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/w/index.php?title=R%C3%A9flexions_sur_la_puissance_motrice_du_feu_et_sur_les_machines_propres_%C3%A0_d%C3%A9velopper_cette_puissance&action=edit&redlink=1" class="new" title="Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance — pagină inexistentă">Réflexions sur la puissance<br />motrice du feu</a></i></div></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> Cronologii</th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li><a href="/w/index.php?title=Cronologia_termodinamicii&action=edit&redlink=1" class="new" title="Cronologia termodinamicii — pagină inexistentă">Termodinamică</a></li> <li><a href="/w/index.php?title=Cronologia_ma%C8%99inilor_termice&action=edit&redlink=1" class="new" title="Cronologia mașinilor termice — pagină inexistentă">mașini termice</a></li></ul> </div></td> </tr><tr><th style="padding:0.1em;font-style:italic;"> <div class="hlist" style="margin-left:0em;"><div class="plainlist"><ul style=""><li style="">Artă</li><li style="">Învățământ</li></ul></div></div></th></tr><tr><td style="padding:0 0.1em 0.4em"> <ul><li><a href="/w/index.php?title=Suprafa%C8%9Ba_termodinamic%C4%83_a_lui_Maxwell&action=edit&redlink=1" class="new" title="Suprafața termodinamică a lui Maxwell — pagină inexistentă">Suprafața termodinamică a lui Maxwell</a></li> <li><a href="/w/index.php?title=Entropia_ca_disipare_a_energiei&action=edit&redlink=1" class="new" title="Entropia ca disipare a energiei — pagină inexistentă">Entropia ca disipare a energiei</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;">Personalități</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li> <li><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li> <li><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li> <li><a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li> <li><a href="/wiki/Rudolf_Clausius" class="mw-redirect" title="Rudolf Clausius">Clausius</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Duhem</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">von Helmholtz</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" class="mw-redirect" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gilbert_N._Lewis" class="mw-redirect" title="Gilbert N. Lewis">Lewis</a></li> <li><a href="/w/index.php?title=Fran%C3%A7ois_Massieu&action=edit&redlink=1" class="new" title="François Massieu — pagină inexistentă">Massieu</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/w/index.php?title=Julius_von_Mayer&action=edit&redlink=1" class="new" title="Julius von Mayer — pagină inexistentă">von Mayer</a></li> <li><a href="/wiki/Walther_Nernst" title="Walther Nernst">Nernst</a></li> <li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/William_John_Macquorn_Rankine" title="William John Macquorn Rankine">Rankine</a></li> <li><a href="/wiki/John_Smeaton" title="John Smeaton">Smeaton</a></li> <li><a href="/wiki/Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li> <li><a href="/w/index.php?title=Peter_Tait&action=edit&redlink=1" class="new" title="Peter Tait — pagină inexistentă">Tait</a></li> <li><a href="/w/index.php?title=Benjamin_Thompson&action=edit&redlink=1" class="new" title="Benjamin Thompson — pagină inexistentă">Thompson</a></li> <li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li> <li><a href="/w/index.php?title=John_James_Waterston&action=edit&redlink=1" class="new" title="John James Waterston — pagină inexistentă">Waterston</a></li></ul> </div></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;text-align:center;">Altele</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Nuclea%C8%9Bie" title="Nucleație">Nucleație</a></li> <li><a href="/w/index.php?title=Autoasamblare&action=edit&redlink=1" class="new" title="Autoasamblare — pagină inexistentă">Autoasamblare</a></li> <li><a href="/w/index.php?title=Autoorganizare&action=edit&redlink=1" class="new" title="Autoorganizare — pagină inexistentă">Autoorganizare</a></li> <li><a href="/w/index.php?title=Ordine_%C8%99i_dezordine&action=edit&redlink=1" class="new" title="Ordine și dezordine — pagină inexistentă">Ordine și dezordine</a></li></ul></div></div></td> </tr><tr><td style="padding:0.3em 0.4em 0.3em;font-weight:bold;border-top: 1px solid #aaa; border-bottom: 1px solid #aaa;"> <ul><li><a href="/wiki/Categorie:Termodinamic%C4%83" title="Categorie:Termodinamică">Categorie</a></li></ul></td></tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Format:Termodinamic%C4%83" title="Format:Termodinamică"><abbr title="Vizualizează acest format">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Discu%C8%9Bie_Format:Termodinamic%C4%83" title="Discuție Format:Termodinamică"><abbr title="Discută acest format">d</abbr></a></li><li class="nv-edit"><a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Termodinamic%C4%83&action=edit"><abbr title="Modifică acest format">m</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:SteamEngine_Boulton%26Watt_1784.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/SteamEngine_Boulton%26Watt_1784.png/280px-SteamEngine_Boulton%26Watt_1784.png" decoding="async" width="280" height="321" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/SteamEngine_Boulton%26Watt_1784.png/420px-SteamEngine_Boulton%26Watt_1784.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/SteamEngine_Boulton%26Watt_1784.png/560px-SteamEngine_Boulton%26Watt_1784.png 2x" data-file-width="2264" data-file-height="2592" /></a><figcaption>Exemplu de aplicație a termodinamicii: <a href="/wiki/Motor_cu_abur" title="Motor cu abur">motor cu abur</a> proiectat de firma Boulton & <a href="/wiki/James_Watt" title="James Watt">Watt</a> (1784)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Day5pressureforecast.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Day5pressureforecast.png/280px-Day5pressureforecast.png" decoding="async" width="280" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Day5pressureforecast.png/420px-Day5pressureforecast.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Day5pressureforecast.png/560px-Day5pressureforecast.png 2x" data-file-width="1024" data-file-height="613" /></a><figcaption>Exemplu de aplicație a termodinamicii: <a href="/wiki/Prognoz%C4%83_meteorologic%C4%83" title="Prognoză meteorologică">Prognoza meteorologică</a>. Distribuția presiunii atmosferice pe 5 zile în <a href="/wiki/America_de_Nord" title="America de Nord">America de Nord</a>, <a href="/wiki/Oceanul_Pacific" title="Oceanul Pacific">Oceanul Pacific</a> și <a href="/wiki/Oceanul_Atlantic" title="Oceanul Atlantic">Oceanul Atlantic</a> (2008)</figcaption></figure> <p><b>Termodinamica</b> se ocupă cu studiul <a href="/wiki/Scar%C4%83_macroscopic%C4%83" title="Scară macroscopică">macroscopic</a> al <a href="/wiki/Fenomen_fizic" title="Fenomen fizic">fenomenelor</a>, de orice natură, în care are loc un transfer de energie sub forma de <a href="/wiki/C%C4%83ldur%C4%83" title="Căldură">căldură</a> și <a href="/wiki/Lucru_mecanic" title="Lucru mecanic">lucru mecanic</a>. Numele este derivat din limba greacă (<i>θέρμη</i> <i>therme</i> = căldură, <i>δύναμις</i> <i>dynamis</i> = forță) și a fost creat de <a href="/wiki/William_Thomson" title="William Thomson">lordul Kelvin</a>, care a formulat și prima definiție a termodinamicii. În germană termodinamica mai poartă și numele de <i>Wärmelehre (teoria căldurii)</i>, creat de <a href="/wiki/Rudolf_Clausius" class="mw-redirect" title="Rudolf Clausius">Rudolf Clausius</a> în lucrările sale despre teoria mecanică a căldurii. </p><p>Termodinamica reprezintă în zilele noastre una din cele mai bine structurate logic ramuri ale fizicii. Născută la începutul <a href="/wiki/Secolul_XIX" class="mw-redirect" title="Secolul XIX">secolului al XIX-lea</a> din necesitatea practică de a optimiza <a href="/wiki/Randament_(fizic%C4%83)" class="mw-redirect" title="Randament (fizică)">randamentul</a> <a href="/wiki/Motor_cu_abur" title="Motor cu abur">motoarelor cu abur</a>, termodinamica a devenit una din disciplinele clasice ale <a href="/wiki/Fizica_teoretic%C4%83" class="mw-redirect" title="Fizica teoretică">fizicii teoretice</a>. Baza teoretică a termodinamicii o constituie un număr restrâns de <i><a href="/wiki/Principiu" title="Principiu">principii</a></i>, care sunt generalizări și <a href="/wiki/Abstractizare" title="Abstractizare">abstractizări</a> ale unor <a href="/wiki/Experiment" title="Experiment">fapte experimentale</a>. Caracterul general al acestor principii, care nu conțin <a href="/wiki/Ipotez%C4%83" title="Ipoteză">ipoteze</a> referitor la natura <a href="/wiki/For%C8%9B%C4%83" title="Forță">forțelor</a> implicate sau la structura <a href="/wiki/Scar%C4%83_microscopic%C4%83" title="Scară microscopică">microscopică</a> a sistemelor studiate, face ca metodele termodinamicii să fie aplicabile unei clase largi de fenomene. Operele lui <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Josiah Willard Gibbs</a> au extins domeniul de preocupare al termodinamicii de la orientarea spre randamentul mașinilor termice către studiul caracteristicilor substanțelor și sistemelor. Câteva exemple, alese oarecum la întâmplare, sunt: proprietățile <a href="/wiki/Fluid" title="Fluid">fluidelor</a> și ale <a href="/wiki/Solu%C8%9Bie" class="mw-redirect" title="Soluție">soluțiilor</a>, echilibrul <a href="/wiki/Stare_de_agregare" title="Stare de agregare">stărilor de agregare</a>, <a href="/wiki/Polarizare_(dezambiguizare)" class="mw-disambig" title="Polarizare (dezambiguizare)">polarizarea dielectrică</a> și <a href="/wiki/Magnetism" title="Magnetism">magnetizarea</a>, <a href="/wiki/For%C8%9B%C4%83_electromotoare" title="Forță electromotoare">forța electromotoare</a> a <a href="/wiki/Element_galvanic" title="Element galvanic">elementelor galvanice</a>, <a href="/wiki/Radia%C8%9Bie_termic%C4%83" title="Radiație termică">radiația termică</a>. Aplicațiile practice sunt și ele numeroase și variate, de la <a href="/wiki/Frigider" title="Frigider">frigider</a> și <a href="/wiki/%C3%8Enc%C4%83lzire_central%C4%83" title="Încălzire centrală">încălzire centrală</a> la <a href="/wiki/Energie_regenerabil%C4%83" title="Energie regenerabilă">energie regenerabilă</a> și <a href="/wiki/Prognoz%C4%83_meteorologic%C4%83" title="Prognoză meteorologică">prognoză meteorologică</a>. </p><p>O abordare alternativă a fenomenelor termodinamice o reprezintă <a href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">mecanica statistică</a>. Pornind de la structura microscopică (<a href="/wiki/Molecul%C4%83" title="Moleculă">molecule</a> și <a href="/wiki/Atom" title="Atom">atomi</a>), luând în considerare interacțiunile (forțele) dintre aceste componente și folosind <a href="/wiki/Statistic%C4%83" title="Statistică">metode statistice</a> (aplicabile sistemelor alcătuite dintr-un număr foarte mare de componente), mecanica statistică poate, prin intermediul unor calcule laborioase, să deducă (și prin aceasta să confirme) rezultatele obținute de termodinamică pe cale fenomenologică. </p><p>Există diverse încercări de axiomatizare a acestei discipline. Prima dintre ele a fost cea a lui <a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a> publicată în 1909 într-un periodic de matematică. Axiomatizarea lui Carathéodory a fost relativ ignorată de fizicieni datorită publicării într-un periodic de matematică și nu a fost bine primită de <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>. </p><p>După accentul pus pe anumite domenii aplicative din termodinamica generală sau fundamentală se individualizează următoarele ramuri: <a href="/wiki/Sistem_fizic" title="Sistem fizic">termodinamica sistemelor fizice</a>, <a href="/wiki/Sistem_chimic" title="Sistem chimic">termodinamica sistemelor chimice</a> și termodinamica tehnică. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Stări_și_transformări"><span id="St.C4.83ri_.C8.99i_transform.C4.83ri"></span>Stări și transformări</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=1" title="Modifică secțiunea: Stări și transformări" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=1" title="Edit section's source code: Stări și transformări"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pentru orice disciplină a fizicii, obiectul de studiu este un <i><a href="/wiki/Sistem_fizic" title="Sistem fizic">sistem</a></i>. În contextul termodinamicii acesta va fi un <i><a href="/wiki/Sistem_termodinamic" title="Sistem termodinamic">sistem termodinamic</a></i>: o porțiune finită, precis delimitată, din <a href="/wiki/Materie" title="Materie">realitatea materială</a>, care poate include atât <a href="/wiki/Substan%C8%9B%C4%83" class="mw-redirect" title="Substanță">substanță</a> cât și <a href="/wiki/Radia%C8%9Bie" title="Radiație">radiație</a>. Delimitarea conceptuală a unui <i>sistem</i> de <i>lumea înconjurătoare</i> nu exclude, ci în general presupune, <i>interacțiunea</i> acestor două elemente; în cazul termodinamicii, această interacțiune se manifestă sub forma de fenomene <i>termice</i> și <i>mecanice</i>. </p><p>Calitativ, se numește <i><a href="/wiki/Stare" class="mw-disambig" title="Stare">stare</a></i> a unui sistem (la un moment dat) totalitatea proprietăților lui (la acel moment). Pentru precizarea cantitativă a acestei noțiuni se recurge la valorile pe care le au diferite <i><a href="/wiki/M%C4%83rime_fizic%C4%83" title="Mărime fizică">mărimi fizice</a></i> în starea respectivă. Între mărimile care exprimă proprietăți ale unui sistem există relații cantitative bine determinate; există însă un număr limitat de mărimi fizice <i>independente</i> care caracterizează <i>complet</i> starea sa, alte proprietăți ale sistemului putând fi derivate din acestea. Alegerea mărimilor care să servească drept <i>variabile independente</i> este un pas preliminar necesar în studiul oricărui sistem. </p><p>O <a href="/wiki/Stare_termodinamic%C4%83" title="Stare termodinamică">stare</a> în care proprietățile sistemului termodinamic nu variază în timp se numește <i>stare de echilibru</i> termodinamic. </p> <div class="mw-heading mw-heading3"><h3 id="Principiul_zero_al_termodinamicii">Principiul zero al termodinamicii</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=2" title="Modifică secțiunea: Principiul zero al termodinamicii" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=2" title="Edit section's source code: Principiul zero al termodinamicii"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Principiul_zero_al_termodinamicii" title="Principiul zero al termodinamicii">Principiul zero al termodinamicii</a>.</div><style data-mw-deduplicate="TemplateStyles:r16505893">@media screen{html.skin-theme-clientpref-night .mw-parser-output .rellink{display:flex}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .rellink{display:flex}}</style> <p>Pentru ca un sistem să se afle în <i><a href="/wiki/Echilibru_termodinamic" title="Echilibru termodinamic">echilibru termodinamic</a></i> este necesar (dar în general nu și suficient) ca lumea înconjurătoare cu care se află în contact să ofere condiții neschimbate în <a href="/wiki/Timp" title="Timp">timp</a>. Următoarea constatare, de natură experimentală, este numită uneori <i>principiul zero al termodinamicii:</i> </p> <dl><dd><i>Un sistem termodinamic situat în condiții externe invariabile în timp va atinge, după un timp suficient de lung, o stare de echilibru termodinamic.</i><sup id="cite_ref-zerotranz_1-0" class="reference"><a href="#cite_note-zerotranz-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Se numește <b><a href="/wiki/Transformare_termodinamic%C4%83" title="Transformare termodinamică">transformare</a></b> orice schimbare a stării unui sistem. Un interes teoretic deosebit îl prezintă transformările care conduc de la o <i>stare inițială</i> de echilibru la o <i>stare finală</i> de echilibru, trecând printr-o înșiruire continuă de <i>stări intermediare</i> de echilibru. Întrucât orice schimbare de stare se petrece într-un timp finit, astfel de transformări nu pot fi realizate, riguros, în realitate. Dar, conform principiului zero al termodinamicii, dacă transformarea se produce suficient de lent, ea se poate apropia oricât de mult de acest model ideal. Astfel de transformări se numesc <a href="/wiki/Proces_cvasistatic" title="Proces cvasistatic"><i>cvasistatice</i></a>, pentru a indica faptul că ele sunt o înșiruire de stări de echilibru; dacă este posibilă transformarea în care aceeași înșiruire de stări să fie parcursă în sens invers ele se numesc <i>reversibile</i>. O transformare se numește <i>ciclică</i> dacă starea finală coincide cu starea inițială. </p> <div class="mw-heading mw-heading3"><h3 id="Lucru_mecanic">Lucru mecanic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=3" title="Modifică secțiunea: Lucru mecanic" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=3" title="Edit section's source code: Lucru mecanic"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O stare de <a href="/wiki/Echilibru_mecanic" title="Echilibru mecanic">echilibru <i>mecanic</i></a> a unui sistem cu <span class="texhtml"> <i>n</i> </span> <a href="/wiki/Grad_de_libertate_(mecanic%C4%83)" title="Grad de libertate (mecanică)">grade de libertate</a> este caracterizată complet de valorile pe care le au <i>variabilele de poziție</i> </p> <dl><dd><span style="padding-right:4em" id="f1"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(1\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(1\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e7a480f5a268e109a52735e63b1575178435307" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(1\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=\left(x_{1},...,x_{n}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=\left(x_{1},...,x_{n}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37ea91c129f7ca74aefddbe328bbb65cf73a85af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.373ex; height:2.843ex;" alt="{\displaystyle x=\left(x_{1},...,x_{n}\right),}"></span></dd></dl> <p><i>variabilele de forță</i> corespunzătoare fiind funcții cunoscute de precedentele: </p> <dl><dd><span style="padding-right:4em" id="f2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(2\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(2\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77d123bf4f8d1d5cbdb53228c892027f6ef510b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(2\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X_{i}=X_{i}\left(x_{1},...,x_{n}\right),\quad i=1,...,n.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X_{i}=X_{i}\left(x_{1},...,x_{n}\right),\quad i=1,...,n.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51fd2866e6db1d841f999f7bf50436ee55ce6c52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.443ex; height:2.843ex;" alt="{\displaystyle \ X_{i}=X_{i}\left(x_{1},...,x_{n}\right),\quad i=1,...,n.}"></span></dd></dl> <p>O transformare în care configurația sistemului este modificată sub acțiunea forțelor are loc cu producere de lucru mecanic.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Lucrul mecanic elementar efectuat de aceste forțe pentru modificări infinitezimale ale pozițiilor </p> <dl><dd><span style="padding-right:4em" id="f3"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(3\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(3\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5acebf7542a9c2596bd2c8a8c0484ef14c4f7ad2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(3\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dx=\left(dx_{1},...,dx_{n}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx=\left(dx_{1},...,dx_{n}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b87519ef722c826761e80ece706dcc54b4bf09d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.987ex; height:2.843ex;" alt="{\displaystyle dx=\left(dx_{1},...,dx_{n}\right)}"></span></dd></dl> <p>este </p> <dl><dd><span style="padding-right:4em" id="f4"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(4\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(4\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d14514d5f2f06e22ecceaf0aa5f6eabe5f01128" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(4\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta L=\sum _{i=1}^{n}X_{i}\,dx_{i}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>L</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta L=\sum _{i=1}^{n}X_{i}\,dx_{i}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3d3323ffb4165cc32f552cc7b0eb5a2f218f56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.962ex; height:6.843ex;" alt="{\displaystyle \delta L=\sum _{i=1}^{n}X_{i}\,dx_{i}\,.}"></span></dd></dl> <p>Lucrul mecanic produs într-o transformare finită de la starea inițială <span class="texhtml"> <i>a</i> = ( <i>a</i><sub><i>1</i></sub> , ... , <i>a</i><sub> <i>n</i></sub> ) </span> la starea finală <span class="texhtml"> <i>b</i> = ( <i>b</i><sub><i>1</i></sub> , ... <i>b</i><sub><i>n</i></sub> ) </span> trecând prin stări intermediare înșiruite de-a lungul curbei continue <span class="texhtml"> <i>C</i> </span> în spațiul variabilelor de poziție <span class="texhtml"> (<i>x</i><sub><i>1</i></sub> , ... , <i>x</i><sub><i>n</i></sub> ) </span> este </p> <dl><dd><span style="padding-right:4em" id="f5"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(5\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(5\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/929cf5508f2c9053cf0ea9e76586f1fd6ea2eddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(5\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{C}=\int _{C}\,\sum _{i=1}^{n}X_{i}\,dx_{i}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{C}=\int _{C}\,\sum _{i=1}^{n}X_{i}\,dx_{i}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6178edaee89ebfb3c0cf1ecfd7cf6f11f3d7ad3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.943ex; height:6.843ex;" alt="{\displaystyle L_{C}=\int _{C}\,\sum _{i=1}^{n}X_{i}\,dx_{i}\,,}"></span></dd></dl> <p>unde <a href="/wiki/Integral%C4%83_curbilinie" title="Integrală curbilinie">integrala curbilinie</a> este calculată urmând curba <span class="texhtml"> <i>C</i> </span> în sensul de la <span class="texhtml"> <i>a</i> </span> spre <span class="texhtml"> <i>b</i> </span>. Relația de mai sus definește lucrul mecanic primit (algebric) de sistem; el nu este o <a href="/wiki/Variabil%C4%83_de_stare" title="Variabilă de stare">mărime de stare</a>, ci o funcție de transformare a cărei valoare depinde, în general, de stările inițială și finală respectiv de curba <span class="texhtml"> <i>C</i> </span> delimitată de punctele <span class="texhtml"> <i>a</i> </span> și <span class="texhtml"> <i>b</i> </span> <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Principiul_întâi_al_termodinamicii"><span id="Principiul_.C3.AEnt.C3.A2i_al_termodinamicii"></span>Principiul întâi al termodinamicii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=4" title="Modifică secțiunea: Principiul întâi al termodinamicii" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=4" title="Edit section's source code: Principiul întâi al termodinamicii"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Clausius.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Clausius.jpg/220px-Clausius.jpg" decoding="async" width="220" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/40/Clausius.jpg 1.5x" data-file-width="275" data-file-height="326" /></a><figcaption><a href="/wiki/Rudolf_Julius_Emanuel_Clausius" title="Rudolf Julius Emanuel Clausius">Rudolf Julius Emanuel Clausius</a> (1822–1888) a dat formularea clasică a principiului întâi al termodinamicii și a reformulat principiul al doilea pe baza noțiunii de <i>entropie</i>.</figcaption></figure> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Principiul_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii">Principiul întâi al termodinamicii</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <div class="mw-heading mw-heading3"><h3 id="Energie_internă"><span id="Energie_intern.C4.83"></span>Energie internă</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=5" title="Modifică secțiunea: Energie internă" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=5" title="Edit section's source code: Energie internă"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O serie de experimente esențiale pentru fundamentarea teoretică a termodinamicii au fost efectuate asupra unor sisteme separate de lumea înconjurătoare printr-un <i>înveliș adiabatic</i>. Un asemenea înveliș are însușirea că, odată aplicat unui sistem aflat în echilibru termodinamic, starea acestui sistem poate fi schimbată numai prin efectuarea de lucru mecanic de către forțe acționând din exterior asupra sistemului. O transformare a unui <a href="/wiki/Sistem_%C3%AEnchis" title="Sistem închis">sistem închis</a> cu înveliș adiabatic se numește <i><a href="/wiki/Transformare_adiabatic%C4%83" class="mw-redirect" title="Transformare adiabatică">transformare adiabatică</a></i>. Sinteza rezultatelor experimentelor amintite constituie formularea clasică a <i>principiului întâi al termodinamicii</i>:<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><i>În orice transformare adiabatică a unui sistem, lucrul mecanic efectuat de forțele exterioare depinde numai de starea inițială și de starea finală a sistemului.</i></dd></dl> <p>Conform unei <a href="/wiki/Teorema_de_integrabilitate_a_lui_Frobenius" title="Teorema de integrabilitate a lui Frobenius">teoreme fundamentale</a><sup id="cite_ref-integr_7-0" class="reference"><a href="#cite_note-integr-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> din <a href="/wiki/Geometrie_diferen%C8%9Bial%C4%83" title="Geometrie diferențială">geometria diferențială</a>, rezultă că lucrul mecanic <span class="texhtml"> <i>L</i><sub><i>C</i></sub> </span> produs într-o transformare adiabatică de la o stare inițială <span class="texhtml"> <i>a</i> </span> la o stare finală <span class="texhtml"> <i>b</i> </span> este independent de stările intermediare și există o funcție <span class="texhtml"> <i>U</i> (<i>x</i>) </span> astfel încât <span class="texhtml"><i>U</i> (<i>b</i>) − <i>U</i> (<i>a</i>) = <i>L</i><sub>C</sub></span>. Funcția </p> <dl><dd><span style="padding-right:4em" id="f6"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(6\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(6\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2f3b13b080d81d56074405a8491b627ec182fa1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(6\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=U\left(x_{1},...,x_{n}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=U\left(x_{1},...,x_{n}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d071c46ee0097d7e40a2ee877d51e45eb71b2efc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.962ex; height:2.843ex;" alt="{\displaystyle U=U\left(x_{1},...,x_{n}\right)}"></span></dd></dl> <p>este o <i><a href="/wiki/Func%C8%9Bie_de_stare" title="Funcție de stare">funcție de stare</a></i> a sistemului care se numește <i><a href="/wiki/Energie_intern%C4%83" title="Energie internă">energie internă</a></i>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Ea este definită până la o constantă aditivă, care poate fi fixată alegând ca origine o stare de referință pornind de la care orice stare a sistemului să poată fi obținută printr-o transformare adiabatică. </p> <div class="mw-heading mw-heading3"><h3 id="Cantitate_de_căldură"><span id="Cantitate_de_c.C4.83ldur.C4.83"></span>Cantitate de căldură</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=6" title="Modifică secțiunea: Cantitate de căldură" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=6" title="Edit section's source code: Cantitate de căldură"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Într-o transformare <i>diatermică</i> (neadiabatică) lucrul mecanic depinde, în general, de stările intermediare, iar <span class="texhtml"><i>U</i> (<i>b</i>) − <i>U</i> (<i>a</i>) ≠ <i>L</i><sub>C</sub></span>. Mărimea definită prin relația </p> <dl><dd><span style="padding-right:4em" id="f7"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(7\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(7\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b911bbe37c248c08d6aad218542bd6ddb13afbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(7\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{C}=U\left(b\right)-U\left(a\right)-L_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{C}=U\left(b\right)-U\left(a\right)-L_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd63722ddbfd8b67f553c41f60c787ed5394334" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.348ex; height:2.843ex;" alt="{\displaystyle Q_{C}=U\left(b\right)-U\left(a\right)-L_{C}}"></span></dd></dl> <p>se numește <i>cantitatea de căldură</i> transferată sistemului (primită sau cedată) în cursul transformării. Rearanjând termenii, se poate scrie </p> <dl><dd><span style="padding-right:4em" id="f8"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(8\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(8\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e24a2bf3ca53c0658d529c1c1054cdb8759da510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(8\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U\left(b\right)-U\left(a\right)=L_{C}+Q_{C}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U\left(b\right)-U\left(a\right)=L_{C}+Q_{C}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04c1313c9e12f715c0d57e9ccbd302ee5d89ed78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.382ex; height:2.843ex;" alt="{\displaystyle U\left(b\right)-U\left(a\right)=L_{C}+Q_{C}\,,}"></span></dd></dl> <p>ceea ce, în cazul unei transformări infinitezimale, devine<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span style="padding-right:4em" id="f9"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(9\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(9\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/223351a863017775e4d332b1a7eef79c12fdc9f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.972ex; height:2.843ex;" alt="{\displaystyle \left(9\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ dU=\delta L+\delta Q\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>L</mi> <mo>+</mo> <mi>δ</mi> <mi>Q</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ dU=\delta L+\delta Q\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24a3863d009deff4a7bb9c0ae3057584a4b8bdf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.07ex; height:2.676ex;" alt="{\displaystyle \ dU=\delta L+\delta Q\,.}"></span></dd></dl> <p>Relațiile <a href="#f8">(8)</a> și <a href="#f9">(9)</a> sunt expresii matematice ale <i>principiului întâi al termodinamicii</i> în forma sa generală: </p> <dl><dd><i>Pentru orice sistem termodinamic există o funcție de stare numită energie internă. În orice transformare prin care trece sistemul, variația energiei interne este egală cu suma dintre lucrul mecanic efectuat asupra sistemului și cantitatea de căldură transferată către sistem.</i></dd></dl> <p>Așadar, lucrul mecanic și cantitatea de căldură sunt <i>forme ale schimbului de energie</i> între un sistem și lumea înconjurătoare. </p><p>Măsurarea cantității de căldură face obiectul <a href="/wiki/Calorimetrie" title="Calorimetrie">calorimetriei</a>. Metodele calorimetrice deduc cantitatea de căldură schimbată cu exteriorul de un sistem oarecare comparând starea sa inițială cu cea finală. Deoarece însă cantitatea de căldură schimbată depinde în general de stările intermediare, măsurătoarea poate fi univocă numai dacă procesul de măsurare e specificat în mai mult detaliu. În măsurători calorimetrice <i>la variabile de poziție constante</i>, lucrul mecanic efectuat de sistem este nul și cantitatea de căldură schimbată este egală cu variația energiei sale interne <span class="texhtml"><i>U</i></span>. Aceasta este o <i>funcție de stare</i> și variația ei este unic determinată de stările inițială și finală ale sistemului. În măsurători calorimetrice <i>la variabile de forță constante</i>, cantitatea de căldură schimbată se dovedește a fi egală cu variația unei alte funcții de stare, numită <i><a href="/wiki/Entalpie" title="Entalpie">entalpie</a></i>, care este legată de energie prin relația: </p> <dl><dd><span style="padding-right:4em" id="f10"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(10\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(10\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3d0a98b640ebfe02e78f1724d46973d69b774a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(10\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H=U-\sum _{i=1}^{n}X_{i}\ x_{i}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mtext> </mtext> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=U-\sum _{i=1}^{n}X_{i}\ x_{i}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/987efcff6a4f39910d34c01988050b2045e0a1c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.995ex; height:6.843ex;" alt="{\displaystyle H=U-\sum _{i=1}^{n}X_{i}\ x_{i}\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Temperatură_empirică"><span id="Temperatur.C4.83_empiric.C4.83"></span>Temperatură empirică</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=7" title="Modifică secțiunea: Temperatură empirică" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=7" title="Edit section's source code: Temperatură empirică"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Temperatur%C4%83" title="Temperatură">Temperatură</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p>Existența schimbului de căldură arată că starea unui sistem termodinamic nu este complet caracterizată de variabilele mecanice <span class="texhtml"><i>x</i> = (<i>x</i><sub>1</sub> , ... , <i>x</i><sub>n</sub>)</span>; principiul întâi al termodinamicii indică existența unei noi <a href="/wiki/Variabil%C4%83_de_stare" title="Variabilă de stare">variabile de stare</a>, energia internă, măsurabilă prin metode calorimetrice. În practică este preferată o altă variabilă, care exprimă cantitativ senzațiile familiare de „cald” și „rece”. Este vorba despre <i>temperatură</i>, care poate fi definită empiric pe baza unui experiment numit <i>contact termic</i>. </p><p>Fie două sisteme, reunite într-un singur sistem, acesta fiind izolat de exterior printr-un înveliș adiabatic. Cele două subsisteme sunt însă separate printr-o interfață <i>diatermă</i> (neadiabatică). Variabilele de poziție ale ambelor subsisteme sunt fixate. În aceste condiții nu există schimb de lucru mecanic nici cu exteriorul, nici între subsisteme; nu există schimb de căldură cu exteriorul, dar subsistemele pot schimba căldură între ele. Se zice că cele două subsisteme se află în contact termic; iar dacă s-a stabilit, conform principiului zero al termodinamicii, echilibrul termodinamic, se zice că cele două subsisteme se află în <i>echilibru termic</i>. </p><p>S-a dovedit în mod empiric corectitudinea următorului enunț, numit <i>principiul tranzitivității echilibrului termic</i>: </p> <dl><dd><i>Dacă sistemul A este în echilibru termic cu sistemul B și sistemul B este în echilibru termic cu sistemul C, atunci sistemul A este în echilibru termic cu sistemul C.</i><sup id="cite_ref-zerotranz_1-1" class="reference"><a href="#cite_note-zerotranz-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Din aceste considerații rezultă pe cale deductivă că,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> pentru orice sistem aflat în echilibru termic, există o funcție </p> <dl><dd><span style="padding-right:4em" id="f11"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(11\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(11\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/847aad2c1acc1d3953a35bf5871ebf21a67de390" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(11\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\theta \left(x_{1},...,x_{n},U\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>θ</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mi>U</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\theta \left(x_{1},...,x_{n},U\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1cf8c6059d430a2239b2305689bd16bef257c9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.394ex; height:2.843ex;" alt="{\displaystyle \theta =\theta \left(x_{1},...,x_{n},U\right)}"></span></dd></dl> <p>care, pentru valori fixate ale variabilelor de poziție, este o <a href="/wiki/Func%C8%9Bie_monoton%C4%83" title="Funcție monotonă">funcție monoton crescătoare</a> de energia internă; se spune că relația <a href="#f11">(11)</a> definește o <i>scară de temperatură</i> pentru sistem. Temperatura empirică astfel definită nu este univocă: relația <span class="texhtml"> <i>θ</i> ' = <i>φ</i> (<i>θ</i>)</span>, unde <span class="texhtml"><i>φ</i>(<i>θ</i>)</span> este o funcție monoton crescătoare de argumentul său, face trecerea de la o scară de temperatură <span class="texhtml"><i>θ</i></span> la altă scară de temperatură posibilă <span class="texhtml"><i>θ</i> '</span>. </p><p>Două sisteme aflate în echilibru termic au temperaturi egale. Acest fapt stă la baza <a href="/wiki/Termometrie" title="Termometrie">termometriei</a>, care se ocupă cu măsurarea temperaturilor. Într-o măsurătoare de temperatură, corpul a cărui temperatură urmează a fi măsurată și instrumentul de măsură sunt puse în contact termic și se așteaptă un timp suficient pentru ca ele să ajungă în echilibru termic. Este necesar ca primul să aibă o <a href="/wiki/Capacitate_termic%C4%83" title="Capacitate termică">capacitate termică</a> suficient de mare ca temperatura sa să nu fie modificată apreciabil în cursul transferului de căldură care duce la stabilirea echilibrului termic (un sistem care satisface aceste condiții se numește <i>termostat</i>), pe când al doilea trebuie să-și adapteze temperatura la aceea a primului fără a i-o modifica apreciabil (un astfel de sistem se numește <i>termometru</i>). </p> <div class="mw-heading mw-heading3"><h3 id="Ecuații_de_stare"><span id="Ecua.C8.9Bii_de_stare"></span>Ecuații de stare</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=8" title="Modifică secțiunea: Ecuații de stare" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=8" title="Edit section's source code: Ecuații de stare"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ținând cont de existența unei variabile de stare termică, pe lângă cele mecanice, și alegând ca nouă variabilă temperatura, mai intuitivă și mai ușor accesibilă măsurătorii decât energia internă, relațiile <a href="#f2">(2)</a> devin </p> <dl><dd><span style="padding-right:4em" id="f12"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(12\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(12\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7c3054f8b575b4e790940d9699c5a3f596e2135" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(12\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X_{i}=X_{i}\left(\theta ,x_{1},...,x_{n}\right),\quad i=1,...,n;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>θ</mi> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X_{i}=X_{i}\left(\theta ,x_{1},...,x_{n}\right),\quad i=1,...,n;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9e0c8ebeb2a129d0eb4c678115e61b8bcb0038e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.568ex; height:2.843ex;" alt="{\displaystyle \ X_{i}=X_{i}\left(\theta ,x_{1},...,x_{n}\right),\quad i=1,...,n;}"></span></dd></dl> <p>ele se numesc ecuații de stare <i>termice</i>. Relația <a href="#f6">(6)</a>, completată și ea cu variabila temperatură, devine ecuația de stare <i>calorică</i> </p> <dl><dd><span style="padding-right:4em" id="f13"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(13\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(13\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cac82ccb6327aa21379f3922633396b9b1f8b22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(13\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=U\left(\theta ,x_{1},...,x_{n}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mi>θ</mi> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=U\left(\theta ,x_{1},...,x_{n}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46daa069b4dc61d7f1efdbdeb801bcf89e4f2b08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.12ex; height:2.843ex;" alt="{\displaystyle U=U\left(\theta ,x_{1},...,x_{n}\right).}"></span></dd></dl> <p>Termodinamica nu poate stabili forma acestor <i>ecuații de stare</i> (sau <i>ecuații caracteristice</i>), care determină complet proprietățile sistemului în stări de echilibru termodinamic. În aplicații, ele sunt determinate experimental. Mecanica statistică le poate calcula, în principiu, dacă este cunoscută structura microscopică a sistemului. </p> <div class="mw-heading mw-heading2"><h2 id="Principiul_al_doilea_al_termodinamicii">Principiul al doilea al termodinamicii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=9" title="Modifică secțiunea: Principiul al doilea al termodinamicii" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=9" title="Edit section's source code: Principiul al doilea al termodinamicii"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Sadi_Carnot.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Sadi_Carnot.jpeg/220px-Sadi_Carnot.jpeg" decoding="async" width="220" height="296" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Sadi_Carnot.jpeg/330px-Sadi_Carnot.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Sadi_Carnot.jpeg/440px-Sadi_Carnot.jpeg 2x" data-file-width="956" data-file-height="1286" /></a><figcaption><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Nicolas Léonard Sadi Carnot</a> (1796–1832) a enunțat <i>teorema lui Carnot</i>, una din formulările primare ale principiului al doilea al termodinamicii.</figcaption></figure> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii">Principiul al doilea al termodinamicii</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p>Studiul schimbului de căldură între sisteme s-a dezvoltat din necesitatea practică de a îmbunătăți funcționarea <a href="/wiki/Ma%C8%99in%C4%83_termic%C4%83" title="Mașină termică">mașinilor termice</a>. Din punct de vedere teoretic, o <i>mașină termică</i> este un sistem care, într-o <i>transformare ciclică</i>, primește căldură și cedează lucru mecanic. În cursul transformării, mașina termică schimbă căldură cu un număr de sisteme numite <i>surse de căldură</i>, care se presupune că sunt <i>termostate</i> având temperaturi cunoscute. Transformarea se numește <i>monotermă</i>, <i>bitermă</i> sau <i>politermă</i>, după numărul de surse de căldură; sunt imaginabile și transformări în care se schimbă căldură cu o infinitate de surse de căldură ale căror temperaturi variază continuu. </p><p>Formularea primară a <i>principiului al doilea al termodinamicii</i> este echivalentă cu constatarea experimentală că nu poate exista o mașină termică cu o singură sursă de căldură: </p> <dl><dd><i>Într-o transformare ciclică monotermă, independent de natura sistemului, cantitatea de căldură primită de sistem este negativă sau nulă; ea este nulă <a href="/wiki/Dac%C4%83_%C8%99i_numai_dac%C4%83" title="Dacă și numai dacă">dacă și numai dacă</a> transformarea este reversibilă.</i><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Cazul unei transformări ciclice biterme reversibile poate fi redus la precedentul printr-un artificiu: sistemului considerat <b>A</b> i se adaugă un al doilea sistem <b>B</b>, ambele sisteme fiind supuse unor transformări ciclice reversibile repetate care sunt ajustate astfel ca sistemul rezultat prin reunirea celor două subsisteme să sufere o transformare ciclică monotermă.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Concluzia este o formulare modificată a principiului al doilea al termodinamicii: </p> <dl><dd><i>Într-o transformare ciclică bitermă reversibilă, raportul cantităților de căldură schimbate de sistem cu cele două termostate nu depinde de natura sistemului; el depinde numai de temperaturile celor două termostate.</i></dd></dl> <p>Notând cu <span class="texhtml"><i>θ</i><sub><i>1</i></sub></span> și <span class="texhtml"><i>θ</i><sub><i>2</i></sub></span> temperaturile termostatelor, iar cu <span class="texhtml"><i>Q</i><sub><i>1</i></sub></span> și <span class="texhtml"><i>Q</i><sub><i>2</i></sub></span> cantitățile de căldură respective, avem așadar </p> <dl><dd><span style="padding-right:4em" id="f14"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(14\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(14\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9629e00c8ff6eb082b6c2b3c638b56bae2c6ea4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(14\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {Q_{1}}{Q_{2}}}=-f\left(\theta _{1},\theta _{2}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {Q_{1}}{Q_{2}}}=-f\left(\theta _{1},\theta _{2}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e84046cc759e86afb7a9e999bb6ef6d5ff50809" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.468ex; height:5.843ex;" alt="{\displaystyle {\frac {Q_{1}}{Q_{2}}}=-f\left(\theta _{1},\theta _{2}\right),}"></span></dd></dl> <p>unde funcția <span class="texhtml"><i>f</i> (<i>θ</i><sub><i>1</i></sub>, <i>θ</i><sub><i>2</i></sub>)</span> nu depinde de natura sistemului. Mașina termică bitermă reversibilă descrisă poartă numele istoric de <i>mașină Carnot</i>, ea funcționând după un <i><a href="/wiki/Ciclu_Carnot" class="mw-redirect" title="Ciclu Carnot">ciclu Carnot</a></i>, iar enunțul precedent este echivalent cu <i>teorema lui Carnot</i>: randamentul unui ciclu Carnot depinde numai de temperaturile celor două surse de căldură.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Temperatură_termodinamică"><span id="Temperatur.C4.83_termodinamic.C4.83"></span>Temperatură termodinamică</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=10" title="Modifică secțiunea: Temperatură termodinamică" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=10" title="Edit section's source code: Temperatură termodinamică"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Analiza detaliată a schimbului de căldură în transformări ciclice biterme <a href="/wiki/Proces_reversibil" title="Proces reversibil">reversibile</a> și <a href="/wiki/Proces_ireversibil" title="Proces ireversibil">ireversibile</a><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> arată că funcția <span class="texhtml"><i>f</i> (<i>θ</i><sub><i>1</i></sub>, <i>θ</i><sub><i>2</i></sub>)</span> definită prin relația <a href="#f14">(14)</a> poate fi factorizată în forma </p> <dl><dd><span style="padding-right:4em" id="f15"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(15\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(15\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6abf4bdbd0cc18a69e6381fde119f08dc68f97bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(15\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\left(\theta _{1},\theta _{2}\right)={\frac {\phi \left(\theta _{1}\right)}{\phi \left(\theta _{2}\right)}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\left(\theta _{1},\theta _{2}\right)={\frac {\phi \left(\theta _{1}\right)}{\phi \left(\theta _{2}\right)}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa8a443f64ec90ba4c763e97de4d3054fbe6d885" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:19.493ex; height:6.509ex;" alt="{\displaystyle f\left(\theta _{1},\theta _{2}\right)={\frac {\phi \left(\theta _{1}\right)}{\phi \left(\theta _{2}\right)}}\,,}"></span></dd></dl> <p>unde <span class="texhtml"><i>φ</i> = <i>φ</i> (<i>θ</i>)</span> este o funcție continuă, monoton crescătoare, cu valori strict pozitive și <a href="/wiki/Func%C8%9Bie_m%C4%83rginit%C4%83" title="Funcție mărginită">mărginită</a> (nu se poate anula și nu poate deveni infinită) de temperatura <span class="texhtml"><i>θ</i></span> definită până la o constantă multiplicativă pozitivă. Ea definește așadar o scară de temperatură. Odată fixat prin convenție factorul multiplicativ, temperatura definită prin relația </p> <dl><dd><span style="padding-right:4em" id="f16"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(16\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(16\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a82f7f13cb412d80dd9ca54975f657853491fb3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(16\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=\phi \left(\theta \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mi>ϕ</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=\phi \left(\theta \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c76c952425d9598f6bb3ac95affae567253f6c75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.407ex; height:2.843ex;" alt="{\displaystyle T=\phi \left(\theta \right)}"></span></dd></dl> <p>se numește <i>temperatura termodinamică</i> sau <i>temperatura absolută</i> corespunzătoare temperaturii empirice <span class="texhtml"><i>θ</i></span>. Introducând temperaturile absolute <span class="texhtml"> <i>T</i><sub><i>1</i></sub></span> și <span class="texhtml"> <i>T</i><sub><i>2</i></sub></span> ale termostatelor cu care se schimbă cantitățile de căldură <span class="texhtml"> <i>Q</i><sub><i>1</i></sub></span> și <span class="texhtml"> <i>Q</i><sub><i>1</i></sub></span> într-o transformare ciclică bitermă reversibilă, relația <a href="#f14">(14)</a> poate fi rescrisă ca </p> <dl><dd><span style="padding-right:4em" id="f17"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(17\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(17\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a68ac45650322179dc920a90b838256ea29d5242" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(17\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {Q_{1}}{T_{1}}}+{\frac {Q_{2}}{T_{2}}}=0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {Q_{1}}{T_{1}}}+{\frac {Q_{2}}{T_{2}}}=0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8f03d62b2b7c53c3add64cfc86f26107c693291" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.593ex; height:5.676ex;" alt="{\displaystyle {\frac {Q_{1}}{T_{1}}}+{\frac {Q_{2}}{T_{2}}}=0\,.}"></span></dd></dl> <p>Acest rezultat se generalizează la cazul unei transformări ciclice politerme <i>reversibile</i> cu <span class="texhtml"><i>s</i></span> surse de căldură sub forma </p> <dl><dd><span style="padding-right:4em" id="f18"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(18\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(18\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a732faf07c5f6def4dc905520adc8ffe9a0c9c97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(18\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53cf9840e7b3bad405468fa7a0d5f058052af09f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:11.864ex; height:6.843ex;" alt="{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}=0\,}"></span></dd></dl> <p>numită <i>egalitatea lui Clausius</i>. </p><p>Conform formulării primare a principiului al doilea al termodinamicii, într-o transformare ciclică monotermă ireversibilă cantitatea de căldură primită de sistem este strict negativă. Pe de altă parte, o transformare complexă care conține atât porțiuni reversibile cât și porțiuni ireversibile este, în ansamblu, ireversibilă. Pornind de la aceste constatări se obține pe cale deductivă<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <i>inegalitatea lui Clausius</i> pentru cazul unei transformări ciclice politerme <i>ireversibile</i>: </p> <dl><dd><span style="padding-right:4em" id="f19"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(19\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(19\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c89c61f5833abd26cda039baef0565a6f6e2d8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(19\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}<0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo><</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}<0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961013c6feebc8d59ed438dfadcdee0973f57385" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.124ex; height:6.843ex;" alt="{\displaystyle \sum _{i=1}^{s}{\frac {Q_{i}}{T_{i}}}<0.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Entropie">Entropie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=11" title="Modifică secțiunea: Entropie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=11" title="Edit section's source code: Entropie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Considerăm acum cazul unei transformări ciclice reversibile care constă dintr-o înșiruire de transformări elementare, în fiecare dintre acestea sistemul schimbând cantitatea de căldură <i><span class="texhtml">δQ</span></i> cu un termostat de temperatură <span class="texhtml"><i>T</i></span>. Reducând „pasul” acestor transformări elementare și crescând numărul lor, se obține la limită o transformare ciclică reversibilă în care se schimbă căldură cu termostate ale căror temperaturi variază continuu. În această limită egalitatea lui Clausius <a href="#f18">(18)</a> devine </p> <dl><dd><span style="padding-right:4em" id="f20"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(20\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(20\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab0679cf19948d772b73ec69cb31706cbd6370db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(20\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{C}\,{\frac {\delta Q}{T}}=0\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{C}\,{\frac {\delta Q}{T}}=0\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0876ba5497901c950cfa323fb00a772acd16e916" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.566ex; height:5.843ex;" alt="{\displaystyle \oint _{C}\,{\frac {\delta Q}{T}}=0\,,}"></span><span style="padding-left:4em">(într-o transformare reversibilă)</span></dd></dl> <p>unde integrala în spațiul variabilelor de stare se calculează de-a lungul unei curbe închise <span class="texhtml"><i>C</i></span> care conține numai stări de echilibru. </p><p>Rezultă atunci din <a href="/wiki/Teorema_de_integrabilitate_a_lui_Frobenius" title="Teorema de integrabilitate a lui Frobenius">teorema de integrabilitate</a><sup id="cite_ref-integr_7-1" class="reference"><a href="#cite_note-integr-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> că există o funcție de stare, definită până la o constantă aditivă, numită <i><a href="/wiki/Entropie" title="Entropie">entropie</a></i> și notată tradițional cu <span class="texhtml"><i>S</i></span>, a cărei diferențială totală este </p> <dl><dd><span style="padding-right:4em" id="f21"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(21\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(21\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49b68ffcc1359fad819072a6508aa68747ce9ee6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(21\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dS={\frac {\delta Q}{T}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dS={\frac {\delta Q}{T}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94b64a84f160f91f230a56c23e991179c2d4caea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.571ex; height:5.343ex;" alt="{\displaystyle dS={\frac {\delta Q}{T}}\,,}"></span><span style="padding-left:4em">(într-o transformare <i>reversibilă</i>)</span></dd></dl> <p>iar integrala acesteia de la o stare inițială <span class="texhtml"><i>a</i></span> la o stare finală <span class="texhtml"><i>b</i></span> este independentă de drumul urmat <span class="texhtml"><i>C</i></span> și reprezintă variația funcției între starea inițială și starea finală: </p> <dl><dd><span style="padding-right:4em" id="f22"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(22\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(22\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4cd45537adc8a2f5c02ff3179082fa63638ceba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(22\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}=S\left(b\right)-S\left(a\right)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mi>S</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>S</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}=S\left(b\right)-S\left(a\right)\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5573e99b1d2d28f440fedf30c117ea57d3470fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.25ex; height:5.843ex;" alt="{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}=S\left(b\right)-S\left(a\right)\,.}"></span><span style="padding-left:4em">(într-o transformare <i>reversibilă</i>)</span></dd></dl> <p>Aplicând același raționament în cazul unei transformări ireversibile, se obține, pe baza inegalității lui Clausius <a href="#f19">(19)</a>: </p> <dl><dd><span style="padding-right:4em" id="f23"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(23\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(23\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6f2aac4dc5f3da8ee7c8b0645249105d2534716" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(23\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}<S\left(b\right)-S\left(a\right)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo><</mo> <mi>S</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>S</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}<S\left(b\right)-S\left(a\right)\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1f6bd742ee8fff99bfd5df8260a9e27e41029a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.25ex; height:5.843ex;" alt="{\displaystyle \int _{C}\,{\frac {\delta Q}{T}}<S\left(b\right)-S\left(a\right)\,.}"></span><span style="padding-left:4em">(într-o transformare <i>ireversibilă</i>)</span></dd></dl> <p>Utilizând noțiunea de entropie, se poate da o formulare generală principiului al doilea al termodinamicii: </p> <dl><dd><i>Pentru orice sistem termodinamic există o funcție de stare numită entropie. În orice transformare prin care trece sistemul, variația entropiei este mărginită inferior de cantitatea <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \int _{C}\,{\frac {\delta Q}{T}},\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \int _{C}\,{\frac {\delta Q}{T}},\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7329cdc72c1c43d6fd43eb7096ec59eb4905a8a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.066ex; height:3.509ex;" alt="{\displaystyle \scriptstyle \int _{C}\,{\frac {\delta Q}{T}},\,}"></span> unde drumul de integrare este curba <span class="texhtml">C </span> care unește starea inițială cu starea finală, trecând prin stări intermediare în care se schimbă cantități de căldură <span class="texhtml">δQ</span> cu o înșiruire continuă de termostate la temperaturi </i><span class="texhtml">T</span><i>. Marginea inferioară este atinsă dacă și numai dacă transformarea este reversibilă</i>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Stări_de_echilibru"><span id="St.C4.83ri_de_echilibru"></span>Stări de echilibru</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=12" title="Modifică secțiunea: Stări de echilibru" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=12" title="Edit section's source code: Stări de echilibru"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Josiah_Willard_Gibbs_-from_MMS-.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/220px-Josiah_Willard_Gibbs_-from_MMS-.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/330px-Josiah_Willard_Gibbs_-from_MMS-.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/440px-Josiah_Willard_Gibbs_-from_MMS-.jpg 2x" data-file-width="888" data-file-height="1184" /></a><figcaption><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Josiah Willard Gibbs</a> (1839–1903) a introdus noțiunea de <i>potențial chimic</i>; lucrările sale au pus bazele teoretice ale <i>termodinamicii chimice</i> și <i>chimiei fizice</i>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Potențiale_termodinamice"><span id="Poten.C8.9Biale_termodinamice"></span>Potențiale termodinamice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=13" title="Modifică secțiunea: Potențiale termodinamice" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=13" title="Edit section's source code: Potențiale termodinamice"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">Potențial termodinamic</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p>În ecuațiile caracteristice <a href="#f12">(12)</a> și <a href="#f13">(13)</a>, transcrise acum în scara termodinamică de temperatură, </p> <dl><dd><span style="padding-right:4em" id="f24"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(24\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(24\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9833a87fcc152968f4e71ba89602c8624ddcaeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(24\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{i}=X_{i}\left(T,x_{1},...,x_{n}\right),\quad i=1,...,n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{i}=X_{i}\left(T,x_{1},...,x_{n}\right),\quad i=1,...,n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/225a1ad6b70fd405a5a40ba32858db5f703b06a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.886ex; height:2.843ex;" alt="{\displaystyle X_{i}=X_{i}\left(T,x_{1},...,x_{n}\right),\quad i=1,...,n}"></span></dd></dl> <dl><dd><span style="padding-right:4em" id="f25"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(25\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(25\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/507731e72f404796e2be45686c7baa837a79924e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(25\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=U\left(T,x_{1},...,x_{n}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=U\left(T,x_{1},...,x_{n}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e29ed2060fb35eebaa98bdc34ef29e5ff21943d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.632ex; height:2.843ex;" alt="{\displaystyle U=U\left(T,x_{1},...,x_{n}\right)}"></span></dd></dl> <p>variabilele de stare independente sunt temperatura și variabilele de poziție. Dar alegerea variabilelor independente utilizate pentru caracterizarea stărilor de echilibru poate fi schimbată, după necesitățile problemei; acest lucru se realizează în termodinamică printr-o schimbare simultană de variabile independente și de funcție numită <i><a href="/wiki/Transformare_Legendre" title="Transformare Legendre">transformare Legendre</a></i>. Efectuând o transformare Legendre asupra perechilor de variabile <span class="texhtml"> (<i>T</i> ↔ <i>S</i> )</span> sau/și <span class="texhtml">(<i>X</i> ↔ <i>x</i> )</span>, se rearanjează expresia diferențială<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span style="padding-right:4em" id="f26"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(26\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(26\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60d923e0a22cfb2caeb9fd0a0832d583ab605cf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(26\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dU=X\,dx\,+T\,dS\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>S</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=X\,dx\,+T\,dS\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad36c9e38893f8396ab6449dc764427da8545bb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.363ex; height:2.343ex;" alt="{\displaystyle dU=X\,dx\,+T\,dS\,}"></span></dd></dl> <p>(obținută combinând formulele <a href="#f9">(9)</a>, <a href="#f4">(4)</a> și <a href="#f21">(21)</a>) după diferențialele noilor variabile, identificând astfel noua funcție. Această funcție este un <i>potențial termodinamic</i>: derivatele ei parțiale furnizează noile ecuații caracteristice (termică și calorice). Unele tratate de termodinamică folosesc termenul de <i>funcție termodinamică</i> pentru desemnarea potențialului termodinamic.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Potențialele termodinamice utilizate curent sunt enumerate mai jos, împreună cu diferențialele lor totale și ecuațiile caracteristice care derivă din ele.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <ul><li><b><a href="/wiki/Energie_intern%C4%83" title="Energie internă">Energie internă</a> U (S, x)</b></li></ul> <dl><dd><span style="padding-right:4em" id="f27"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(27\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(27\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10593ab4b7b124fbd94e04ecb092a292e443a523" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(27\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dU=T\,dS+X\,dx;\quad \left({\frac {\partial U}{\partial S}}\right)_{x}=T\,,\quad \left({\frac {\partial U}{\partial x}}\right)_{S}=X\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>S</mi> <mo>+</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>;</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=T\,dS+X\,dx;\quad \left({\frac {\partial U}{\partial S}}\right)_{x}=T\,,\quad \left({\frac {\partial U}{\partial x}}\right)_{S}=X\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fa64ad9dbd411539f89a810273be2056bdf4bcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.717ex; height:6.176ex;" alt="{\displaystyle dU=T\,dS+X\,dx;\quad \left({\frac {\partial U}{\partial S}}\right)_{x}=T\,,\quad \left({\frac {\partial U}{\partial x}}\right)_{S}=X\,.}"></span></dd></dl> <ul><li><b><a href="/wiki/Entropie" title="Entropie">Entropie</a> S (U, x)</b></li></ul> <dl><dd><span style="padding-right:4em" id="f28"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(28\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(28\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35f55cd144e16eece5540ec7857ad44a3cf0d0fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(28\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dS={\frac {dU}{T}}\,-{\frac {X\,dx}{T}};\quad \left({\frac {\partial S}{\partial U}}\right)_{x}={\frac {1}{T}}\,,\quad \left({\frac {\partial S}{\partial x}}\right)_{U}=-{\frac {X}{T}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>U</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>X</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>;</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>X</mi> <mi>T</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dS={\frac {dU}{T}}\,-{\frac {X\,dx}{T}};\quad \left({\frac {\partial S}{\partial U}}\right)_{x}={\frac {1}{T}}\,,\quad \left({\frac {\partial S}{\partial x}}\right)_{U}=-{\frac {X}{T}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a5dc64036d86041c98f633a23bd48c3ff53d47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.15ex; height:6.176ex;" alt="{\displaystyle dS={\frac {dU}{T}}\,-{\frac {X\,dx}{T}};\quad \left({\frac {\partial S}{\partial U}}\right)_{x}={\frac {1}{T}}\,,\quad \left({\frac {\partial S}{\partial x}}\right)_{U}=-{\frac {X}{T}}\,.}"></span></dd></dl> <ul><li><b><a href="/wiki/Entalpie" title="Entalpie">Entalpie</a> H (S, X)</b></li></ul> <dl><dd><span style="padding-right:4em" id="f29"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(29\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(29\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3ec65294d2d6324c8a0bb9e5870f95b143dbadc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(29\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H=U-X\,x\,;\quad dH=T\,dS-x\,dX\,;\quad \left({\frac {\partial H}{\partial S}}\right)_{X}=T\,,\quad \left({\frac {\partial H}{\partial X}}\right)_{S}=-x\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>S</mi> <mo>−</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>X</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>X</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=U-X\,x\,;\quad dH=T\,dS-x\,dX\,;\quad \left({\frac {\partial H}{\partial S}}\right)_{X}=T\,,\quad \left({\frac {\partial H}{\partial X}}\right)_{S}=-x\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e597df8809112e73dd8a8c17c7e974f0493bd5ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:73.79ex; height:6.176ex;" alt="{\displaystyle H=U-X\,x\,;\quad dH=T\,dS-x\,dX\,;\quad \left({\frac {\partial H}{\partial S}}\right)_{X}=T\,,\quad \left({\frac {\partial H}{\partial X}}\right)_{S}=-x\,.}"></span></dd></dl> <ul><li><b><a href="/wiki/Energie_liber%C4%83" title="Energie liberă">Energie liberă</a> F (T, x)</b></li></ul> <dl><dd><span style="padding-right:4em" id="f30"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(30\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(30\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f48ae889dd1ddf7fdb1f2226b7067fee8777a63d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(30\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=U-TS\,;\quad dF=-S\,dT+X\,dx\,;\quad \left({\frac {\partial F}{\partial T}}\right)_{x}=-S\,,\quad \left({\frac {\partial F}{\partial x}}\right)_{T}=X\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <mi>d</mi> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>T</mi> <mo>+</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>X</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=U-TS\,;\quad dF=-S\,dT+X\,dx\,;\quad \left({\frac {\partial F}{\partial T}}\right)_{x}=-S\,,\quad \left({\frac {\partial F}{\partial x}}\right)_{T}=X\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fab08d81d2a4fbbed8f8f7a0eb1121d89c83cc34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:73.896ex; height:6.176ex;" alt="{\displaystyle F=U-TS\,;\quad dF=-S\,dT+X\,dx\,;\quad \left({\frac {\partial F}{\partial T}}\right)_{x}=-S\,,\quad \left({\frac {\partial F}{\partial x}}\right)_{T}=X\,.}"></span></dd></dl> <ul><li><b><a href="/wiki/Entalpie_liber%C4%83" title="Entalpie liberă">Entalpie liberă</a> G (T, X)</b></li></ul> <dl><dd><span style="padding-right:4em" id="f31"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(31\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(31\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c84b24ca3cdf40fb16b9af4f4475da23899dd5bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(31\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G=U-Xx-TS\,;\quad dG=-S\,dT-x\,dX\,;\quad \left({\frac {\partial G}{\partial T}}\right)_{X}=-S\,,\quad \left({\frac {\partial G}{\partial X}}\right)_{T}=-x\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>X</mi> <mi>x</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>T</mi> <mo>−</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>X</mi> <mspace width="thinmathspace" /> <mo>;</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>X</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G=U-Xx-TS\,;\quad dG=-S\,dT-x\,dX\,;\quad \left({\frac {\partial G}{\partial T}}\right)_{X}=-S\,,\quad \left({\frac {\partial G}{\partial X}}\right)_{T}=-x\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d59e15cdd8a12175c27ce9eb36781d508258828" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:82.16ex; height:6.176ex;" alt="{\displaystyle G=U-Xx-TS\,;\quad dG=-S\,dT-x\,dX\,;\quad \left({\frac {\partial G}{\partial T}}\right)_{X}=-S\,,\quad \left({\frac {\partial G}{\partial X}}\right)_{T}=-x\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Schimb_de_căldură"><span id="Schimb_de_c.C4.83ldur.C4.83"></span>Schimb de căldură</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=14" title="Modifică secțiunea: Schimb de căldură" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=14" title="Edit section's source code: Schimb de căldură"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Parametrizările de mai jos ale cantității de căldură schimbată într-o transformare elementară reversibilă definesc proprietăți ale sistemului numite (impropriu) <i>constante de material</i>. Ele se determină prin metode calorimetrice și sunt importante în aplicațiile practice. </p> <ul><li><a href="/wiki/C%C4%83ldur%C4%83#Terminologie" title="Căldură">Capacitatea termică</a> la variabile<span class="texhtml"> <i>x</i> </span> constante <span class="texhtml"> (<i>C</i><sub><i>x</i></sub>)</span> și <a href="/wiki/C%C4%83ldur%C4%83#Terminologie" title="Căldură">căldura latentă</a> la variația variabilei <span class="texhtml"> <i>x</i><sub><i>i</i></sub></span> <span class="texhtml"> (<i>λ</i><sub><i>i</i></sub>) </span>:</li></ul> <dl><dd><span style="padding-right:4em" id="f32"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(32\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(32\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a2e1d5a7c070dc7b97855d0b6630c604b49be9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(32\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=C_{x}\left(T,x\right)\,dT+\sum _{i=1}^{n}\lambda _{i}\left(T,x\right)\,dx_{i}\,,\quad C_{x}=\left({\frac {\partial U}{\partial T}}\right)_{x}>0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q=C_{x}\left(T,x\right)\,dT+\sum _{i=1}^{n}\lambda _{i}\left(T,x\right)\,dx_{i}\,,\quad C_{x}=\left({\frac {\partial U}{\partial T}}\right)_{x}>0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdc2bb3454816a7c93528d1eb5423673090d3786" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:61.197ex; height:6.843ex;" alt="{\displaystyle \delta Q=C_{x}\left(T,x\right)\,dT+\sum _{i=1}^{n}\lambda _{i}\left(T,x\right)\,dx_{i}\,,\quad C_{x}=\left({\frac {\partial U}{\partial T}}\right)_{x}>0\,.}"></span></dd></dl> <ul><li><i>Capacitatea termică la variabile</i><span class="texhtml"> <i>X</i> </span> constante <span class="texhtml"> (<i>C</i><sub><i>X</i></sub>)</span> și <i>căldura latentă la variația variabilei</i> <span class="texhtml"> <i>X</i><sub><i>i</i></sub></span> <span class="texhtml"> (<i>λ'<sub>i</sub></i>) </span>:</li></ul> <dl><dd><span style="padding-right:4em" id="f33"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(33\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(33\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e313adf41bdf371d491205386408a570049312f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(33\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=C_{X}\left(T,X\right)\,dT+\sum _{i=1}^{n}\lambda _{i}'\left(T,X\right)\,dX_{i}\,,\quad C_{X}=\left({\frac {\partial H}{\partial T}}\right)_{X}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>X</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>X</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="1em" /> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q=C_{X}\left(T,X\right)\,dT+\sum _{i=1}^{n}\lambda _{i}'\left(T,X\right)\,dX_{i}\,,\quad C_{X}=\left({\frac {\partial H}{\partial T}}\right)_{X}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccdf1a6f5a4729502f6c09c12df07a95bfdcaf5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:60.492ex; height:6.843ex;" alt="{\displaystyle \delta Q=C_{X}\left(T,X\right)\,dT+\sum _{i=1}^{n}\lambda _{i}'\left(T,X\right)\,dX_{i}\,,\quad C_{X}=\left({\frac {\partial H}{\partial T}}\right)_{X}\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Schimb_de_substanță"><span id="Schimb_de_substan.C8.9B.C4.83"></span>Schimb de substanță</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=15" title="Modifică secțiunea: Schimb de substanță" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=15" title="Edit section's source code: Schimb de substanță"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Există transformări în care, pe lângă schimb de <i>căldură</i> și <i>lucru mecanic</i>, are loc un schimb de <i>substanță</i>. De exemplu, o cantitate de fluid schimbă <a href="/wiki/Substan%C8%9B%C4%83" class="mw-redirect" title="Substanță">substanță</a> cu exteriorul în cursul proceselor de <a href="/wiki/Evaporare" title="Evaporare">evaporare</a> și <a href="/wiki/Condensare" title="Condensare">condensare</a>. Noțiunea <a href="/wiki/Sistem_termodinamic" title="Sistem termodinamic">sistem termodinamic</a> poate fi așadar lărgită, pentru a include astfel de fenomene în care <a href="/wiki/Mas%C4%83" title="Masă">masele</a> componentelor sistemului se modifică. </p><p>Fie un sistem cu <span class="texhtml"><i>c</i></span> componente, de mase variabile <span class="texhtml"> <i>M</i> = (<i>M</i><sub><i>1</i></sub>, ..., <i>M</i><sub><i>c</i></sub>)</span>, care se adaugă variabilelor de stare. Alegând ca <a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">potențial termodinamic</a> entalpia liberă, aceasta va fi o funcție <span class="texhtml"> <i>G</i> = ( <i>T</i>, <i>X</i><sub><i>1</i></sub>, ..., <i>X</i><sub><i>n</i></sub>, <i>M</i><sub><i>1</i></sub> ..., <i>M</i><sub><i>c</i></sub>)</span>. Relațiiile <a href="#f31">(31)</a> trebuie ajustate pentru a ține cont de noile variabile: </p> <dl><dd><span style="padding-right:4em" id="f34"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(34\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(34\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43b1961ac7efc21912b78cb09e4c7dea79f943d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(34\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dG=-S\,dT-\sum _{i=1}^{n}x_{i}\,dX_{i}+\sum _{k=1}^{c}\mu _{k}\,dM_{k}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>T</mi> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG=-S\,dT-\sum _{i=1}^{n}x_{i}\,dX_{i}+\sum _{k=1}^{c}\mu _{k}\,dM_{k}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6d57566ffcb2e7cd47e26fbae8d22180826b23d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:40.132ex; height:6.843ex;" alt="{\displaystyle dG=-S\,dT-\sum _{i=1}^{n}x_{i}\,dX_{i}+\sum _{k=1}^{c}\mu _{k}\,dM_{k}\,}"></span></dd></dl> <p>unde </p> <dl><dd><span style="padding-right:4em" id="f35"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(35\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>35</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(35\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57fcefac1b4d0287db1fac766e26a689d950ec65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(35\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial G}{\partial T}}=-S,\quad {\frac {\partial G}{\partial X_{i}}}=-x_{i},\quad {\frac {\partial G}{\partial M_{k}}}=\mu _{k}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial G}{\partial T}}=-S,\quad {\frac {\partial G}{\partial X_{i}}}=-x_{i},\quad {\frac {\partial G}{\partial M_{k}}}=\mu _{k}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549aa79c2a329e2a857f8d8a151b9d79f89549b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.134ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial G}{\partial T}}=-S,\quad {\frac {\partial G}{\partial X_{i}}}=-x_{i},\quad {\frac {\partial G}{\partial M_{k}}}=\mu _{k}\,.}"></span></dd></dl> <p>Funcțiile <span class="texhtml"><i>μ</i> = (<i>μ</i><sub><i>1</i></sub>, ..., <i>μ</i><sub><i>c</i></sub>)</span> definite în <a href="#f35">(35)</a> se numesc <i><a href="/wiki/Poten%C8%9Bial_chimic" title="Potențial chimic">potențiale chimice</a></i> ale substanțelor componente respective. În acest formalism masele componentelor apar ca variabile de poziție, potențialele chimice asociate apar ca variabile de forță, iar contribuția schimbului de substanță <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </munderover> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce759642a7daf85e13f738f7c7043f077170641e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:3.355ex; height:6.843ex;" alt="{\displaystyle \sum _{k=1}^{c}}"></span> <span class="texhtml"><i>μ</i><sub><i>k</i></sub> d<i>M</i><sub><i>k</i></sub></span> are aspectul unui lucru mecanic. Aplicațiile în <i>termodinamica chimică</i> și <i><a href="/wiki/Categorie:Chimie_fizic%C4%83" title="Categorie:Chimie fizică">chimia fizică</a></i> sunt numeroase, la procese ca <a href="/wiki/Faz%C4%83_(termodinamic%C4%83)" title="Fază (termodinamică)">tranziții de fază</a> sau <a href="/wiki/Reac%C8%9Bie_chimic%C4%83" title="Reacție chimică">reacții chimice</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Transformări_ireversibile"><span id="Transform.C4.83ri_ireversibile"></span>Transformări ireversibile</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=16" title="Modifică secțiunea: Transformări ireversibile" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=16" title="Edit section's source code: Transformări ireversibile"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Prin definiție, un sistem aflat într-o stare de echilibru va rămâne în această stare un timp indefinit, dacă nu se schimbă condițiile exterioare. Dacă aceste condiții se schimbă, echilibrul va fi perturbat și sistemul va începe o transformare care, după un timp suficient de lung, se va termina într-o nouă stare de echilibru, compatibil cu noile condiții. Dacă transformarea este ireversibilă, termodinamica nu-i poate descrie desfășurarea, fiindcă stările intermediare nu sunt stări de echilibru. Dată o stare inițială <span class="texhtml"><i>a</i></span>, termodinamica poate doar indica unele caracteristici ale stării finale <span class="texhtml"><i>b</i></span>, compatibilă cu noile condiții de echilibru. </p> <ul><li>Pentru o transformare ireversibilă <i>adiabatică</i> (în care nu se schimbă căldură cu exteriorul), din relația <a href="#f23">(23)</a> rezultă <span class="texhtml"><i>S</i> (<i>b</i>) > <i>S</i> (<i>a</i>)</span>. Starea finală de echilibru este realizată atunci când <i>entropia</i> are valoarea <i>maximă</i> compatibilă cu noile condiții de echilibru.</li></ul> <ul><li>Pentru o transformare ireversibilă <i>izotermă</i> (sistemul este tot timpul în contact cu un termostat) în care <i>variabilele de poziție rămân constante</i>, inegalitatea precedentă poate fi transcrisă în funcție de <i>energia liberă</i> <a href="#f30">(30)</a> sub forma <span class="texhtml"><i>F</i> (<i>b</i>) < <i>F</i> (<i>a</i>)</span>. Starea finală de echilibru se realizează atunci când energia liberă are valoarea <i>minimă</i>.</li></ul> <ul><li>Pentru o transformare ireversibilă <i>izotermă</i> în care <i>variabilele de forță rămân constante</i> în tot timpul procesului, inegalitatea, transcrisă în funcție de <i>entalpia liberă</i> <a href="#f31">(31)</a>, devine <span class="texhtml"><i>G</i> (<i>b</i>) < <i>G</i> (<i>a</i>)</span>. Starea finală de echilibru se realizează atunci când entalpia liberă are valoarea <i>minimă</i>.</li></ul> <p>Aceste exemple arată cât de importantă este precizarea condițiilor în care are loc o transformare ireversibilă. Afirmația „într-un proces ireversibil entropia sistemului crește” induce în eroare. În primul rând, a vorbi despre o „creștere” a entropiei sugerează o continuitate de la starea inițială la starea finală care nu există, fiindcă entropia nu este definită în stările intermediare, care nu sunt stări de echilibru. În al doilea rând, se poate spune că entropia stării finale va fi mai mare decât entropia stării inițiale numai dacă transformarea este adiabatică. Iar formulări de genul „entropia <a href="/wiki/Univers" title="Univers">Universului</a> crește” sunt fundamental greșite, întrucât Universul, care nu poate fi delimitat precis, nu este un sistem termodinamic. </p> <div class="mw-heading mw-heading2"><h2 id="Principiul_al_treilea_al_termodinamicii">Principiul al treilea al termodinamicii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=17" title="Modifică secțiunea: Principiul al treilea al termodinamicii" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=17" title="Edit section's source code: Principiul al treilea al termodinamicii"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Walther_Nernst.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Walther_Nernst.jpg/220px-Walther_Nernst.jpg" decoding="async" width="220" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Walther_Nernst.jpg/330px-Walther_Nernst.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Walther_Nernst.jpg/440px-Walther_Nernst.jpg 2x" data-file-width="735" data-file-height="1002" /></a><figcaption><a href="/wiki/Walther_Nernst" title="Walther Nernst">Walther Nernst</a> (1864–1941) a enunțat <i>teorema lui Nernst</i> care, în reformularea lui <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>, a devenit principiul al treilea al termodinamicii.</figcaption></figure> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Principiul_al_treilea_al_termodinamicii" title="Principiul al treilea al termodinamicii">Principiul al treilea al termodinamicii</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p>Din principiul al doilea al termodinamicii rezultă că, în transformări în care variabilele de poziție rămân constante, ca și în transformări în care variabilele de forță rămân constante, entropia este o funcție monoton crescătoare de temperatura absolută.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Conform unei teoreme elementare din <a href="/wiki/Analiz%C4%83_matematic%C4%83" class="mw-redirect" title="Analiză matematică">analiza matematică</a>, atunci când, în cursul unei asemenea transformări, temperatura se apropie de <a href="/wiki/Zero_absolut" title="Zero absolut">zero absolut</a> (valoare pe care nu o poate atinge), entropia va tinde către o valoare finită sau către <span class="texhtml"> −∞</span>. Dacă tinde către o valoare finită, aceasta este independentă de celelalte variabile de stare și, întrucât entropia este definită până la o constantă aditivă, ea poate fi aleasă zero prin convenție. Afirmația că acesta este cazul, pentru orice sistem, constituie <i>principiul al treilea al termodinamicii</i>: </p> <dl><dd><i>Când temperatura tinde către zero absolut, entropia oricărui sistem tinde către zero.</i></dd></dl> <p>Rezultă de aici comportarea câtorva mărimi termodinamice atunci când temperatura tinde către zero absolut:<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span style="padding-right:4em" id="f36"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(36\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(36\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ce9831c0f52a6fbcaf594e7cf4f3ec69ae17758" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(36\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{T\to \infty }\ C_{x}\left(T,x\right)=0,\quad \lim _{T\to \infty }{\frac {\partial X\left(T,x\right)}{\partial T}}=0;\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mtext> </mtext> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="1em" /> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>X</mi> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>;</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{T\to \infty }\ C_{x}\left(T,x\right)=0,\quad \lim _{T\to \infty }{\frac {\partial X\left(T,x\right)}{\partial T}}=0;\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c658722a9d1bd71e10b0440a094261442ca3bb49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:42.515ex; height:5.843ex;" alt="{\displaystyle \lim _{T\to \infty }\ C_{x}\left(T,x\right)=0,\quad \lim _{T\to \infty }{\frac {\partial X\left(T,x\right)}{\partial T}}=0;\,}"></span></dd></dl> <dl><dd><span style="padding-right:4em" id="f37"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(37\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mn>37</mn> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(37\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70b602d22296a724b5d87aa0694dfcbabf00f358" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.134ex; height:2.843ex;" alt="{\displaystyle \left(37\right)}"></span></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{T\to \infty }\ C_{X}\left(T,X\right)=0,\quad \lim _{T\to \infty }{\frac {\partial x\left(T,X\right)}{\partial T}}=0.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mtext> </mtext> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>X</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="1em" /> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>X</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{T\to \infty }\ C_{X}\left(T,X\right)=0,\quad \lim _{T\to \infty }{\frac {\partial x\left(T,X\right)}{\partial T}}=0.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92f6dfdeaa903a309f32cffec6a24a968a4e54e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:43.625ex; height:5.843ex;" alt="{\displaystyle \lim _{T\to \infty }\ C_{X}\left(T,X\right)=0,\quad \lim _{T\to \infty }{\frac {\partial x\left(T,X\right)}{\partial T}}=0.\,}"></span></dd></dl> <div style="clear:both"></div> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=18" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=18" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-zerotranz-1">^ <a href="#cite_ref-zerotranz_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-zerotranz_1-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text">Pentru a preîntâmpina neînțelegeri, este util a semnala că, în <a href="/wiki/Entropia_termodinamic%C4%83_(dup%C4%83_Carath%C3%A9odory)" title="Entropia termodinamică (după Carathéodory)">formulări alternative</a> ale teoriei, denumirea <i>principiul zero al termodinamicii</i> se referă la ceea ce în acest articol se numește <i>principiul tranzitivității echilibrului termic</i>.</span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text">Țițeica, p. 16.</span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text">Prin convenție, în acest articol variabilele de forță reprezintă forțele exercitate de lumea externă asupra sistemului, deci lucrul mecanic este cel efectuat de lumea externă asupra sistemului. În convenția opusă semnul forțelor și al lucrului mecanic ar fi inversate.</span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text">Ținând cont de sensul în care se face intergrarea, dacă <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L_{C}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L_{C}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7aa2bcb6ad1a828d77f6556a2f3458c424314fff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.685ex; height:2.009ex;" alt="{\displaystyle \scriptstyle L_{C}\,}"></span> definit de (5) este pozitiv atunci sistemul primește lucru mecanic din exterior, iar dacă <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L_{C}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L_{C}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7aa2bcb6ad1a828d77f6556a2f3458c424314fff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.685ex; height:2.009ex;" alt="{\displaystyle \scriptstyle L_{C}\,}"></span> este negativ, sistemul cedează lucru mecanic .</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text">Țițeica, p. 20</span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text">Țițeica, p. 33.</span> </li> <li id="cite_note-integr-7">^ <a href="#cite_ref-integr_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-integr_7-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text">Țițeica, pp. 24–32.</span> </li> <li id="cite_note-8"><b><a href="#cite_ref-8">^</a></b> <span class="reference-text">În context strict termodinamic, atunci când nu sunt posibile confuzii, se folosește în loc de <i>energie internă</i> abrevierea <i>energie</i>.</span> </li> <li id="cite_note-9"><b><a href="#cite_ref-9">^</a></b> <span class="reference-text">Variațiile infinitezimale sunt indicate prin simbolul <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle d\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>d</mi> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0dbbeb40ab2e40488a2a69bce9a54e00e8727b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.247ex; height:1.676ex;" alt="{\displaystyle \scriptstyle d\,}"></span> pentru mărimi care se referă la o <i>stare</i> (când sunt satisfăcute condițiile <a href="/wiki/Teorema_de_integrabilitate_a_lui_Frobenius" title="Teorema de integrabilitate a lui Frobenius">teoremei de integrabilitate</a>) și prin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \delta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>δ</mi> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \delta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cb794f2f273cd87aeca453a9302a0615f716af4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.129ex; height:1.843ex;" alt="{\displaystyle \scriptstyle \delta \,}"></span> pentru mărimi care se referă la o <i>transformare</i> (când, în general, aceste condiții nu sunt satisfăcute).</span> </li> <li id="cite_note-10"><b><a href="#cite_ref-10">^</a></b> <span class="reference-text">Țițeica, pp. 40–41.</span> </li> <li id="cite_note-11"><b><a href="#cite_ref-11">^</a></b> <span class="reference-text">Țițeica, pp. 41–45.</span> </li> <li id="cite_note-12"><b><a href="#cite_ref-12">^</a></b> <span class="reference-text">Țițeica, pp. 47–48.</span> </li> <li id="cite_note-13"><b><a href="#cite_ref-13">^</a></b> <span class="reference-text">Lucrul mecanic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>L</mi> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2959babeccbbc2c49a3891a9c25dbc59cc014f53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.506ex; height:1.676ex;" alt="{\displaystyle \scriptstyle L\,}"></span> și cantitatea de căldură <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle Q\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>Q</mi> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle Q\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9333c6218b2dc9ae480c6819d70b1a340083b86e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.687ex; height:1.843ex;" alt="{\displaystyle \scriptstyle Q\,}"></span> schimbate în cursul transformării ciclice sunt legate, conform principiului întâi, prin condiția <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L+Q=0.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>L</mi> <mo>+</mo> <mi>Q</mi> <mo>=</mo> <mn>0.</mn> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L+Q=0.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0acbb1133ec29d3baacc032be5e66ac3d8cddf19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.643ex; height:1.843ex;" alt="{\displaystyle \scriptstyle L+Q=0.\,}"></span> Principiul al doilea afirmă că, într-o transformare monotermă, întotdeauna <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle Q\leq 0\left(L\geq 0\right),\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>Q</mi> <mo>≤</mo> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>≥</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle Q\leq 0\left(L\geq 0\right),\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e21e6cdddaab8834fdf3ddfb705803c3961155" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.744ex; height:2.176ex;" alt="{\displaystyle \scriptstyle Q\leq 0\left(L\geq 0\right),\,}"></span> posibilitatea <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle Q=0\left(L=0\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>Q</mi> <mo>=</mo> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>=</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle Q=0\left(L=0\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6fc6799671def4993266e12ba94703d041fac41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.9ex; height:2.176ex;" alt="{\displaystyle \scriptstyle Q=0\left(L=0\right)}"></span> fiind realizată numai dacă transformarea este reversibilă.</span> </li> <li id="cite_note-14"><b><a href="#cite_ref-14">^</a></b> <span class="reference-text">Țițeica, pp. 48–50.</span> </li> <li id="cite_note-15"><b><a href="#cite_ref-15">^</a></b> <span class="reference-text">Dacă lucrul mecanic într-un ciclu Carnot este <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>L</mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfe4a5bd48536c6b84975e7ad963c98331e03c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.964ex; height:1.843ex;" alt="{\displaystyle \scriptstyle L\,,}"></span> conform principiului întâi al termodinamicii vom avea <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L+Q_{1}+Q_{2}=0.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>L</mi> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.</mn> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L+Q_{1}+Q_{2}=0.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/355d52ac07a73ef8f513304c4f8b1f7caef01234" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.884ex; height:2.009ex;" alt="{\displaystyle \scriptstyle L+Q_{1}+Q_{2}=0.\,}"></span> Sistemul funcționează ca mașină termică, deci <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle L<0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>L</mi> <mo><</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle L<0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc2803538e6f375a76a1184dc4ac20d2ade48169" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.607ex; height:1.676ex;" alt="{\displaystyle \scriptstyle L<0\,}"></span> iar <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle Q_{1}+Q_{2}>0:\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> <mo>:</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle Q_{1}+Q_{2}>0:\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9dbd5f1fdbe9d94e026ddb5d553ff098ca5fd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.486ex; height:2.009ex;" alt="{\displaystyle \scriptstyle Q_{1}+Q_{2}>0:\,}"></span> mașina primește căldură la una din surse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \left(Q_{1}>0\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo>(</mo> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left(Q_{1}>0\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc5d3191a4600f336133de36bd71d8b091c70954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.898ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \left(Q_{1}>0\right)\,}"></span> și cedează căldură la cealaltă sursă <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \left(Q_{2}<0\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo>(</mo> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left(Q_{2}<0\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3072756df77190300fd5504065e0e842f1ba609d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.969ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \left(Q_{2}<0\right).}"></span> Randamentul este definit ca raportul dintre lucrul mecanic cedat și cantitatea de căldură primită: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \eta =-{\frac {L}{Q_{1}}}={\frac {Q_{1}+Q_{2}}{Q_{1}}}=1+{\frac {Q_{2}}{Q_{1}}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>η</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \eta =-{\frac {L}{Q_{1}}}={\frac {Q_{1}+Q_{2}}{Q_{1}}}=1+{\frac {Q_{2}}{Q_{1}}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4e7e648b93da66166692e4181bf95b1e887e09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:19.856ex; height:4.176ex;" alt="{\displaystyle \scriptstyle \eta =-{\frac {L}{Q_{1}}}={\frac {Q_{1}+Q_{2}}{Q_{1}}}=1+{\frac {Q_{2}}{Q_{1}}}\,.}"></span></span> </li> <li id="cite_note-16"><b><a href="#cite_ref-16">^</a></b> <span class="reference-text">Țițeica, pp. 50–54 și 60–62.</span> </li> <li id="cite_note-17"><b><a href="#cite_ref-17">^</a></b> <span class="reference-text">Țițeica, pp. 58–59.</span> </li> <li id="cite_note-18"><b><a href="#cite_ref-18">^</a></b> <span class="reference-text">Pentru simplificarea scrierii, în formulele care urmează indicele variabilelor mecanice <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle x=\left(x_{1},...,x_{n}\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>x</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle x=\left(x_{1},...,x_{n}\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da3dc2d07b6a7c01ca59333a59280dd542db75aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.849ex; height:2.176ex;" alt="{\displaystyle \scriptstyle x=\left(x_{1},...,x_{n}\right)\,}"></span> și <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle X=\left(X_{1},...,X_{n}\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>X</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle X=\left(X_{1},...,X_{n}\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b668106dbc934dcd7c1f0795360dee664e19bfcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.15ex; height:2.176ex;" alt="{\displaystyle \scriptstyle X=\left(X_{1},...,X_{n}\right)\,}"></span> este considerat implicit, iar pentru sumări se folosește notația condensată de <a href="/wiki/Produs_scalar" title="Produs scalar">produs scalar</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle X\,x=\sum _{i=1}^{n}X_{i}\,x_{i}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>X</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle X\,x=\sum _{i=1}^{n}X_{i}\,x_{i}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b8640093e80b653e5395b7e3d70b09ae40c29bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.241ex; height:2.176ex;" alt="{\displaystyle \scriptstyle X\,x=\sum _{i=1}^{n}X_{i}\,x_{i}\,.}"></span></span> </li> <li id="cite_note-19"><b><a href="#cite_ref-19">^</a></b> <span class="reference-text">Țițeica, pp. 100-106.</span> </li> <li id="cite_note-20"><b><a href="#cite_ref-20">^</a></b> <span class="reference-text">Efectuând transformarea Legendre doar asupra unora dintre perechile <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \left(X\leftrightarrow x\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo stretchy="false">↔</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left(X\leftrightarrow x\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b9692bba3dac47191220732566a1cf2c4f99ab5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.72ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \left(X\leftrightarrow x\right),}"></span> se pot defini potențiale termodinamice mixte de tipul energie/entalpie sau energie/entalpie liberă. Rar utilizate în termodinamică dar de interes pentru fizica statistică sunt funcția termodinamică a lui Planck <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \Phi \left(T,x\right)=-{\frac {F}{T}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi mathvariant="normal">Φ</mi> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>T</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \Phi \left(T,x\right)=-{\frac {F}{T}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76ed9be350feea63f8eaab2758f5ba220e474cdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.8ex; height:3.176ex;" alt="{\displaystyle \scriptstyle \Phi \left(T,x\right)=-{\frac {F}{T}}\,}"></span> și entropia <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle S=S\left(H,X\right).\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>S</mi> <mo>=</mo> <mi>S</mi> <mrow> <mo>(</mo> <mrow> <mi>H</mi> <mo>,</mo> <mi>X</mi> </mrow> <mo>)</mo> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle S=S\left(H,X\right).\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c847fdc1e01f8b1327a278eea5f6ed4a03c17f82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.839ex; height:2.176ex;" alt="{\displaystyle \scriptstyle S=S\left(H,X\right).\,}"></span></span> </li> <li id="cite_note-21"><b><a href="#cite_ref-21">^</a></b> <span class="reference-text">Țițeica, pp. 185–194.</span> </li> <li id="cite_note-22"><b><a href="#cite_ref-22">^</a></b> <span class="reference-text">Țițeica, pp. 197–199.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=19" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=19" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%C8%98erban_%C8%9Ai%C8%9Beica" title="Șerban Țițeica">Țițeica, Șerban</a>: <i>Termodinamica</i>, Editura Academiei Republicii Socialiste România, București, 1982</li></ul> <div class="mw-heading mw-heading2"><h2 id="Lectură_suplimentară"><span id="Lectur.C4.83_suplimentar.C4.83"></span>Lectură suplimentară</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=20" title="Modifică secțiunea: Lectură suplimentară" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=20" title="Edit section's source code: Lectură suplimentară"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Stoian, Petrescu: <i>Principiile termodinamicii</i>, Editura Tehnică, București, 1986</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Bridgman, P. W. : <i>Nature of Thermodynamics</i>, Peter Smith, 1978, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0844605123" class="internal mw-magiclink-isbn">ISBN 0-8446-0512-3</a>, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780844605128" class="internal mw-magiclink-isbn">ISBN 978-0-8446-0512-8</a>.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi, Enrico</a> : <i>Thermodynamics</i>, Dover Publications, 1956, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780486603612" class="internal mw-magiclink-isbn">ISBN 978-0-486-60361-2</a>. <a rel="nofollow" class="external text" href="http://books.google.com/">Google books</a>.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Guggenheim, E.A. : <i>Thermodynamics: an advanced treatment for chemists and physicists</i>, North-Holland, 1986, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0444869514" class="internal mw-magiclink-isbn">ISBN 0-444-86951-4</a>, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780444869517" class="internal mw-magiclink-isbn">ISBN 978-0-444-86951-7</a>. <a rel="nofollow" class="external text" href="http://www.torrentdownloads.net/search/?search=guggenheim+thermodynamics">Download</a>.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Gyftopoulos, E.P. și Beretta, G.P.: <i>Thermodynamics: Foundations and Applications</i>, Dover, 2005, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0486439321" class="internal mw-magiclink-isbn">ISBN 0-486-43932-1</a>, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780486439327" class="internal mw-magiclink-isbn">ISBN 978-0-486-43932-7</a>. <a rel="nofollow" class="external text" href="http://dl-access.com/location.php?aid=10102020&q=gyftopoulos%20beretta%20thermodynamics">Download</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160305052900/http://dl-access.com/location.php?aid=10102020&q=gyftopoulos%20beretta%20thermodynamics">Arhivat</a> în <time datetime="2016-03-05">5 martie 2016</time>, la <a href="/wiki/Wayback_Machine" class="mw-redirect" title="Wayback Machine">Wayback Machine</a>..</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Zemanski, M.W. și Dittman, R.H. : <i>Heat and Thermodynamics</i>, McGraw-Hill, 1997, <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0070170592" class="internal mw-magiclink-isbn">ISBN 0-07-017059-2</a>. <a rel="nofollow" class="external text" href="http://rapidshare.com/files/118523171/Zemansky.rar">Ebook</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Vezi_și"><span id="Vezi_.C8.99i"></span>Vezi și</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=21" title="Modifică secțiunea: Vezi și" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=21" title="Edit section's source code: Vezi și"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Glosar_de_termodinamic%C4%83" title="Glosar de termodinamică">Glosar de termodinamică</a></li> <li><a href="/wiki/Entropia_termodinamic%C4%83_(dup%C4%83_Carath%C3%A9odory)" title="Entropia termodinamică (după Carathéodory)">Entropia termodinamică (după Carathéodory)</a></li> <li><a href="/wiki/Principiul_al_doilea:_Planck_versus_Carath%C3%A9odory" class="mw-redirect" title="Principiul al doilea: Planck versus Carathéodory">Principiul al doilea: Planck versus Carathéodory</a></li> <li><a href="/wiki/Istoria_termodinamicii" title="Istoria termodinamicii">Istoria termodinamicii</a></li> <li><a href="/wiki/For%C8%9B%C4%83_generalizat%C4%83" title="Forță generalizată">Forță generalizată</a></li> <li><a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">Potențial termodinamic</a></li> <li><a href="/wiki/Ciclu_termodinamic" title="Ciclu termodinamic">Ciclu termodinamic</a></li> <li><a href="/wiki/Pil%C4%83_Karpen" title="Pilă Karpen">Pilă Karpen</a></li> <li><a href="/wiki/Energie_termic%C4%83" title="Energie termică">Energie termică</a></li> <li><a href="/wiki/Termochimie" title="Termochimie">Termochimie</a></li> <li><a href="/wiki/Termodifuziune" title="Termodifuziune">Termodifuziune</a></li> <li><a href="/wiki/Termodinamica_g%C4%83urii_negre" title="Termodinamica găurii negre">Termodinamica găurii negre</a></li> <li><a href="/wiki/Lista_propriet%C4%83%C8%9Bilor_termodinamice" title="Lista proprietăților termodinamice">Lista proprietăților termodinamice</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodinamic%C4%83&veaction=edit&section=22" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodinamic%C4%83&action=edit&section=22" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon">Heat and Thermodynamics</a>, Department of Physics and Astronomy, Georgia State University.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Z.S. Spakovszky: <i><a rel="nofollow" class="external text" href="http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node8.html">The first law of Thermodynamics</a></i>, Massachusetts Institute of Technology.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Z.S. Spakovszky: <i><a rel="nofollow" class="external text" href="http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node30.html">The second law of Thermodynamics</a></i>, Massachusetts Institute of Technology.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a href="/wiki/IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a> Technical Report: <i><a rel="nofollow" class="external text" href="http://www.iupac.org/publications/pac/2001/pdf/7308x1349.pdf">Use of Legendre transforms in chemical thermodynamics</a></i>, Pure and Applied Chemistry, Vol. 73, Nr. 8, pp. 1349–1380, 2001.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://webbook.nist.gov/chemistry/">NIST Chemistry WebBook</a>, National Institute of Standards and Technology.</li></ul> <div class="noprint tright portal" style="border:solid #aaa 1px; margin:0.5em 0 0.5em 0.5em;"> <table style="background:var(--background-color-interactive-subtle, #f9f9f9); color:inherit; font-size:85%; line-height:110%; max-width:175px;"> <tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="Portal icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </td> <td style="padding: 0 0.2em; vertical-align: middle; font-style: italic; font-weight: bold"><b><a href="/wiki/Portal:Fizic%C4%83" title="Portal:Fizică">Portal Fizică </a></b> </td></tr> </tbody></table></div> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://www.math.uni-hamburg.de/home/gunesch/entropy.html">Entropy on the World Wide Web</a>, Universität Hamburg, Fachbereich Mathematik.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://www.eoht.info/page/Thermodynamics+quotes">Thermodynamics quotes</a>, <a rel="nofollow" class="external text" href="http://www.eoht.info/">Encyclopedia of Human Thermodynamics</a>.</li></ul> <table class="navbox" cellspacing="0" style=""> <tbody><tr> <td style="padding:2px;"> <table cellspacing="0" class="nowraplinks collapsible autocollapse" style="width:100%;background:transparent;color:inherit;;"> <tbody><tr> <th style=";" colspan="2" class="navbox-title"><div style="float:left; width:6em;text-align:left;"><div class="noprint plainlinks" style="padding:0; font-size:xx-small; color:var(--color-base, #000); white-space:nowrap; ;"><span style=";;border:none;"><a href="/wiki/Format:Ramurile_fizicii" title="Format:Ramurile fizicii"><span title="Vizualizare format" style=";;border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a href="/wiki/Discu%C8%9Bie_Format:Ramurile_fizicii" title="Discuție Format:Ramurile fizicii"><span title="Discuție format" style=";;border:none;;">d</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Ramurile_fizicii&action=edit"><span title="Acest format se poate modifica. 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href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">Mecanică statistică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Mecanica_fluidelor" title="Mecanica fluidelor">Mecanica fluidelor</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Mecanic%C4%83_cuantic%C4%83" title="Mecanică cuantică">Mecanică cuantică</a>)</div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;"><a href="/wiki/Und%C4%83" title="Undă">Unde</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/C%C3%A2mp_(fizic%C4%83)" title="Câmp (fizică)">Câmpuri</a> </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"><div style="padding:0em 0.25em"> <a href="/wiki/Gravita%C8%9Bie" title="Gravitație">Gravitație</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Teoria_cuantic%C4%83_a_c%C3%A2mpurilor" title="Teoria cuantică a câmpurilor">Teoria cuantică a câmpurilor</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii" title="Teoria relativității">Relativitate</a> (<a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse" title="Teoria relativității restrânse">restrânsă</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_generale" title="Teoria relativității generale">generală</a>)</div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">După specialitate </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-even"><div style="padding:0em 0.25em"> <a href="/w/index.php?title=Accelerator_(tehnic%C4%83)&action=edit&redlink=1" class="new" title="Accelerator (tehnică) — pagină inexistentă">Accelerator</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Acustic%C4%83" title="Acustică">Acustică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Astrofizic%C4%83" title="Astrofizică">Astrofizică</a>  <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Fizic%C4%83_spa%C8%9Bial%C4%83&action=edit&redlink=1" class="new" title="Fizică spațială — pagină inexistentă">Fizică spațială</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Chimie_fizic%C4%83" title="Chimie fizică">Fizică chimică</a>  <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Fizic%C4%83_computa%C8%9Bional%C4%83&action=edit&redlink=1" class="new" title="Fizică computațională — pagină inexistentă">Fizică computațională</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizica_materiei_condensate" title="Fizica materiei condensate">Fizica materiei condensate</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Inginerie_fizic%C4%83" title="Inginerie fizică">Inginerie fizică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizic%C4%83_matematic%C4%83" title="Fizică matematică">Fizică matematică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizic%C4%83_nuclear%C4%83" title="Fizică nucleară">Fizică nucleară</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Optic%C4%83" title="Optică">Optică</a> (<a href="/wiki/Optic%C4%83_geometric%C4%83" title="Optică geometrică">geometrică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Optic%C4%83_cuantic%C4%83" title="Optică cuantică">cuantică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Optic%C4%83_ondulatorie" title="Optică ondulatorie">ondulatorie</a>)  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizica_particulelor_elementare" title="Fizica particulelor elementare">Fizica particulelor elementare</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Plasm%C4%83" title="Plasmă">Fizica plasmei</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizic%C4%83_statistic%C4%83" title="Fizică statistică">Fizică statistică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Spectroscopie" title="Spectroscopie">Spectroscopie</a></div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Combinate cu<br />alte științe </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"><div style="padding:0em 0.25em"> <a href="/wiki/Biofizic%C4%83" title="Biofizică">Biofizică</a> (<a href="/wiki/Bioelectronic%C4%83" title="Bioelectronică">Bioelectronică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Biomagnetism" title="Biomagnetism">Biomagnetism</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Biomecanic%C4%83" title="Biomecanică">Biomecanică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizic%C4%83_medical%C4%83" title="Fizică medicală">medicală</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Neurobiofizic%C4%83" title="Neurobiofizică">Neurofizică</a>)  <span style="font-weight:bold;">·</span>  <a href="/wiki/Chimie_biofizic%C4%83" title="Chimie biofizică">Chimie biofizică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Econofizic%C4%83" title="Econofizică">Econofizică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Chimie_fizic%C4%83" title="Chimie fizică">Chimie fizică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Geofizic%C4%83" title="Geofizică">Geofizică</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Psihofizic%C4%83" title="Psihofizică">Psihofizică</a></div> </td></tr></tbody></table> </td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r16513826">.mw-parser-output .navbox{margin:0 auto 0}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox-abovebelow[style],html.skin-theme-clientpref-night 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colspan="2" class="navbox-title"><div style="float:left; width:6em;text-align:left;"><div class="noprint plainlinks" style="padding:0; font-size:xx-small; color:var(--color-base, #000); white-space:nowrap; ;"><span style=";;border:none;"><a href="/wiki/Format:Fizic%C4%83_statistic%C4%83" title="Format:Fizică statistică"><span title="Vizualizare format" style=";;border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a href="/w/index.php?title=Discu%C8%9Bie_Format:Fizic%C4%83_statistic%C4%83&action=edit&redlink=1" class="new" title="Discuție Format:Fizică statistică — pagină inexistentă"><span title="Discuție format" style=";;border:none;;">d</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Fizic%C4%83_statistic%C4%83&action=edit"><span title="Acest format se poate modifica. Folosiți butonul de previzualizare înainte de a salva." style=";;border:none;;">m</span></a></span></div></div><span class="" style="font-size: 110%;"><a href="/wiki/Fizic%C4%83_statistic%C4%83" title="Fizică statistică">Fizică statistică</a></span> </th></tr> <tr style="height:2px;"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Termodinamică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"> <div style="padding:0em 0.25em"> <a href="/wiki/Calorimetrie" title="Calorimetrie">Calorimetrie</a> • <a href="/wiki/Capacitate_termic%C4%83" title="Capacitate termică">Capacitate termică</a> • <a href="/wiki/C%C4%83ldur%C4%83_latent%C4%83" title="Căldură latentă">Căldură latentă</a> • <a href="/wiki/Ciclu_termodinamic" title="Ciclu termodinamic">Ciclu termodinamic</a> • <a href="/wiki/Ciclul_Carnot" title="Ciclul Carnot">Ciclul Carnot</a> • <a href="/wiki/Ciclul_Clausius-Rankine" title="Ciclul Clausius-Rankine">Ciclul Clausius-Rankine</a> • <a href="/wiki/Coeficient_de_transformare_adiabatic%C4%83" title="Coeficient de transformare adiabatică">Coeficient de transformare adiabatică</a> • <a href="/wiki/Constanta_universal%C4%83_a_gazului_ideal" title="Constanta universală a gazului ideal">Constanta universală a gazului ideal</a> • <a href="/wiki/Echilibru_termodinamic" title="Echilibru termodinamic">Echilibru termodinamic</a> • <a href="/wiki/Energie_intern%C4%83" title="Energie internă">Energie internă</a> • <a href="/wiki/Energie_liber%C4%83" title="Energie liberă">Energie liberă</a> • <a href="/wiki/Entalpie" title="Entalpie">Entalpie</a> • <a href="/wiki/Entalpie_liber%C4%83" title="Entalpie liberă">Entalpie liberă</a> • <a href="/wiki/Entropia_radia%C8%9Biei_electromagnetice" title="Entropia radiației electromagnetice">Entropia radiației electromagnetice</a> • <a href="/wiki/Entropia_termodinamic%C4%83_(dup%C4%83_Carath%C3%A9odory)" title="Entropia termodinamică (după Carathéodory)">Entropia termodinamică (după Carathéodory)</a> • <a href="/wiki/Entropie" title="Entropie">Entropie</a> • <a href="/wiki/Entropie_termodinamic%C4%83" title="Entropie termodinamică">Entropie termodinamică</a> • <a href="/wiki/Evaporare" title="Evaporare">Evaporare</a> • <a href="/wiki/Faz%C4%83_(termodinamic%C4%83)" title="Fază (termodinamică)">Fază (termodinamică)</a> • <a href="/wiki/Fierbere" title="Fierbere">Fierbere</a> • <a href="/wiki/Formula_lui_Planck" title="Formula lui Planck">Formula lui Planck</a> • <a href="/wiki/Frac%C8%9Bie_molar%C4%83" title="Fracție molară">Fracție molară</a> • <a href="/wiki/Gaz_ideal" title="Gaz ideal">Gaz ideal</a> • <a href="/wiki/Gaz_perfect" title="Gaz perfect">Gaz perfect</a> • <a href="/wiki/Gaz_real" title="Gaz real">Gaz real</a> • <a href="/wiki/Legea_Boyle-Mariotte" title="Legea Boyle-Mariotte">Legea Boyle-Mariotte</a> • <a href="/wiki/Legea_Dulong-Petit" title="Legea Dulong-Petit">Legea Dulong-Petit</a> • <a href="/wiki/Legea_lui_Avogadro" title="Legea lui Avogadro">Legea lui Avogadro</a> • <a href="/wiki/Legea_lui_Dalton" title="Legea lui Dalton">Legea lui Dalton</a> • <a href="/wiki/Legea_lui_Henry" title="Legea lui Henry">Legea lui Henry</a> • <a href="/wiki/Legea_lui_Raoult" title="Legea lui Raoult">Legea lui Raoult</a> • <a href="/wiki/Legile_de_deplasare_ale_lui_Wien" title="Legile de deplasare ale lui Wien">Legile de deplasare ale lui Wien</a> • <a href="/wiki/Legile_lui_Kirchhoff_(radia%C8%9Bie)" title="Legile lui Kirchhoff (radiație)">Legile lui Kirchhoff (radiație)</a> • <a href="/wiki/Lema_lui_Carath%C3%A9odory_(termodinamic%C4%83)" title="Lema lui Carathéodory (termodinamică)">Lema lui Carathéodory (termodinamică)</a> • <a href="/wiki/M%C4%83rimi_molare_de_exces" title="Mărimi molare de exces">Mărimi molare de exces</a> • <a href="/wiki/Paradoxul_lui_Gibbs_(termodinamic%C4%83)" title="Paradoxul lui Gibbs (termodinamică)">Paradoxul lui Gibbs (termodinamică)</a> • <a href="/wiki/Perpetuum_mobile" title="Perpetuum mobile">Perpetuum mobile</a> • <a href="/wiki/Poten%C8%9Bial_chimic" title="Potențial chimic">Potențial chimic</a> • <a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">Potențial termodinamic</a> • <a href="/wiki/Presiune_de_vapori" title="Presiune de vapori">Presiune de vapori</a> • <a href="/wiki/Principiile_termodinamicii" title="Principiile termodinamicii">Principiile termodinamicii</a> • <a href="/wiki/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii">Principiul al doilea al termodinamicii</a> • <a href="/wiki/Principiul_al_doilea_al_termodinamicii:_Planck_versus_Carath%C3%A9odory" title="Principiul al doilea al termodinamicii: Planck versus Carathéodory">Principiul al doilea al termodinamicii: Planck versus Carathéodory</a> • <a href="/wiki/Principiul_al_treilea_al_termodinamicii" title="Principiul al treilea al termodinamicii">Principiul al treilea al termodinamicii</a> • <a href="/wiki/Principiul_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii">Principiul întâi al termodinamicii</a> • <a href="/wiki/Principiul_zero_al_termodinamicii" title="Principiul zero al termodinamicii">Principiul zero al termodinamicii</a> • <a href="/wiki/Proces_adiabatic" title="Proces adiabatic">Proces adiabatic</a> • <a href="/wiki/Punct_de_fierbere" title="Punct de fierbere">Punct de fierbere</a> • <a href="/wiki/Punct_de_topire" title="Punct de topire">Punct de topire</a> • <a href="/wiki/Radia%C8%9Bie_termic%C4%83" title="Radiație termică">Radiație termică</a> • <a href="/wiki/Rela%C8%9Bia_lui_Mayer" title="Relația lui Mayer">Relația lui Mayer</a> • <a href="/wiki/Rezonatorul_lui_Planck" title="Rezonatorul lui Planck">Rezonatorul lui Planck</a> • <a href="/wiki/Sistem_termodinamic" title="Sistem termodinamic">Sistem termodinamic</a> • <a href="/wiki/Temperatur%C4%83" title="Temperatură">Temperatură</a> • <a href="/wiki/Termochimie" title="Termochimie">Termochimie</a> • <a class="mw-selflink selflink">Termodinamică</a> • <a href="/wiki/Transformare_Legendre" title="Transformare Legendre">Transformare Legendre</a> • <a href="/wiki/Transformare_termodinamic%C4%83" title="Transformare termodinamică">Transformare termodinamică</a> • <a href="/wiki/Termodinamic%C4%83_chimic%C4%83" title="Termodinamică chimică">Termodinamică chimică</a> •</div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Mecanică statistică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-even"><div style="padding:0em 0.25em"> <a href="/wiki/Entropie_statistic%C4%83" title="Entropie statistică">Entropie statistică</a> • <a href="/wiki/Faz%C4%83_(mecanic%C4%83_statistic%C4%83)" title="Fază (mecanică statistică)">Fază (mecanică statistică)</a> • <a href="/wiki/Grad_de_libertate" title="Grad de libertate">Grad de libertate</a> • <a href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">Mecanică statistică</a> • <a href="/wiki/Operator_statistic" title="Operator statistic">Operator statistic</a></div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Teorie cinetică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"><div style="padding:0em 0.25em"> <a href="/wiki/Agita%C8%9Bie_termic%C4%83" class="mw-redirect" title="Agitație termică">Agitație termică</a> • <a href="/wiki/Constanta_Boltzmann" title="Constanta Boltzmann">Constanta Boltzmann</a> • <a href="/wiki/Demonul_lui_Maxwell" title="Demonul lui Maxwell">Demonul lui Maxwell</a> • <a href="/wiki/Num%C4%83rul_lui_Avogadro" title="Numărul lui Avogadro">Numărul lui Avogadro</a> • <a href="/wiki/Teoria_cinetic%C4%83_a_gazelor" title="Teoria cinetică a gazelor">Teoria cinetică a gazelor</a> • <a href="/wiki/Teoria_haosului" title="Teoria haosului">Teoria haosului</a></div> </td></tr></tbody></table> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16513826"> <p><br /> </p> <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ajutor:Control_de_autoritate" title="Ajutor:Control de autoritate">Control de autoritate</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11933671c">cb11933671c</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb11933671c">(data)</a></span></span></li> <li><span class="nowrap"><a href="/wiki/Integrated_Authority_File" class="mw-redirect" title="Integrated Authority File">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4059827-5">4059827-5</a></span></span></li> <li><span class="nowrap"><a href="/wiki/Library_of_Congress_Control_Number" class="mw-redirect" title="Library of Congress Control Number">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85134783">sh85134783</a></span></span></li> <li><span class="nowrap"><a href="/wiki/National_Library_of_Latvia" class="mw-redirect" title="National Library of Latvia">LNB</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000051835&P_CON_LNG=ENG">000051835</a></span></span></li> <li><span class="nowrap"><a 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