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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Witryna"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Spis treści" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Spis treści</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">przypnij</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ukryj</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Początek</div> </a> </li> <li id="toc-Entalpia_jako_zawartość_ciepła" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Entalpia_jako_zawartość_ciepła"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Entalpia jako zawartość ciepła</span> </div> </a> <button aria-controls="toc-Entalpia_jako_zawartość_ciepła-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>Przełącz podsekcję Entalpia jako zawartość ciepła</span> </button> <ul id="toc-Entalpia_jako_zawartość_ciepła-sublist" class="vector-toc-list"> <li id="toc-Zależność_entalpii_od_temperatury" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zależność_entalpii_od_temperatury"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Zależność entalpii od temperatury</span> </div> </a> <ul id="toc-Zależność_entalpii_od_temperatury-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Entalpia_standardowa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Entalpia_standardowa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Entalpia standardowa</span> </div> </a> <ul id="toc-Entalpia_standardowa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Entalpia_przemian" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Entalpia_przemian"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Entalpia przemian</span> </div> </a> <ul id="toc-Entalpia_przemian-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inne" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Inne"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Inne</span> </div> </a> <ul id="toc-Inne-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Entalpia_jako_transformata_Legendre’a" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Entalpia_jako_transformata_Legendre’a"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Entalpia jako transformata Legendre’a</span> </div> </a> <ul id="toc-Entalpia_jako_transformata_Legendre’a-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zobacz_też" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zobacz_też"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Zobacz też</span> </div> </a> <ul id="toc-Zobacz_też-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uwagi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uwagi"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Uwagi</span> </div> </a> <ul id="toc-Uwagi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Przypisy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Przypisy"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Przypisy</span> </div> </a> <ul id="toc-Przypisy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-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="Spis treści" 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="Przełącz stan spisu treści" > <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">Przełącz stan spisu treści</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">Entalpia</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="Przejdź do artykułu w innym języku. Treść dostępna w 69 językach" > <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-69" 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">69 języków</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/Entalpie" title="Entalpie – afrikaans" lang="af" hreflang="af" data-title="Entalpie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D8%AA%D9%88%D9%89_%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A" title="محتوى حراري – arabski" lang="ar" hreflang="ar" data-title="محتوى حراري" data-language-autonym="العربية" data-language-local-name="arabski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Entalp%C3%ADa" title="Entalpía – asturyjski" lang="ast" hreflang="ast" data-title="Entalpía" data-language-autonym="Asturianu" data-language-local-name="asturyjski" 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/Entalpiya" title="Entalpiya – azerbejdżański" lang="az" hreflang="az" data-title="Entalpiya" data-language-autonym="Azərbaycanca" data-language-local-name="azerbejdżański" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AD%E0%A7%8D%E0%A6%AF%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0%E0%A7%80%E0%A6%A3_%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%AC" title="অভ্যন্তরীণ তাপগতীয় বিভব – bengalski" lang="bn" hreflang="bn" data-title="অভ্যন্তরীণ তাপগতীয় বিভব" data-language-autonym="বাংলা" data-language-local-name="bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Enthalpy" title="Enthalpy – minnański" lang="nan" hreflang="nan" data-title="Enthalpy" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnański" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D1%96%D1%8F" title="Энтальпія – białoruski" lang="be" hreflang="be" data-title="Энтальпія" data-language-autonym="Беларуская" data-language-local-name="białoruski" 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%AD%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D1%96%D1%8F" title="Энтальпія – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Энтальпія" 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-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Entalpiya" title="Entalpiya – Central Bikol" lang="bcl" hreflang="bcl" data-title="Entalpiya" 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-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D0%B0%D0%BB%D0%BF%D0%B8%D1%8F" title="Енталпия – bułgarski" lang="bg" hreflang="bg" data-title="Енталпия" data-language-autonym="Български" data-language-local-name="bułgarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Entalpija" title="Entalpija – bośniacki" lang="bs" hreflang="bs" data-title="Entalpija" data-language-autonym="Bosanski" data-language-local-name="bośniacki" 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/Entalpia" title="Entalpia – kataloński" lang="ca" hreflang="ca" data-title="Entalpia" data-language-autonym="Català" data-language-local-name="kataloński" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Entalpie" title="Entalpie – czeski" lang="cs" hreflang="cs" data-title="Entalpie" data-language-autonym="Čeština" data-language-local-name="czeski" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Entalpi" title="Entalpi – duński" lang="da" hreflang="da" data-title="Entalpi" data-language-autonym="Dansk" data-language-local-name="duński" 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/Enthalpie" title="Enthalpie – niemiecki" lang="de" hreflang="de" data-title="Enthalpie" data-language-autonym="Deutsch" data-language-local-name="niemiecki" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Entalpia" title="Entalpia – estoński" lang="et" hreflang="et" data-title="Entalpia" data-language-autonym="Eesti" data-language-local-name="estoński" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BD%CE%B8%CE%B1%CE%BB%CF%80%CE%AF%CE%B1" title="Ενθαλπία – grecki" lang="el" hreflang="el" data-title="Ενθαλπία" data-language-autonym="Ελληνικά" data-language-local-name="grecki" 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/Enthalpy" title="Enthalpy – angielski" lang="en" hreflang="en" data-title="Enthalpy" data-language-autonym="English" data-language-local-name="angielski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Entalp%C3%ADa" title="Entalpía – hiszpański" lang="es" hreflang="es" data-title="Entalpía" data-language-autonym="Español" data-language-local-name="hiszpański" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Entalpio" title="Entalpio – esperanto" lang="eo" hreflang="eo" data-title="Entalpio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Entalpia" title="Entalpia – baskijski" lang="eu" hreflang="eu" data-title="Entalpia" data-language-autonym="Euskara" data-language-local-name="baskijski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%86%D8%AA%D8%A7%D9%84%D9%BE%DB%8C" title="آنتالپی – perski" lang="fa" hreflang="fa" data-title="آنتالپی" data-language-autonym="فارسی" data-language-local-name="perski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Enthalpie" title="Enthalpie – francuski" lang="fr" hreflang="fr" data-title="Enthalpie" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Eantalpacht" title="Eantalpacht – irlandzki" lang="ga" hreflang="ga" data-title="Eantalpacht" data-language-autonym="Gaeilge" data-language-local-name="irlandzki" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Entalp%C3%ADa" title="Entalpía – galicyjski" lang="gl" hreflang="gl" data-title="Entalpía" data-language-autonym="Galego" data-language-local-name="galicyjski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%94%ED%83%88%ED%94%BC" title="엔탈피 – koreański" lang="ko" hreflang="ko" data-title="엔탈피" data-language-autonym="한국어" data-language-local-name="koreański" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%B6%D5%BF%D5%A1%D5%AC%D5%BA%D5%AB%D5%A1" title="Էնտալպիա – ormiański" lang="hy" hreflang="hy" data-title="Էնտալպիա" data-language-autonym="Հայերեն" data-language-local-name="ormiański" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3_%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE" title="पूर्ण ऊष्मा – hindi" lang="hi" hreflang="hi" data-title="पूर्ण ऊष्मा" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Entalpija" title="Entalpija – chorwacki" lang="hr" hreflang="hr" data-title="Entalpija" data-language-autonym="Hrvatski" data-language-local-name="chorwacki" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Entalpi" title="Entalpi – indonezyjski" lang="id" hreflang="id" data-title="Entalpi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezyjski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Entalpia" title="Entalpia – włoski" lang="it" hreflang="it" data-title="Entalpia" data-language-autonym="Italiano" data-language-local-name="włoski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A0%D7%AA%D7%9C%D7%A4%D7%99%D7%94" title="אנתלפיה – hebrajski" lang="he" hreflang="he" data-title="אנתלפיה" data-language-autonym="עברית" data-language-local-name="hebrajski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D0%B8%D1%8F" title="Энтальпия – kazachski" lang="kk" hreflang="kk" data-title="Энтальпия" data-language-autonym="Қазақша" data-language-local-name="kazachski" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Antalfi" title="Antalfi – kreolski haitański" lang="ht" hreflang="ht" data-title="Antalfi" data-language-autonym="Kreyòl ayisyen" data-language-local-name="kreolski haitański" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Entalpija" title="Entalpija – łotewski" lang="lv" hreflang="lv" data-title="Entalpija" data-language-autonym="Latviešu" data-language-local-name="łotewski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Entalpija" title="Entalpija – litewski" lang="lt" hreflang="lt" data-title="Entalpija" data-language-autonym="Lietuvių" data-language-local-name="litewski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Entalpia" title="Entalpia – węgierski" lang="hu" hreflang="hu" data-title="Entalpia" data-language-autonym="Magyar" data-language-local-name="węgierski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D0%B0%D0%BB%D0%BF%D0%B8%D1%98%D0%B0" title="Енталпија – macedoński" lang="mk" hreflang="mk" data-title="Енталпија" data-language-autonym="Македонски" data-language-local-name="macedoński" 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%8E%E0%B5%BB%E0%B4%A4%E0%B4%BE%E0%B5%BD%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B4%BF" title="എൻതാൽപ്പി – malajalam" lang="ml" hreflang="ml" data-title="എൻതാൽപ്പി" data-language-autonym="മലയാളം" data-language-local-name="malajalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Entalpi" title="Entalpi – malajski" lang="ms" hreflang="ms" data-title="Entalpi" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D0%B8" title="Энтальпи – mongolski" lang="mn" hreflang="mn" data-title="Энтальпи" data-language-autonym="Монгол" data-language-local-name="mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%84%E1%80%BA%E1%80%9E%E1%80%AC%E1%80%95%E1%80%AE" title="အင်သာပီ – birmański" lang="my" hreflang="my" data-title="အင်သာပီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmański" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Enthalpie" title="Enthalpie – niderlandzki" lang="nl" hreflang="nl" data-title="Enthalpie" data-language-autonym="Nederlands" data-language-local-name="niderlandzki" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A8%E3%83%B3%E3%82%BF%E3%83%AB%E3%83%94%E3%83%BC" title="エンタルピー – japoński" lang="ja" hreflang="ja" data-title="エンタルピー" data-language-autonym="日本語" data-language-local-name="japoński" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Entalpi" title="Entalpi – norweski (bokmål)" lang="nb" hreflang="nb" data-title="Entalpi" data-language-autonym="Norsk bokmål" data-language-local-name="norweski (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Entalpi" title="Entalpi – norweski (nynorsk)" lang="nn" hreflang="nn" data-title="Entalpi" data-language-autonym="Norsk nynorsk" data-language-local-name="norweski (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Entalpiya" title="Entalpiya – uzbecki" lang="uz" hreflang="uz" data-title="Entalpiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Entalpia" title="Entalpia – portugalski" lang="pt" hreflang="pt" data-title="Entalpia" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Entalpie" title="Entalpie – rumuński" lang="ro" hreflang="ro" data-title="Entalpie" data-language-autonym="Română" data-language-local-name="rumuński" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D0%B8%D1%8F" title="Энтальпия – rosyjski" lang="ru" hreflang="ru" data-title="Энтальпия" data-language-autonym="Русский" data-language-local-name="rosyjski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%AE%E1%B1%B1%E1%B1%9B%E1%B1%B7%E1%B1%9F%E1%B1%9E%E1%B1%AF%E1%B1%A4" title="ᱮᱱᱛᱷᱟᱞᱯᱤ – santali" lang="sat" hreflang="sat" data-title="ᱮᱱᱛᱷᱟᱞᱯᱤ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Enthalpy" title="Enthalpy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Enthalpy" 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/Entalpia" title="Entalpia – słowacki" lang="sk" hreflang="sk" data-title="Entalpia" data-language-autonym="Slovenčina" data-language-local-name="słowacki" 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/Entalpija" title="Entalpija – słoweński" lang="sl" hreflang="sl" data-title="Entalpija" data-language-autonym="Slovenščina" data-language-local-name="słoweński" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%8E%D9%86%D8%AA%D8%A7%D9%84%D9%BE%DB%8C" title="ئێنتالپی – sorani" lang="ckb" hreflang="ckb" data-title="ئێنتالپی" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D0%B0%D0%BB%D0%BF%D0%B8%D1%98%D0%B0" title="Енталпија – serbski" lang="sr" hreflang="sr" data-title="Енталпија" data-language-autonym="Српски / srpski" data-language-local-name="serbski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Entalpija" title="Entalpija – serbsko-chorwacki" lang="sh" hreflang="sh" data-title="Entalpija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbsko-chorwacki" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Entalpia" title="Entalpia – fiński" lang="fi" hreflang="fi" data-title="Entalpia" data-language-autonym="Suomi" data-language-local-name="fiński" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Entalpi" title="Entalpi – szwedzki" lang="sv" hreflang="sv" data-title="Entalpi" data-language-autonym="Svenska" data-language-local-name="szwedzki" class="interlanguage-link-target"><span>Svenska</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%85%E0%AE%9F%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%AE%E0%AF%8D" title="வெப்ப அடக்கம் – tamilski" lang="ta" hreflang="ta" data-title="வெப்ப அடக்கம்" data-language-autonym="தமிழ்" data-language-local-name="tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%AD%E0%B8%99%E0%B8%97%E0%B8%B2%E0%B8%A5%E0%B8%9B%E0%B8%B5" title="เอนทาลปี – tajski" lang="th" hreflang="th" data-title="เอนทาลปี" data-language-autonym="ไทย" data-language-local-name="tajski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Entalpi" title="Entalpi – turecki" lang="tr" hreflang="tr" data-title="Entalpi" data-language-autonym="Türkçe" data-language-local-name="turecki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BF%D1%96%D1%8F" title="Ентальпія – ukraiński" lang="uk" hreflang="uk" data-title="Ентальпія" data-language-autonym="Українська" data-language-local-name="ukraiński" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Entalp%C3%ACa" title="Entalpìa – wenecki" lang="vec" hreflang="vec" data-title="Entalpìa" data-language-autonym="Vèneto" data-language-local-name="wenecki" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Enthalpy" title="Enthalpy – wietnamski" lang="vi" hreflang="vi" data-title="Enthalpy" data-language-autonym="Tiếng Việt" data-language-local-name="wietnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%84%93" title="焓 – chiński klasyczny" lang="lzh" hreflang="lzh" data-title="焓" data-language-autonym="文言" data-language-local-name="chiński klasyczny" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%84%93" title="焓 – wu" lang="wuu" hreflang="wuu" data-title="焓" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%84%93" title="焓 – kantoński" lang="yue" hreflang="yue" data-title="焓" data-language-autonym="粵語" data-language-local-name="kantoński" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%84%93" title="焓 – chiński" lang="zh" hreflang="zh" data-title="焓" data-language-autonym="中文" data-language-local-name="chiński" class="interlanguage-link-target"><span>中文</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/Q161064#sitelinks-wikipedia" title="Edytuj linki pomiędzy wersjami językowymi" class="wbc-editpage">Edytuj linki</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="Przestrzenie nazw"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Entalpia" title="Zobacz stronę treści [c]" accesskey="c"><span>Artykuł</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Dyskusja:Entalpia" rel="discussion" title="Dyskusja o zawartości tej strony [t]" accesskey="t"><span>Dyskusja</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Zmień wariant języka" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled 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href="/w/index.php?title=Entalpia&action=edit" title="Edycja kodu źródłowego strony [e]" accesskey="e"><span>Edytuj kod źródłowy</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Entalpia&action=history" title="Starsze wersje tej strony [h]" accesskey="h"><span>Wyświetl historię</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Narzędzia dla stron"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Narzędzia" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Narzędzia</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Narzędzia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">przypnij</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ukryj</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Więcej opcji" > <div class="vector-menu-heading"> Działania </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Entalpia"><span>Czytaj</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Entalpia&veaction=edit" title="Edytuj tę stronę [v]" accesskey="v"><span>Edytuj</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Entalpia&action=edit" title="Edycja kodu źródłowego strony [e]" accesskey="e"><span>Edytuj kod źródłowy</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Entalpia&action=history"><span>Wyświetl historię</span></a></li> </ul> </div> </div> <div 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Wikipedii, wolnej encyklopedii</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="pl" dir="ltr"><p><b>Entalpia</b> (zawartość ciepła) – w <a href="/wiki/Termodynamika" title="Termodynamika">termodynamice</a> <a href="/wiki/Wielko%C5%9B%C4%87_fizyczna" title="Wielkość fizyczna">wielkość fizyczna</a> będąca <a href="/wiki/Funkcja_stanu" title="Funkcja stanu">funkcją stanu</a> mająca wymiar <a href="/wiki/Energia_(fizyka)" class="mw-redirect" title="Energia (fizyka)">energii</a>, będąca też <a href="/wiki/Potencja%C5%82y_termodynamiczne" title="Potencjały termodynamiczne">potencjałem termodynamicznym</a><sup id="cite_ref-epwn_1-0" class="reference"><a href="#cite_note-epwn-1">[1]</a></sup>, oznaczana przez <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,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef601e1519093ba6c2944b945882c119f990e704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.71ex; height:2.509ex;" alt="{\displaystyle H,}"></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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[a]</a></sup>,<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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> lub <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 \chi ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca6e76392f8c9247f2413a0b8dd44a33e31ac123" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.102ex; height:2.009ex;" alt="{\displaystyle \chi ,}"></span> którą definiuje zależność: </p> <dl><dd><dl><dd><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+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab5d07861627786ff90e0d882a95bd4b36d2c710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.742ex; height:2.509ex;" alt="{\displaystyle H=U+pV}"></span></dd></dl></dd></dl> <p>gdzie: </p> <ul><li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" 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 H}"></span> – entalpia układu,</li> <li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> – <a href="/wiki/Energia_wewn%C4%99trzna" title="Energia wewnętrzna">energia wewnętrzna</a> układu,</li> <li><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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> – <a href="/wiki/Ci%C5%9Bnienie" title="Ciśnienie">ciśnienie</a>,</li> <li><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> – <a href="/wiki/Obj%C4%99to%C5%9B%C4%87" title="Objętość">objętość</a>.</li></ul> <p>Z powyższego wzoru wynika sens fizyczny entalpii. Entalpia jest równa sumie: </p> <ul><li><a href="/wiki/Energia_wewn%C4%99trzna" title="Energia wewnętrzna">energii wewnętrznej</a>, czyli energii, jaka jest potrzebna do utworzenia układu, gdy jest on tworzony w otoczeniu próżni,</li> <li>iloczynu <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 pV,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>V</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pV,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e590556c16e84b39809b447b8ed233b5466218d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:3.693ex; height:2.509ex;" alt="{\displaystyle pV,}"></span> który jest równy <a href="/wiki/Praca_(fizyka)" title="Praca (fizyka)">pracy</a>, jaką należy wykonać nad otoczeniem, by w danych warunkach uzyskać miejsce na układ<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[3]</a></sup>.</li></ul> <p>Wszystkie wielkości definiujące entalpię są parametrami stanu, dlatego entalpia też jest funkcją stanu. </p><p>Nieskończenie małą zmianę entalpii określa wzór: </p> <dl><dd><dl><dd><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 dH=dU+pdV+Vdp.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>d</mi> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>d</mi> <mi>V</mi> <mo>+</mo> <mi>V</mi> <mi>d</mi> <mi>p</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=dU+pdV+Vdp.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47ce22a76039d45a2fea93c32bd8ad55b12f7dfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.049ex; height:2.509ex;" alt="{\displaystyle dH=dU+pdV+Vdp.}"></span></dd></dl></dd></dl> <p>Dla procesów, zachodzących dla <a href="/wiki/Cia%C5%82o_sta%C5%82e" title="Ciało stałe">ciał stałych</a> i <a href="/wiki/Ciecz" title="Ciecz">cieczy</a> pod niezbyt dużym ciśnieniem składniki <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 pdV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pdV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad06b0f1a22b81644d748a11a6297b5a764fac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:4.262ex; height:2.509ex;" alt="{\displaystyle pdV}"></span> i <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 Vdp}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mi>d</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Vdp}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fe8f7713f6cbd3c4770bb9168345247a55e41a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.173ex; height:2.509ex;" alt="{\displaystyle Vdp}"></span> są małe w porównaniu do <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fad9083e6f626fcc9e4217e8fd3d751e1126da9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.998ex; height:2.176ex;" alt="{\displaystyle dU}"></span> i mogą być pominięte, wówczas zmiana entalpii jest równa zmianie energii wewnętrznej: </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Entalpia_jako_zawartość_ciepła"><span id="Entalpia_jako_zawarto.C5.9B.C4.87_ciep.C5.82a"></span>Entalpia jako zawartość ciepła</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=1" title="Edytuj sekcję: Entalpia jako zawartość ciepła" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=1" title="Edytuj kod źródłowy sekcji: Entalpia jako zawartość ciepła"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Z definicji entalpii i <a href="/wiki/Pierwsza_zasada_termodynamiki" title="Pierwsza zasada termodynamiki">I zasady termodynamiki</a>: </p> <dl><dd><dl><dd><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 dH=dQ+dW_{e}+Vdp.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>d</mi> <mi>Q</mi> <mo>+</mo> <mi>d</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>+</mo> <mi>V</mi> <mi>d</mi> <mi>p</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=dQ+dW_{e}+Vdp.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/123ec395ac82248cfdafc3826a722ea46f90bd18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.34ex; height:2.509ex;" alt="{\displaystyle dH=dQ+dW_{e}+Vdp.}"></span></dd></dl></dd></dl> <p>Gdy układ wykonuje wyłącznie pracę objętościową oraz gdy ciśnienie jest stałe, wówczas zmiana entalpii jest równa ciepłu dostarczonemu do układu: </p> <dl><dd><dl><dd><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 dH=dQ.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>d</mi> <mi>Q</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=dQ.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/218c3e9a146b38cfbbc5f54d5da30bc498da04f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.079ex; height:2.509ex;" alt="{\displaystyle dH=dQ.}"></span></dd></dl></dd></dl> <p>Z tego, że entalpia jest funkcją stanu oraz powyższego wynika, że dla dowolnego procesu, w którym ciśnienie początkowe jest równe ciśnieniu końcowemu, ilość ciepła dostarczonego do układu jest równa zmianie entalpii: </p> <dl><dd><dl><dd><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=\Delta H.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta Q=\Delta H.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/734155338917fe493df6b9c0ef6433da9a285697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.519ex; height:2.509ex;" alt="{\displaystyle \Delta Q=\Delta H.}"></span></dd></dl></dd></dl> <p>Przemiany przebiegające przy stałym ciśnieniu są bardzo często spotykane w praktyce (np. <a href="/wiki/Kocio%C5%82_parowy" title="Kocioł parowy">kocioł parowy</a>, przemiany fazowe, <a href="/wiki/Reakcja_chemiczna" title="Reakcja chemiczna">reakcje chemiczne</a>), stąd entalpia jest bardzo często wykorzystywaną w obliczeniach funkcją stanu. </p><p>W termodynamice technicznej przydatne są wielkości termodynamiczne właściwe (odniesione do jednostki masy rozpatrywanego czynnika termodynamicznego). Wprowadza się więc entalpię właściwą: </p> <dl><dd><dl><dd><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={\frac {H}{m}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>H</mi> <mi>m</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h={\frac {H}{m}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9de1aca31fee6cf7e99642fb5fc360106175bf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.984ex; height:5.176ex;" alt="{\displaystyle h={\frac {H}{m}}.}"></span></dd></dl></dd></dl> <p>Dla entalpii właściwej można zapisać wzór definicyjny w następującej postaci: </p> <dl><dd><dl><dd><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+pv,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>=</mo> <mi>u</mi> <mo>+</mo> <mi>p</mi> <mi>v</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h=u+pv,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e58e08ea88904b63fa7279571852e55e0c522df4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.551ex; height:2.509ex;" alt="{\displaystyle h=u+pv,}"></span></dd></dl></dd></dl> <p>gdzie: </p> <ul><li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> – energia wewnętrzna właściwa,</li> <li><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/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> – <a href="/wiki/Obj%C4%99to%C5%9B%C4%87_w%C5%82a%C5%9Bciwa" title="Objętość właściwa">objętość właściwa</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Zależność_entalpii_od_temperatury"><span id="Zale.C5.BCno.C5.9B.C4.87_entalpii_od_temperatury"></span>Zależność entalpii od temperatury</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=2" title="Edytuj sekcję: Zależność entalpii od temperatury" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=2" title="Edytuj kod źródłowy sekcji: Zależność entalpii od temperatury"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Entalpia substancji zależy od jej temperatury. Przy stałym ciśnieniu <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_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc37470431fbf62081b69ba870ad3f855178361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.721ex; height:2.843ex;" alt="{\displaystyle C_{p}}"></span> jest nazywana <a href="/wiki/Pojemno%C5%9B%C4%87_cieplna" title="Pojemność cieplna">pojemnością cieplną</a> </p> <dl><dd><dl><dd><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 dH=C_{p}dT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>d</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=C_{p}dT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37fc8fa980f61f9eebd4efcf1e54d77176c887a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.951ex; height:2.843ex;" alt="{\displaystyle dH=C_{p}dT}"></span></dd></dl></dd></dl> <p>lub </p> <dl><dd><dl><dd><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 dH=c_{p}mdT,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>m</mi> <mi>d</mi> <mi>T</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=c_{p}mdT,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5ab33d4300fd2f929049bf8da714aef86f3a2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.983ex; height:2.843ex;" alt="{\displaystyle dH=c_{p}mdT,}"></span></dd></dl></dd></dl> <p>gdzie: <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_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span> – <a href="/wiki/Ciep%C5%82o_w%C5%82a%C5%9Bciwe" title="Ciepło właściwe">ciepło właściwe</a> przy stałym ciśnieniu, <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> – masa substancji. </p> <div class="mw-heading mw-heading2"><h2 id="Entalpia_standardowa">Entalpia standardowa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=3" title="Edytuj sekcję: Entalpia standardowa" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=3" title="Edytuj kod źródłowy sekcji: Entalpia standardowa"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Entalpia standardowa to entalpia danej substancji w jej czystej postaci w <a href="/wiki/Warunki_standardowe" title="Warunki standardowe">ciśnieniu standardowym</a> (tj. 1 bar) w danej temperaturze<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[4]</a></sup>. Zmianę entalpii standardowej oznacza się symbolem <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 H^{\Theta }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Θ</mi> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H^{\Theta }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ad70fa27ef501f2c7d4ba4a58f071bded3a79da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.197ex; height:2.676ex;" alt="{\displaystyle \Delta H^{\Theta }.}"></span> Oznaczając entalpie, jak i entalpie standardowe, wprowadza się do symbolu entalpii oznaczenie przemiany <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 _{przem}H,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>z</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mi>H</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{przem}H,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1edeb4da6570dbf1bb1e5d0ab891501bdf8e636" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.425ex; height:2.843ex;" alt="{\displaystyle \Delta _{przem}H,}"></span> gdzie <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 _{przem}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>z</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{przem}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2ec2add0ef132256ee8e1e977f8632704f14263" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.063ex; width:4.842ex; height:1.676ex;" alt="{\displaystyle _{przem}}"></span> oznacza przemianę. Stosowany jest też zapis <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 H_{przem}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>z</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H_{przem}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c48503d93da0965a5ecf94ea4516705181e3dc17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.293ex; height:2.843ex;" alt="{\displaystyle \Delta H_{przem}.}"></span> </p><p>Entalpie standardowe tworzenia 1 mola (zobacz <a href="/wiki/Standardowa_entalpia_tworzenia_zwi%C4%85zku_chemicznego" title="Standardowa entalpia tworzenia związku chemicznego">Standardowe molowe ciepło tworzenia</a>) substancji są podawane w tabelach <a href="/wiki/W%C5%82a%C5%9Bciwo%C5%9B%C4%87_fizyczna" title="Właściwość fizyczna">własności fizycznych</a> substancji. Przyjmuje się, że pierwiastki w ich podstawowym stanie w warunkach standardowych mają entalpię równą 0. </p><p>Przykłady entalpii standardowych tworzenia: </p> <ul><li><a href="/wiki/Wod%C3%B3r" title="Wodór">wodór</a> cząsteczkowy (<span style="white-space:nowrap">H<span style="display:inline-block; margin-bottom:-0.3em; vertical-align:-0.3em; line-height:1.0em; font-size:80%; text-align:left;"><br />2</span></span>): 0</li> <li>wodór atomowy (H): +217,97 kJ/mol</li> <li><a href="/wiki/Tlen" title="Tlen">tlen</a> (<span style="white-space:nowrap">O<span style="display:inline-block; margin-bottom:-0.3em; vertical-align:-0.3em; line-height:1.0em; font-size:80%; text-align:left;"><br />2</span></span>): 0</li> <li><a href="/wiki/Woda" title="Woda">woda</a> ciekła (<span style="white-space:nowrap">H<span style="display:inline-block; margin-bottom:-0.3em; vertical-align:-0.3em; line-height:1.0em; font-size:80%; text-align:left;"><br />2</span>O</span>): −285,83 kJ/mol</li> <li><a href="/wiki/Para_wodna" title="Para wodna">para wodna</a>: −241,82 kJ/mol</li></ul> <div class="mw-heading mw-heading2"><h2 id="Entalpia_przemian">Entalpia przemian</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=4" title="Edytuj sekcję: Entalpia przemian" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=4" title="Edytuj kod źródłowy sekcji: Entalpia przemian"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption>Wybrane oznaczenia entalpii przemian </caption> <tbody><tr> <th>Przemiana </th> <th>Opis </th> <th>Oznaczenie </th></tr> <tr> <td><a href="/wiki/Przemiana_fazowa" title="Przemiana fazowa">Przemiana fazowa</a> </td> <td>faza a → faza b </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 \Delta _{p.f.}H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>.</mo> <mi>f</mi> <mo>.</mo> </mrow> </msub> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{p.f.}H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08bd56e60a4b5dbfbe24f4f19b16b68056854d4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.878ex; height:2.843ex;" alt="{\displaystyle \Delta _{p.f.}H}"></span> </td></tr> <tr> <td><a href="/wiki/Rozpuszczanie" title="Rozpuszczanie">Rozpuszczanie</a> </td> <td>substancja rozpuszczana → roztwór </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 \Delta _{roz}H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>o</mi> <mi>z</mi> </mrow> </msub> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{roz}H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37ad2b5cf869cbeb0096de0fd2848eb1af49274f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.54ex; height:2.509ex;" alt="{\displaystyle \Delta _{roz}H}"></span> </td></tr> <tr> <td><a href="/wiki/Reakcja_chemiczna" title="Reakcja chemiczna">Reakcja chemiczna</a> </td> <td>substraty → produkty </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 \Delta _{r}H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{r}H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfbd0bba20a57655ff78139cacbd3dc0d4f01ce3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.973ex; height:2.509ex;" alt="{\displaystyle \Delta _{r}H}"></span> </td></tr> <tr> <td>Tworzenie (synteza związku z pierwiastków) </td> <td>pierwiastki → związek chemiczny </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 \Delta _{tw}H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>w</mi> </mrow> </msub> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{tw}H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8e629dec2cb35b001d576fc85180a6147074469" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.002ex; height:2.509ex;" alt="{\displaystyle \Delta _{tw}H}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Inne">Inne</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=5" title="Edytuj sekcję: Inne" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=5" title="Edytuj kod źródłowy sekcji: Inne"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Z definicji oraz wyrażenia na energię wewnętrzną dla procesów odwracalnych: </p> <dl><dd><dl><dd><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=TS-pV+\sum _{i=1}^{k}{\mu _{i}N_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mi>V</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>k</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=TS-pV+\sum _{i=1}^{k}{\mu _{i}N_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e71ade896aa33b247c18a0bd4fa77131addd82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.263ex; height:7.343ex;" alt="{\displaystyle U=TS-pV+\sum _{i=1}^{k}{\mu _{i}N_{i}}}"></span></dd></dl></dd></dl> <p>wynika: </p> <dl><dd><dl><dd><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 dH=TdS+Vdp+\sum _{i=1}^{k}{\mu _{i}dN_{i}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>+</mo> <mi>V</mi> <mi>d</mi> <mi>p</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>k</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>d</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=TdS+Vdp+\sum _{i=1}^{k}{\mu _{i}dN_{i}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1574f142e8339702ce330ccc5aef9b1bfe1bfee6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.055ex; height:7.343ex;" alt="{\displaystyle dH=TdS+Vdp+\sum _{i=1}^{k}{\mu _{i}dN_{i}}.}"></span></dd></dl></dd></dl> <p>Z zależności tej wynika: </p> <dl><dd><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=\left({\frac {\partial H}{\partial S}}\right)_{p,N_{1},\dots ,N_{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <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>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=\left({\frac {\partial H}{\partial S}}\right)_{p,N_{1},\dots ,N_{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bae1d570a22105bd2862195cc59f5e6dae99bb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.061ex; height:6.676ex;" alt="{\displaystyle T=\left({\frac {\partial H}{\partial S}}\right)_{p,N_{1},\dots ,N_{k}}}"></span> – związek z temperaturą,</dd> <dd><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=\left({\frac {\partial H}{\partial p}}\right)_{S,N_{1},\dots ,N_{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <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>p</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=\left({\frac {\partial H}{\partial p}}\right)_{S,N_{1},\dots ,N_{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99f25b01577ac176e88eaaa979fc507e712dfc46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.445ex; height:6.676ex;" alt="{\displaystyle V=\left({\frac {\partial H}{\partial p}}\right)_{S,N_{1},\dots ,N_{k}}}"></span> – związek z objętością,</dd> <dd><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 \mu _{i}=\left({\frac {\partial H}{\partial N_{i}}}\right)_{S,p,N_{1},\dots ,N_{i-1},N_{i+1},\dots ,N_{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</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> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}=\left({\frac {\partial H}{\partial N_{i}}}\right)_{S,p,N_{1},\dots ,N_{i-1},N_{i+1},\dots ,N_{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bd13999ee6191ac996f7a1619954f9d4d9eb764" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:34.343ex; height:6.676ex;" alt="{\displaystyle \mu _{i}=\left({\frac {\partial H}{\partial N_{i}}}\right)_{S,p,N_{1},\dots ,N_{i-1},N_{i+1},\dots ,N_{k}}}"></span> – związek z <a href="/wiki/Potencja%C5%82_chemiczny" title="Potencjał chemiczny">potencjałem chemicznym</a>,</dd></dl> <p>gdzie: </p> <ul><li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> – <a href="/wiki/Energia_wewn%C4%99trzna" title="Energia wewnętrzna">energia wewnętrzna</a>,</li> <li><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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> – <a href="/wiki/Ci%C5%9Bnienie" title="Ciśnienie">ciśnienie</a>,</li> <li><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> – <a href="/wiki/Obj%C4%99to%C5%9B%C4%87" title="Objętość">objętość</a>,</li> <li><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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> – <a href="/wiki/Entropia" title="Entropia">entropia</a>.</li></ul> <p>Entalpia <a href="/wiki/Gaz_rzeczywisty" title="Gaz rzeczywisty">gazów rzeczywistych</a> i innych substancji zależy w sposób bardziej skomplikowany od temperatury, konieczne jest zastosowanie bardziej skomplikowanych zależności, uwzględniających m.in. ciśnienie. Szczególnie skomplikowane jest wyznaczenie entalpii stosowanej w technice <a href="/wiki/Para_wodna" title="Para wodna">pary wodnej</a> (np. w <a href="/wiki/Kocio%C5%82_parowy" title="Kocioł parowy">kotłach</a> i <a href="/wiki/Turbina_parowa" title="Turbina parowa">turbinach parowych</a>, <a href="/wiki/Suszarnia" title="Suszarnia">suszarniach</a>, <a href="/wiki/Wymiennik_ciep%C5%82a" title="Wymiennik ciepła">wymiennikach ciepła</a>, <a href="/wiki/Spr%C4%99%C5%BCarka" title="Sprężarka">sprężarkach</a> i <a href="/wiki/Wentylator" title="Wentylator">wentylatorach</a> do <a href="/wiki/Gaz" title="Gaz">gazów</a> wilgotnych, <a href="/wiki/Silnik_cieplny" title="Silnik cieplny">silnikach cieplnych</a>, zwłaszcza z wtryskiem wody bądź pary wodnej, sieci i węzłów ciepłowniczych i innych), gdyż jej parametry są oddalone w stosunkowo niewielkim stopniu od <a href="/w/index.php?title=Linia_nasycenia&action=edit&redlink=1" class="new" title="Linia nasycenia (strona nie istnieje)">linii nasycenia</a> i <a href="/wiki/Punkt_krytyczny_(fizyka)" title="Punkt krytyczny (fizyka)">punktu krytycznego</a>. </p><p>W termodynamice nie jest istotna wartość całkowitej entalpii, lecz jej przyrost lub zmniejszenie w danym procesie. Przyrost entalpii występuje w <a href="/wiki/Spr%C4%99%C5%BCarka" title="Sprężarka">sprężarkach</a>, natomiast zmniejszenie – w <a href="/wiki/Turbina_cieplna" title="Turbina cieplna">turbinach cieplnych</a>. </p><p><a href="/wiki/Moc" title="Moc">Moc</a> <a href="/wiki/Maszyna_cieplna#Cieplne_maszyny_przepływowe" title="Maszyna cieplna">maszyny przepływowej</a> (<a href="/wiki/Turbina" title="Turbina">turbiny</a>, <a href="/wiki/Spr%C4%99%C5%BCarka" title="Sprężarka">sprężarki</a>) obliczana jest jako iloczyn zmniejszenia (bądź przyrostu) wewnętrznego entalpii <a href="/wiki/Czynnik_termodynamiczny" title="Czynnik termodynamiczny">czynnika przepływowego</a> i <a href="/wiki/Nat%C4%99%C5%BCenie_przep%C5%82ywu" title="Natężenie przepływu">strumienia masy</a> rozprężanego (lub sprężanego) czynnika. </p> <div class="mw-heading mw-heading2"><h2 id="Entalpia_jako_transformata_Legendre’a"><span id="Entalpia_jako_transformata_Legendre.E2.80.99a"></span>Entalpia jako transformata Legendre’a</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=6" title="Edytuj sekcję: Entalpia jako transformata Legendre’a" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=6" title="Edytuj kod źródłowy sekcji: Entalpia jako transformata Legendre’a"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Entalpia <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)}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd5896cd30f7224f46cff6ccf760e76679294fd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.576ex; height:2.843ex;" alt="{\displaystyle H(S,p)}"></span> jest <a href="/wiki/Transformata_Legendre%E2%80%99a" class="mw-disambig" title="Transformata Legendre’a">transformatą Legendre’a</a> energii wewnętrznej <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> po zmiennej <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"> <mo>−</mo> <mi>V</mi> <mo>.</mo> </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/09ffb47800df1823a9435690d4c2ccc04d87fb80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.242ex; height:2.343ex;" alt="{\displaystyle -V.}"></span> </p><p>W równaniu: </p> <dl><dd><dl><dd><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=TdS-pdV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=TdS-pdV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6471405a619695a5a5821cebe195bdc5be51377" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.461ex; height:2.509ex;" alt="{\displaystyle dU=TdS-pdV}"></span></dd></dl></dd></dl> <p><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> jest zmienną niezależną, 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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> zależną (funkcją objętości). </p><p>Dokonując transformacji Legendre’a, otrzymuje się nową funkcję <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,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef601e1519093ba6c2944b945882c119f990e704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.71ex; height:2.509ex;" alt="{\displaystyle H,}"></span> w której <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> jest zmienną niezależną, 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 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> zależną (funkcją ciśnienia), czyli: </p> <dl><dd><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 dH=TdS+Vdp.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>H</mi> <mo>=</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>+</mo> <mi>V</mi> <mi>d</mi> <mi>p</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dH=TdS+Vdp.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3552071b297f20a61f6d37686b8412a7556fb2a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.389ex; height:2.509ex;" alt="{\displaystyle dH=TdS+Vdp.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Zobacz_też"><span id="Zobacz_te.C5.BC"></span>Zobacz też</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=7" title="Edytuj sekcję: Zobacz też" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=7" title="Edytuj kod źródłowy sekcji: Zobacz też"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="infobox noprint plainlinks" cellpadding="4" role="presentation"> <tbody><tr> <td style="vertical-align:middle; text-align:center; width:30px;"><span class="notpageimage" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/WiktionaryPl_nodesc.svg/28px-WiktionaryPl_nodesc.svg.png" decoding="async" width="28" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/WiktionaryPl_nodesc.svg/42px-WiktionaryPl_nodesc.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/WiktionaryPl_nodesc.svg/56px-WiktionaryPl_nodesc.svg.png 2x" data-file-width="122" data-file-height="117" /></span></span> </td> <td style="line-height:normal; vertical-align:middle; text-align:center; flex:unset;"><a href="https://pl.wiktionary.org/wiki/entalpia" class="extiw" title="wikt:entalpia"><strong>Zobacz hasło</strong> <em>entalpia</em> w Wikisłowniku</a> </td></tr></tbody></table> <ul><li><a href="/wiki/Energia_swobodna" title="Energia swobodna">energia swobodna</a></li> <li><a href="/wiki/Energia_wewn%C4%99trzna" title="Energia wewnętrzna">energia wewnętrzna</a></li> <li><a href="/wiki/Entalpia_swobodna" title="Entalpia swobodna">entalpia swobodna</a></li> <li><a href="/wiki/Funkcja_stanu" title="Funkcja stanu">funkcja stanu</a></li> <li><a href="/wiki/Maszyna_cieplna" title="Maszyna cieplna">maszyna cieplna</a></li> <li><a href="/wiki/Potencja%C5%82y_termodynamiczne" title="Potencjały termodynamiczne">potencjały termodynamiczne</a></li> <li><a href="/wiki/Rozpr%C4%99%C5%BCanie" title="Rozprężanie">rozprężanie</a></li> <li><a href="/wiki/Spalanie" title="Spalanie">spalanie</a></li> <li><a href="/wiki/Spr%C4%99%C5%BCanie" title="Sprężanie">sprężanie</a></li> <li><a href="/wiki/Turbina_parowa" title="Turbina parowa">turbina parowa</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Uwagi">Uwagi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=8" title="Edytuj sekcję: Uwagi" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=8" title="Edytuj kod źródłowy sekcji: Uwagi"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="do-not-make-smaller refsection refsection-uwagi ll-script ll-script-uwagi"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Małą literę stosuje się w ujęciu ogólnym, dużą dla wielkości molowej<sup id="cite_ref-ChF_2-0" class="reference"><a href="#cite_note-ChF-2">[2]</a></sup>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Przypisy">Przypisy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=9" title="Edytuj sekcję: Przypisy" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=9" title="Edytuj kod źródłowy sekcji: Przypisy"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="do-not-make-smaller refsection"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-epwn-1"><span class="mw-cite-backlink"><a href="#cite_ref-epwn_1-0">↑</a></span> <span class="reference-text"><cite class="citation web open-access"><a rel="nofollow" class="external text" href="https://encyklopedia.pwn.pl/haslo/;3898097"><i>entalpia</i></a>, [w:] <i><a href="/wiki/Encyklopedia_PWN_(internetowa)" title="Encyklopedia PWN (internetowa)">Encyklopedia PWN</a></i> [online], <a href="/wiki/Wydawnictwo_Naukowe_PWN" title="Wydawnictwo Naukowe PWN">Wydawnictwo Naukowe PWN</a><span class="accessdate"> [dostęp 2021-12-20]</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft.gengre=unknown&rft.atitle=entalpia&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=%5B%5BWydawnictwo+Naukowe+PWN%5D%5D&rft_id=https%3A%2F%2Fencyklopedia.pwn.pl%2Fhaslo%2F%3B3898097" style="display:none"> </span>.</cite></span> </li> <li id="cite_note-ChF-2"><span class="mw-cite-backlink"><a href="#cite_ref-ChF_2-0">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Witold_Tomassi" title="Witold Tomassi">Witold Tomassi</a>, Helena Jankowska: <i>Chemia fizyczna</i>. Warszawa: Wydawnictwa Naukowo-Techniczne, 1980, s. 34. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8320401798" title="Specjalna:Książki/8320401798">ISBN <span class="isbn">83-204-0179-8</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemia+fizyczna&rft.au=%5B%5BWitold+Tomassi%5D%5D%2C+Helena+Jankowska&rft.date=1980&rft.pub=Wydawnictwa+Naukowo-Techniczne&rft.place=Warszawa&rft.pages=34&rft.isbn=83-204-0179-8"></span></cite></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/firlaw.html#c2">First Law of Thermodynamics</a>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><cite class="citation book nourl"><a href="/wiki/Peter_Atkins" title="Peter Atkins"><span class="cite-name-before"><span class="cite-name-full">Peter</span><span class="cite-name-initials" title="Peter" style="display:none">P.</span> </span><span class="cite-lastname">Atkins</span><span class="cite-name-after" style="display:none"> <span class="cite-name-full">Peter</span><span class="cite-name-initials" title="Peter">P.</span></span></a>, <i>Chemia fizyczna</i>, wyd. 1 (3 dodr.), Warszawa: Wydawnictwo Naukowe PWN, 2012, s. 65, <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/9788301135027" title="Specjalna:Książki/9788301135027">ISBN <span class="isbn">978-83-01-13502-7</span></a><span class="Z3988" title="ctx_ver=Z39.88-2004&rft.gengre=book&rft.place=Warszawa&rft.edition=1+%283+dodr.%29&rft.aufirst=Peter&rft.aulast=Atkins&rft.date=2012&rft.isbn=978-83-01-13502-7&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.btitle=Chemia+fizyczna&rft.pub=Wydawnictwo+Naukowe+PWN" style="display:none"> </span>.</cite></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entalpia&veaction=edit&section=10" title="Edytuj sekcję: Bibliografia" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entalpia&action=edit&section=10" title="Edytuj kod źródłowy sekcji: Bibliografia"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070304011507/http://www.ichf.edu.pl/SKRYPT/book.pdf">R. Hołyst, A. Poniewierski, A. Ciach, <i>Termodynamika</i></a>. ichf.edu.pl. [zarchiwizowane z <a rel="nofollow" class="external text" href="http://www.ichf.edu.pl/SKRYPT/book.pdf">tego adresu</a> (2007-03-04)].</cite></li> <li><cite class="citation book"><a href="/wiki/Peter_Atkins" title="Peter Atkins">Peter William Atkins</a>: <i>Chemia fizyczna</i>. Warszawa: Wydawnictwo Naukowe PWN, 2001, s. 124. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8301135026" title="Specjalna:Książki/8301135026">ISBN <span class="isbn">83-01-13502-6</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemia+fizyczna&rft.aulast=Atkins&rft.aufirst=Peter+William&rft.pub=Wydawnictwo+Naukowe+PWN&rft.place=Warszawa&rft.pages=124&rft.isbn=83-01-13502-6"></span></cite></li></ul> <style data-mw-deduplicate="TemplateStyles:r74016753">.mw-parser-output #normdaten>div+div{margin-top:0.5em}.mw-parser-output #normdaten>div>div{background:var(--background-color-neutral,#eaecf0);padding:.2em .5em}.mw-parser-output #normdaten ul{margin:0;padding:0}.mw-parser-output #normdaten ul li:first-child{padding-left:.5em;border-left:1px solid var(--border-color-base,#a2a9b1)}</style> <div id="normdaten" class="catlinks"><div class="normdaten-typ-fehlt"><div><a href="/wiki/Kontrola_autorytatywna" title="Kontrola autorytatywna">Kontrola autorytatywna</a> (<span class="description"><a href="/wiki/Wielko%C5%9B%C4%87_fizyczna" title="Wielkość fizyczna">wielkość fizyczna</a></span>):</div><ul><li><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://lccn.loc.gov/sh85044109">sh85044109</a></span></li><li><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4152355-6">4152355-6</a></span></li><li><a href="/wiki/Biblioth%C3%A8que_nationale" title="Bibliothèque nationale">BnF</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://catalogue.bnf.fr/ark:/12148/cb122863012">122863012</a></span></li><li><a href="/wiki/Centralna_Biblioteka_Narodowa_we_Florencji" title="Centralna Biblioteka Narodowa we Florencji">BNCF</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://thes.bncf.firenze.sbn.it/termine.php?id=19352">19352</a></span></li><li><a href="/wiki/Biblioteka_Narodowa_Republiki_Czeskiej" title="Biblioteka Narodowa Republiki Czeskiej">NKC</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://aut.nkp.cz/ph311255">ph311255</a></span></li><li><a href="/wiki/Biblioteka_Narodowa_Izraela" title="Biblioteka Narodowa Izraela">J9U</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007550788605171">987007550788605171</a></span></li></ul></div><div class="normdaten-andere"><div><a href="/wiki/Encyklopedia_internetowa" title="Encyklopedia internetowa">Encyklopedie internetowe</a>:</div> <ul><li><a href="/wiki/Encyklopedia_Britannica" title="Encyklopedia Britannica">Britannica</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/enthalpy">science/enthalpy</a></span></li> <li><a href="/wiki/Wielka_Encyklopedia_Rosyjska" title="Wielka Encyklopedia Rosyjska">БРЭ</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://old.bigenc.ru/text/4936148">4936148</a></span></li> <li><a href="/wiki/Store_norske_leksikon" title="Store norske leksikon">SNL</a>: <span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=4342&url_prefix=https://snl.no/&id=entalpi">entalpi</a></span></li> <li><a href="https://www.wikidata.org/wiki/Property:P1296" class="extiw" title="d:Property:P1296">Catalana</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://www.enciclopedia.cat/ec-gec-0103014.xml">0103014</a></span></li> <li><a href="/wiki/Den_Store_Danske_Encyklop%C3%A6di" title="Den Store Danske Encyklopædi">DSDE</a>: <span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8313&url_prefix=https://lex.dk/&id=entalpi">entalpi</a></span></li></ul> </div></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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