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thermodynamics subsection</span> </button> <ul id="toc-Branches_of_thermodynamics-sublist" class="vector-toc-list"> <li id="toc-Classical_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classical_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Classical thermodynamics</span> </div> </a> <ul id="toc-Classical_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistical_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistical_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Statistical mechanics</span> </div> </a> <ul id="toc-Statistical_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chemical_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chemical_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Chemical thermodynamics</span> </div> </a> <ul id="toc-Chemical_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equilibrium_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equilibrium_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Equilibrium thermodynamics</span> </div> </a> <ul id="toc-Equilibrium_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-equilibrium_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-equilibrium_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Non-equilibrium thermodynamics</span> </div> </a> <ul id="toc-Non-equilibrium_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Laws_of_thermodynamics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Laws_of_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Laws of thermodynamics</span> </div> </a> <button aria-controls="toc-Laws_of_thermodynamics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Laws of thermodynamics subsection</span> </button> <ul id="toc-Laws_of_thermodynamics-sublist" class="vector-toc-list"> <li id="toc-Zeroth_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zeroth_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Zeroth law</span> </div> </a> <ul id="toc-Zeroth_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-First_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#First_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>First law</span> </div> </a> <ul id="toc-First_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Second_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Second_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Second law</span> </div> </a> <ul id="toc-Second_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Third_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Third_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Third law</span> </div> </a> <ul id="toc-Third_law-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-System_models" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#System_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>System models</span> </div> </a> <ul id="toc-System_models-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-States_and_processes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#States_and_processes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>States and processes</span> </div> </a> <ul id="toc-States_and_processes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Instrumentation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Instrumentation"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Instrumentation</span> </div> </a> <ul id="toc-Instrumentation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conjugate_variables" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Conjugate_variables"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Conjugate variables</span> </div> </a> <ul id="toc-Conjugate_variables-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potentials" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Potentials</span> </div> </a> <ul id="toc-Potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Axiomatic_thermodynamics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Axiomatic_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Axiomatic thermodynamics</span> </div> </a> <ul id="toc-Axiomatic_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applied_fields" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applied_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Applied fields</span> </div> </a> <ul id="toc-Applied_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>See also</span> </div> </a> <button aria-controls="toc-See_also-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle See also subsection</span> </button> <ul id="toc-See_also-sublist" class="vector-toc-list"> <li id="toc-Lists_and_timelines" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lists_and_timelines"> <div class="vector-toc-text"> <span class="vector-toc-numb">13.1</span> <span>Lists and timelines</span> </div> </a> <ul id="toc-Lists_and_timelines-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">17</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Thermodynamics</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="Go to an article in another language. Available in 125 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-125" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">125 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Afrikaans" lang="af" hreflang="af" data-title="Termodinamika" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – Alemannic" lang="gsw" hreflang="gsw" data-title="Thermodynamik" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – Angika" lang="anp" hreflang="anp" data-title="उष्मागतिकी" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A%D8%A9" title="ديناميكا حرارية – Arabic" lang="ar" hreflang="ar" data-title="ديناميكا حرارية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Termodinamica" title="Termodinamica – Aragonese" lang="an" hreflang="an" data-title="Termodinamica" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF_%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="তাপগতি বিজ্ঞান – Assamese" lang="as" hreflang="as" data-title="তাপগতি বিজ্ঞান" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – Asturian" lang="ast" hreflang="ast" data-title="Termodinámica" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – Guarani" lang="gn" hreflang="gn" data-title="Termodinámica" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Azerbaijani" lang="az" hreflang="az" data-title="Termodinamika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترمودینامیک – South Azerbaijani" lang="azb" hreflang="azb" data-title="ترمودینامیک" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="তাপগতিবিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="তাপগতিবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" 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/Jia%CC%8Dt-le%CC%8Dk-ha%CC%8Dk" title="Jia̍t-le̍k-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Jia̍t-le̍k-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Bashkir" lang="ba" hreflang="ba" data-title="Термодинамика" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Тэрмадынаміка – Belarusian" lang="be" hreflang="be" data-title="Тэрмадынаміка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Тэрмадынаміка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэрмадынаміка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Termodinamika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Bulgarian" lang="bg" hreflang="bg" data-title="Термодинамика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – Bavarian" lang="bar" hreflang="bar" data-title="Thermodynamik" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Bosnian" lang="bs" hreflang="bs" data-title="Termodinamika" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – Catalan" lang="ca" hreflang="ca" data-title="Termodinàmica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Chuvash" lang="cv" hreflang="cv" data-title="Термодинамика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Termodynamika" title="Termodynamika – Czech" lang="cs" hreflang="cs" data-title="Termodynamika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Thermodynameg" title="Thermodynameg – Welsh" lang="cy" hreflang="cy" data-title="Thermodynameg" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Termodynamik" title="Termodynamik – Danish" lang="da" hreflang="da" data-title="Termodynamik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B7%D9%8A%D8%B1%D9%85%D9%88%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83" title="طيرموديناميك – Moroccan Arabic" lang="ary" hreflang="ary" data-title="طيرموديناميك" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – German" lang="de" hreflang="de" data-title="Thermodynamik" data-language-autonym="Deutsch" data-language-local-name="German" 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/Termod%C3%BCnaamika" title="Termodünaamika – Estonian" lang="et" hreflang="et" data-title="Termodünaamika" data-language-autonym="Eesti" data-language-local-name="Estonian" 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%98%CE%B5%CF%81%CE%BC%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE" title="Θερμοδυναμική – Greek" lang="el" hreflang="el" data-title="Θερμοδυναμική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – Spanish" lang="es" hreflang="es" data-title="Termodinámica" data-language-autonym="Español" data-language-local-name="Spanish" 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/Termodinamiko" title="Termodinamiko – Esperanto" lang="eo" hreflang="eo" data-title="Termodinamiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Termodin%C3%A1mica" title="Termodinámica – Extremaduran" lang="ext" hreflang="ext" data-title="Termodinámica" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Basque" lang="eu" hreflang="eu" data-title="Termodinamika" data-language-autonym="Euskara" data-language-local-name="Basque" 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%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترمودینامیک – Persian" lang="fa" hreflang="fa" data-title="ترمودینامیک" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – Fiji Hindi" lang="hif" hreflang="hif" data-title="Thermodynamics" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Thermodynamique" title="Thermodynamique – French" lang="fr" hreflang="fr" data-title="Thermodynamique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Termodynamika" title="Termodynamika – Western Frisian" lang="fy" hreflang="fy" data-title="Termodynamika" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teirmidinimic" title="Teirmidinimic – Irish" lang="ga" hreflang="ga" data-title="Teirmidinimic" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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/Termodin%C3%A1mica" title="Termodinámica – Galician" lang="gl" hreflang="gl" data-title="Termodinámica" data-language-autonym="Galego" data-language-local-name="Galician" 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%B4%EC%97%AD%ED%95%99" title="열역학 – Korean" lang="ko" hreflang="ko" data-title="열역학" data-language-autonym="한국어" data-language-local-name="Korean" 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/%D5%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1" title="Ջերմադինամիկա – Armenian" lang="hy" hreflang="hy" data-title="Ջերմադինամիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – Hindi" lang="hi" hreflang="hi" data-title="उष्मागतिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Croatian" lang="hr" hreflang="hr" data-title="Termodinamika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Termodinamiko" title="Termodinamiko – Ido" lang="io" hreflang="io" data-title="Termodinamiko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Iloko" lang="ilo" hreflang="ilo" data-title="Termodinamika" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Indonesian" lang="id" hreflang="id" data-title="Termodinamika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Thermodynamica" title="Thermodynamica – Interlingua" lang="ia" hreflang="ia" data-title="Thermodynamica" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Varmafr%C3%A6%C3%B0i" title="Varmafræði – Icelandic" lang="is" hreflang="is" data-title="Varmafræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Termodinamica" title="Termodinamica – Italian" lang="it" hreflang="it" data-title="Termodinamica" data-language-autonym="Italiano" data-language-local-name="Italian" 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%AA%D7%A8%D7%9E%D7%95%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94" title="תרמודינמיקה – Hebrew" lang="he" hreflang="he" data-title="תרמודינמיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/So%C5%8Bga%C9%A3_n%C9%9B_%C9%96o%C5%8B_kp%C9%9Bl%C9%9Bk%CA%8B%CA%8B_t%C9%9B" title="Soŋgaɣ nɛ ɖoŋ kpɛlɛkʋʋ tɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Soŋgaɣ nɛ ɖoŋ kpɛlɛkʋʋ tɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="თერმოდინამიკა – Georgian" lang="ka" hreflang="ka" data-title="თერმოდინამიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Kazakh" lang="kk" hreflang="kk" data-title="Термодинамика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mwendojoto" title="Mwendojoto – Swahili" lang="sw" hreflang="sw" data-title="Mwendojoto" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/T%C3%A8modinamik" title="Tèmodinamik – Haitian Creole" lang="ht" hreflang="ht" data-title="Tèmodinamik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Termodinamik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Termod%C3%AEnam%C3%AEk" title="Termodînamîk – Kurdish" lang="ku" hreflang="ku" data-title="Termodînamîk" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Kyrgyz" lang="ky" hreflang="ky" data-title="Термодинамика" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Thermodynamica" title="Thermodynamica – Latin" lang="la" hreflang="la" data-title="Thermodynamica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Latvian" lang="lv" hreflang="lv" data-title="Termodinamika" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – Luxembourgish" lang="lb" hreflang="lb" data-title="Thermodynamik" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Lithuanian" lang="lt" hreflang="lt" data-title="Termodinamika" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Termudinamica" title="Termudinamica – Lombard" lang="lmo" hreflang="lmo" data-title="Termudinamica" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Hungarian" lang="hu" hreflang="hu" data-title="Termodinamika" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Macedonian" lang="mk" hreflang="mk" data-title="Термодинамика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A4%E0%B4%BE%E0%B4%AA%E0%B4%97%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B4%82" title="താപഗതികം – Malayalam" lang="ml" hreflang="ml" data-title="താപഗതികം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="ऊष्मागतिकी – Marathi" lang="mr" hreflang="mr" data-title="ऊष्मागतिकी" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="თერმოდინამიკა – Mingrelian" lang="xmf" hreflang="xmf" data-title="თერმოდინამიკა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Malay" lang="ms" hreflang="ms" data-title="Termodinamik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA" title="Термодинамик – Mongolian" lang="mn" hreflang="mn" data-title="Термодинамик" data-language-autonym="Монгол" data-language-local-name="Mongolian" 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%9E%E1%80%AC%E1%80%99%E1%80%AD%E1%80%AF%E1%80%92%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%94%E1%80%99%E1%80%85%E1%80%BA" title="သာမိုဒိုင်းနမစ် – Burmese" lang="my" hreflang="my" data-title="သာမိုဒိုင်းနမစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" 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/Thermodynamica" title="Thermodynamica – Dutch" lang="nl" hreflang="nl" data-title="Thermodynamica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="उष्मागतिकी – Nepali" lang="ne" hreflang="ne" data-title="उष्मागतिकी" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%A6" title="熱力学 – Japanese" lang="ja" hreflang="ja" data-title="熱力学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Termod%C3%BCnaamik" title="Termodünaamik – Northern Frisian" lang="frr" hreflang="frr" data-title="Termodünaamik" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Termodynamikk" title="Termodynamikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Termodynamikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian 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/Termodynamikk" title="Termodynamikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Termodynamikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Termodinamica" title="Termodinamica – Occitan" lang="oc" hreflang="oc" data-title="Termodinamica" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Daayinaamiksii_Ho%E2%80%99aa" title="Daayinaamiksii Ho’aa – Oromo" lang="om" hreflang="om" data-title="Daayinaamiksii Ho’aa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Uzbek" lang="uz" hreflang="uz" data-title="Termodinamika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%BE%E0%A8%AA_%E0%A8%97%E0%A8%A4%E0%A9%80_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਤਾਪ ਗਤੀ ਵਿਗਿਆਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਤਾਪ ਗਤੀ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%DA%BE%D8%B1%D9%85%D9%88%DA%88%D8%A7%D8%A6%DB%8C%D9%86%D8%A7%D9%85%DA%A9%D8%B3" title="تھرموڈائینامکس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="تھرموڈائینامکس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%DA%89%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="ترموډینامیک – Pashto" lang="ps" hreflang="ps" data-title="ترموډینامیک" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Toermodainamix" title="Toermodainamix – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Toermodainamix" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – Piedmontese" lang="pms" hreflang="pms" data-title="Termodinàmica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Thermodynamik" title="Thermodynamik – Low German" lang="nds" hreflang="nds" data-title="Thermodynamik" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Termodynamika" title="Termodynamika – Polish" lang="pl" hreflang="pl" data-title="Termodynamika" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Termodin%C3%A2mica" title="Termodinâmica – Portuguese" lang="pt" hreflang="pt" data-title="Termodinâmica" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Termodinamic%C4%83" title="Termodinamică – Romanian" lang="ro" hreflang="ro" data-title="Termodinamică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D1%96%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Термодінаміка – Rusyn" lang="rue" hreflang="rue" data-title="Термодінаміка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Russian" lang="ru" hreflang="ru" data-title="Термодинамика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Yakut" lang="sah" hreflang="sah" data-title="Термодинамика" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Termodin%C3%A0mica" title="Termodinàmica – Sardinian" lang="sc" hreflang="sc" data-title="Termodinàmica" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – Scots" lang="sco" hreflang="sco" data-title="Thermodynamics" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Albanian" lang="sq" hreflang="sq" data-title="Termodinamika" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Termudin%C3%A0mica" title="Termudinàmica – Sicilian" lang="scn" hreflang="scn" data-title="Termudinàmica" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8F%E0%B6%B4_%E0%B6%9C%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80" title="තාප ගති විද්‍යාව – Sinhala" lang="si" hreflang="si" data-title="තාප ගති විද්‍යාව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Thermodynamics" title="Thermodynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Thermodynamics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%BF%D8%B1%D9%85%D9%88%DA%8A%D8%A7%D8%A6%D9%86%D8%A7%D9%85%DA%AA%D8%B3" title="ٿرموڊائنامڪس – Sindhi" lang="sd" hreflang="sd" data-title="ٿرموڊائنامڪس" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Termodynamika" title="Termodynamika – Slovak" lang="sk" hreflang="sk" data-title="Termodynamika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Slovenian" lang="sl" hreflang="sl" data-title="Termodinamika" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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%AA%DB%8E%D8%B1%D9%85%DB%86%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="تێرمۆدینامیک – Central Kurdish" lang="ckb" hreflang="ckb" data-title="تێرمۆدینامیک" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Serbian" lang="sr" hreflang="sr" data-title="Термодинамика" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Termodinamika" title="Termodinamika – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Termodinamika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" 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/Termodynamiikka" title="Termodynamiikka – Finnish" lang="fi" hreflang="fi" data-title="Termodynamiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://sv.wikipedia.org/wiki/Termodynamik" title="Termodynamik – Swedish" lang="sv" hreflang="sv" data-title="Termodynamik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Tagalog" lang="tl" hreflang="tl" data-title="Termodinamika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA_%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="வெப்ப இயக்கவியல் – Tamil" lang="ta" hreflang="ta" data-title="வெப்ப இயக்கவியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Ta%E1%BA%93%C9%A3lasmussut" title="Taẓɣlasmussut – Tachelhit" lang="shi" hreflang="shi" data-title="Taẓɣlasmussut" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Tatar" lang="tt" hreflang="tt" data-title="Термодинамика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%89%E0%B0%B7%E0%B1%8D%E0%B0%A3%E0%B0%97%E0%B0%A4%E0%B0%BF%E0%B0%95%E0%B0%B6%E0%B0%BE%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%82" title="ఉష్ణగతికశాస్త్రం – Telugu" lang="te" hreflang="te" data-title="ఉష్ణగతికశాస్త్రం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B8%E0%B8%93%E0%B8%AB%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="อุณหพลศาสตร์ – Thai" lang="th" hreflang="th" data-title="อุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Термодинамика – Tajik" lang="tg" hreflang="tg" data-title="Термодинамика" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Turkish" lang="tr" hreflang="tr" data-title="Termodinamik" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Термодинаміка – Ukrainian" lang="uk" hreflang="uk" data-title="Термодинаміка" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%B1_%D8%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA" title="حر حرکیات – Urdu" lang="ur" hreflang="ur" data-title="حر حرکیات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Termodinamik" title="Termodinamik – Veps" lang="vep" hreflang="vep" data-title="Termodinamik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nhi%E1%BB%87t_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Nhiệt động lực học – Vietnamese" lang="vi" hreflang="vi" data-title="Nhiệt động lực học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/L%C3%A4mm%C3%A4oppus" title="Lämmäoppus – Võro" lang="vro" hreflang="vro" data-title="Lämmäoppus" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8" title="熱力學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="熱力學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Termodinamika" title="Termodinamika – Waray" lang="war" hreflang="war" data-title="Termodinamika" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6" title="热力学 – Wu" lang="wuu" hreflang="wuu" data-title="热力学" 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-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%98%D7%A2%D7%A8%D7%9E%D7%90%D7%93%D7%99%D7%A0%D7%90%D7%9E%D7%99%D7%A7" title="טערמאדינאמיק – Yiddish" lang="yi" hreflang="yi" data-title="טערמאדינאמיק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8" title="熱力學 – Cantonese" lang="yue" hreflang="yue" data-title="熱力學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Termuodinam%C4%97ka" title="Termuodinamėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Termuodinamėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" 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class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a class="mw-selflink selflink">Thermodynamics</a></th></tr><tr><td class="sidebar-image" style="display:block;margin:0.3em 0 0.4em;"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Carnot_heat_engine" title="Carnot heat engine"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/220px-Carnot_heat_engine_2.svg.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/330px-Carnot_heat_engine_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/440px-Carnot_heat_engine_2.svg.png 2x" data-file-width="840" data-file-height="370" /></a></span><div class="sidebar-caption">The classical <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a></div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Branches</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a class="mw-selflink selflink">Classical</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul> </div> <ul><li><a href="/wiki/Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium</a> / <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth</a></li> <li><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First</a></li> <li><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second</a></li> <li><a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">Third</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Systems</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Closed_system" title="Closed system">Closed system</a></li> <li><a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">Open system</a></li> <li><a href="/wiki/Isolated_system" title="Isolated system">Isolated system</a></li></ul> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">State</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Ideal_gas" title="Ideal gas">Ideal gas</a></li> <li><a href="/wiki/Real_gas" title="Real gas">Real gas</a></li> <li><a href="/wiki/State_of_matter" title="State of matter">State of matter</a></li> <li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium</a></li> <li><a href="/wiki/Control_volume" title="Control volume">Control volume</a></li> <li><a href="/wiki/Thermodynamic_instruments" title="Thermodynamic instruments">Instruments</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">Processes</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Isobaric_process" title="Isobaric process">Isobaric</a></li> <li><a href="/wiki/Isochoric_process" title="Isochoric process">Isochoric</a></li> <li><a href="/wiki/Isothermal_process" title="Isothermal process">Isothermal</a></li> <li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic</a></li> <li><a href="/wiki/Isentropic_process" title="Isentropic process">Isentropic</a></li> <li><a href="/wiki/Isenthalpic_process" title="Isenthalpic process">Isenthalpic</a></li> <li><a href="/wiki/Quasistatic_process" title="Quasistatic process">Quasistatic</a></li> <li><a href="/wiki/Polytropic_process" title="Polytropic process">Polytropic</a></li> <li><a href="/wiki/Free_expansion" class="mw-redirect" title="Free expansion">Free expansion</a></li> <li><a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversibility</a></li> <li><a href="/wiki/Irreversible_process" title="Irreversible process">Irreversibility</a></li> <li><a href="/wiki/Endoreversible_thermodynamics" title="Endoreversible thermodynamics">Endoreversibility</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_cycle" title="Thermodynamic cycle">Cycles</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Heat_engine" title="Heat engine">Heat engines</a></li> <li><a href="/wiki/Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Heat pumps</a></li> <li><a href="/wiki/Thermal_efficiency" title="Thermal efficiency">Thermal efficiency</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">System properties</a></div><div class="sidebar-list-content mw-collapsible-content"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Note: <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> in <i>italics</i></div> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;margin-top:0.4em;"><tbody><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_diagrams" title="Thermodynamic diagrams">Property diagrams</a></li> <li><a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">Intensive and extensive properties</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Process_function" title="Process function">Process functions</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;;padding-bottom:0.4em;"> <div class="hlist"> <ul><li><a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">Work</a></li> <li><a href="/wiki/Heat" title="Heat">Heat</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/State_function" title="State function">Functions of state</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> / <i><a href="/wiki/Entropy" title="Entropy">Entropy</a></i> (<a href="/wiki/Introduction_to_entropy" title="Introduction to entropy">introduction</a>)</li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a> / <i><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></i></li> <li><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a> / <i><a href="/wiki/Particle_number" title="Particle number">Particle number</a></i></li> <li><a href="/wiki/Vapor_quality" title="Vapor quality">Vapor quality</a></li> <li><a href="/wiki/Reduced_properties" title="Reduced properties">Reduced properties</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Material_properties_(thermodynamics)" title="Material properties (thermodynamics)">Material properties</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Property databases</a></li></ul> <div style="font-size:90%;margin-top:0.4em;border-top:1px solid #aaa;text-align:center;"> <table> <tbody><tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Heat_capacity" title="Heat capacity">Specific heat capacity</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891d40a9b18752b04065caee655d008b3ec11428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:1.676ex;" alt="{\displaystyle c=}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c609f4d3c5692ea4495479ef47594dc67f9fa464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.817ex; height:2.176ex;" alt="{\displaystyle \partial S}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Compressibility" title="Compressibility">Compressibility</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.239ex; height:2.509ex;" alt="{\displaystyle \beta =-}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc4a48eb2412f08b54fe438b5139c88f9cfa372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.487ex; height:2.509ex;" alt="{\displaystyle \partial p}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Thermal_expansion" title="Thermal expansion">Thermal expansion</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92d4583d351f08c1c70985f0c843b2fff1b01e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.941ex; height:1.676ex;" alt="{\displaystyle \alpha =}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> </tbody></table></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_equations" title="Thermodynamic equations">Equations</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Carnot%27s_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li> <li><a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li> <li><a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental relation</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div> <ul><li><a href="/wiki/Maxwell_relations" title="Maxwell relations">Maxwell relations</a></li> <li><a href="/wiki/Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a></li> <li><a href="/wiki/Bridgman%27s_thermodynamic_equations" title="Bridgman's thermodynamic equations">Bridgman's equations</a></li> <li><i><a href="/wiki/Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></i></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">Potentials</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a></li> <li><a href="/wiki/Free_entropy" title="Free entropy">Free entropy</a></li></ul> </div> <div class="plainlist"><ul><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(S,V)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/921f33f9c6551562ec836007b035c2de6323d2d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.912ex; height:2.843ex;" alt="{\displaystyle U(S,V)}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(S,p)=U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6407d78e5f39d07f70e2414a92e08e2e068519f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(T,V)=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e93692f031ba6484d82731c54db83a69daed3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(T,p)=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd7a8f0b8ae04963da133e3b202432e1b6caed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}"></span></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><div class="hlist"><ul><li>History</li><li>Culture</li></ul></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> History</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">General</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/Gas_laws" title="Gas laws">Gas laws</a></li></ul> </div> <ul><li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">"Perpetual motion" machines</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Entropy_(arrow_of_time)" class="mw-redirect" title="Entropy (arrow of time)">Entropy and time</a></li> <li><a href="/wiki/Entropy_and_life" title="Entropy and life">Entropy and life</a></li> <li><a href="/wiki/Brownian_ratchet" title="Brownian ratchet">Brownian ratchet</a></li> <li><a href="/wiki/Maxwell%27s_demon" title="Maxwell's demon">Maxwell's demon</a></li> <li><a href="/wiki/Heat_death_paradox" title="Heat death paradox">Heat death paradox</a></li> <li><a href="/wiki/Loschmidt%27s_paradox" title="Loschmidt's paradox">Loschmidt's paradox</a></li> <li><a href="/wiki/Synergetics_(Haken)" title="Synergetics (Haken)">Synergetics</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Theories</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Caloric_theory" title="Caloric theory">Caloric theory</a></li></ul> </div> <ul><li><a href="/wiki/Vis_viva" title="Vis viva"><i>Vis viva</i> <span style="font-size:85%;">("living force")</span></a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Mechanical equivalent of heat</a></li> <li><a href="/wiki/Power_(physics)" title="Power (physics)">Motive power</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/List_of_important_publications_in_physics" title="List of important publications in physics">Key publications</a></th></tr><tr><td class="sidebar-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction" title="An Inquiry Concerning the Source of the Heat Which Is Excited by Friction">An Inquiry Concerning the<br />Source ... Friction</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br />Heterogeneous Substances</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the<br />Motive Power of Fire</a></i></div></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Timelines</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Timeline_of_heat_engine_technology" title="Timeline of heat engine technology">Heat engines</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <div class="hlist"><ul><li>Art</li><li>Education</li></ul></div></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a></li> <li><a href="/wiki/Entropy_(energy_dispersal)" title="Entropy (energy dispersal)">Entropy as energy dispersal</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li> <li><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li> <li><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li> <li><a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li> <li><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Duhem</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">von Helmholtz</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis</a></li> <li><a href="/wiki/Fran%C3%A7ois_Massieu" title="François Massieu">Massieu</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">von Mayer</a></li> <li><a href="/wiki/Walther_Nernst" title="Walther Nernst">Nernst</a></li> <li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine</a></li> <li><a href="/wiki/John_Smeaton" title="John Smeaton">Smeaton</a></li> <li><a href="/wiki/Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li> <li><a href="/wiki/Peter_Tait_(physicist)" class="mw-redirect" title="Peter Tait (physicist)">Tait</a></li> <li><a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Thompson</a></li> <li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li> <li><a href="/wiki/John_James_Waterston" title="John James Waterston">Waterston</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Other</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nucleation" title="Nucleation">Nucleation</a></li> <li><a href="/wiki/Self-assembly" title="Self-assembly">Self-assembly</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li> <li><a href="/wiki/Order_and_disorder" title="Order and disorder">Order and disorder</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Thermodynamics" title="Category:Thermodynamics">Category</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Thermodynamics_sidebar" title="Template:Thermodynamics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Thermodynamics_sidebar" title="Template talk:Thermodynamics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Thermodynamics_sidebar" title="Special:EditPage/Template:Thermodynamics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Thermodynamics</b> is the branch of <a href="/wiki/Physics" title="Physics">physics</a> that studies <a href="/wiki/Heat" title="Heat">heat</a>, <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, and <a href="/wiki/Temperature" title="Temperature">temperature</a> and their relation to <a href="/wiki/Energy" title="Energy">energy</a>, <a href="/wiki/Entropy" title="Entropy">entropy</a>, and the physical properties of <a href="/wiki/Matter" title="Matter">matter</a> and <a href="/wiki/Radiation" title="Radiation">radiation</a>. The behavior of these quantities is governed by the four <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>, which convey a quantitative description using measurable macroscopic <a href="/wiki/Physical_quantity" title="Physical quantity">physical quantities</a>, but may be explained in terms of <a href="/wiki/Microscopic" class="mw-redirect" title="Microscopic">microscopic</a> constituents by <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a>. Thermodynamics plays a role in a wide variety of topics in <a href="/wiki/Science" title="Science">science</a> and <a href="/wiki/Engineering" title="Engineering">engineering</a>. </p><p>Historically, thermodynamics developed out of a desire to increase the <a href="/wiki/Thermodynamic_efficiency" class="mw-redirect" title="Thermodynamic efficiency">efficiency</a> of early <a href="/wiki/Steam_engine" title="Steam engine">steam engines</a>, particularly through the work of French physicist <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a> (1824) who believed that engine efficiency was the key that could help France win the <a href="/wiki/Napoleonic_Wars" title="Napoleonic Wars">Napoleonic Wars</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Scots-Irish physicist <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">Lord Kelvin</a> was the first to formulate a concise definition of thermodynamics in 1854<sup id="cite_ref-kelvin1854_2-0" class="reference"><a href="#cite_note-kelvin1854-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." German physicist and mathematician <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> restated Carnot's principle known as the <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a> and gave to the <a href="/wiki/Theory_of_heat" class="mw-redirect" title="Theory of heat">theory of heat</a> a truer and sounder basis. His most important paper, "On the Moving Force of Heat",<sup id="cite_ref-Theory_of_Heat_3-0" class="reference"><a href="#cite_note-Theory_of_Heat-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> published in 1850, first stated the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>. In 1865 he introduced the concept of entropy. In 1870 he introduced the <a href="/wiki/Virial_theorem" title="Virial theorem">virial theorem</a>, which applied to heat.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The initial application of thermodynamics to <a href="/wiki/Mechanical_heat_engine" class="mw-redirect" title="Mechanical heat engine">mechanical heat engines</a> was quickly extended to the study of chemical compounds and chemical reactions. <a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a> studies the nature of the role of entropy in the process of <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged. <a href="/wiki/Statistical_thermodynamics" class="mw-redirect" title="Statistical thermodynamics">Statistical thermodynamics</a>, or statistical mechanics, concerns itself with <a href="/wiki/Statistics" title="Statistics">statistical</a> predictions of the collective motion of particles from their microscopic behavior. In 1909, <a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a> presented a purely mathematical approach in an <a href="/wiki/Axiomatic" class="mw-redirect" title="Axiomatic">axiomatic</a> formulation, a description often referred to as <i>geometrical thermodynamics</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2></div> <p>A description of any thermodynamic system employs the four <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a> that form an axiomatic basis. <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">The first law</a> specifies that energy can be transferred between physical systems as <a href="/wiki/Heat" title="Heat">heat</a>, as <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, and with transfer of matter.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">The second law</a> defines the existence of a quantity called <a href="/wiki/Entropy" title="Entropy">entropy</a>, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic <i><a href="/wiki/System_(thermodynamics)" class="mw-redirect" title="System (thermodynamics)">system</a></i> and its <i><a href="/wiki/Surroundings_(thermodynamics)" class="mw-redirect" title="Surroundings (thermodynamics)">surroundings</a></i>. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through <a href="/wiki/Equation_of_state" title="Equation of state">equations of state</a>. Properties can be combined to express <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> and <a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">thermodynamic potentials</a>, which are useful for determining conditions for <a href="/wiki/Dynamic_equilibrium" title="Dynamic equilibrium">equilibrium</a> and <a href="/wiki/Spontaneous_process" title="Spontaneous process">spontaneous processes</a>. </p><p>With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in <a href="/wiki/Science" title="Science">science</a> and <a href="/wiki/Engineering" title="Engineering">engineering</a>, such as <a href="/wiki/Engine" title="Engine">engines</a>, <a href="/wiki/Phase_transition" title="Phase transition">phase transitions</a>, <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>, <a href="/wiki/Transport_phenomena" title="Transport phenomena">transport phenomena</a>, and even <a href="/wiki/Black_hole" title="Black hole">black holes</a>. The results of thermodynamics are essential for other fields of <a href="/wiki/Physics" title="Physics">physics</a> and for <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Chemical_engineering" title="Chemical engineering">chemical engineering</a>, <a href="/wiki/Corrosion_engineering" title="Corrosion engineering">corrosion engineering</a>, <a href="/wiki/Aerospace_engineering" title="Aerospace engineering">aerospace engineering</a>, <a href="/wiki/Mechanical_engineering" title="Mechanical engineering">mechanical engineering</a>, <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, <a href="/wiki/Cell_biology" title="Cell biology">cell biology</a>, <a href="/wiki/Biomedical_engineering" title="Biomedical engineering">biomedical engineering</a>, <a href="/wiki/Materials_science" title="Materials science">materials science</a>, and <a href="/wiki/Economics" title="Economics">economics</a>, to name a few.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>This article is focused mainly on classical thermodynamics which primarily studies systems in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium thermodynamics</a> is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Eight_founding_schools.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Eight_founding_schools.png/400px-Eight_founding_schools.png" decoding="async" width="400" height="351" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/85/Eight_founding_schools.png 1.5x" data-file-width="518" data-file-height="454" /></a><figcaption>The <a href="/wiki/Thermodynamicist" title="Thermodynamicist">thermodynamicists</a> of the original eight founding schools of thermodynamics. The schools with the most-lasting influence on the modern versions of thermodynamics are the Berlin school, particularly <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>'s 1865 textbook <i>The Mechanical Theory of Heat</i>, the Vienna school, with the <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> of <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a>, and the Gibbsian school at Yale University of <a href="/wiki/Willard_Gibbs" class="mw-redirect" title="Willard Gibbs">Willard Gibbs</a>' 1876 and his book <i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a></i> which launched <a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">chemical thermodynamics</a>.<sup id="cite_ref-auto_9-0" class="reference"><a href="#cite_note-auto-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></figcaption></figure><p>The <a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">history of thermodynamics</a> as a scientific discipline generally begins with <a href="/wiki/Otto_von_Guericke" title="Otto von Guericke">Otto von Guericke</a> who, in 1650, built and designed the world's first <a href="/wiki/Vacuum_pump" title="Vacuum pump">vacuum pump</a> and demonstrated a <a href="/wiki/Vacuum" title="Vacuum">vacuum</a> using his <a href="/wiki/Magdeburg_hemispheres" title="Magdeburg hemispheres">Magdeburg hemispheres</a>. Guericke was driven to make a vacuum to disprove <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the Anglo-Irish physicist and chemist <a href="/wiki/Robert_Boyle" title="Robert Boyle">Robert Boyle</a> had learned of Guericke's designs and, in 1656, in coordination with English scientist <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a>, built an air pump.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Using this pump, Boyle and Hooke noticed a correlation between <a href="/wiki/Pressure" title="Pressure">pressure</a>, <a href="/wiki/Temperature" title="Temperature">temperature</a>, and <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>. In time, <a href="/wiki/Boyle%27s_Law" class="mw-redirect" title="Boyle's Law">Boyle's Law</a> was formulated, which states that pressure and volume are <a href="/wiki/Inverse_proportion" class="mw-redirect" title="Inverse proportion">inversely proportional</a>. Then, in 1679, based on these concepts, an associate of Boyle's named <a href="/wiki/Denis_Papin" title="Denis Papin">Denis Papin</a> built a <a href="/wiki/Steam_digester" title="Steam digester">steam digester</a>, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated. </p><p>Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a <a href="/wiki/Piston" title="Piston">piston</a> and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer <a href="/wiki/Thomas_Savery" title="Thomas Savery">Thomas Savery</a> built the first engine, followed by <a href="/wiki/Thomas_Newcomen" title="Thomas Newcomen">Thomas Newcomen</a> in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time. </p><p>The fundamental concepts of <a href="/wiki/Heat_capacity" title="Heat capacity">heat capacity</a> and <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a>, which were necessary for the development of thermodynamics, were developed by Professor <a href="/wiki/Joseph_Black" title="Joseph Black">Joseph Black</a> at the University of Glasgow, where <a href="/wiki/James_Watt" title="James Watt">James Watt</a> was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the <a href="/wiki/Watt_steam_engine#Separate_condenser" title="Watt steam engine">external condenser</a> which resulted in a large increase in <a href="/wiki/Steam_engine" title="Steam engine">steam engine</a> efficiency.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Drawing on all the previous work led <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a>, the "father of thermodynamics", to publish <i><a href="/wiki/Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the Motive Power of Fire</a></i> (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the <a href="/wiki/Carnot_engine" class="mw-redirect" title="Carnot engine">Carnot engine</a>, the <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a>, and motive power. It marked the start of thermodynamics as a modern science.<sup id="cite_ref-Perrot_12-0" class="reference"><a href="#cite_note-Perrot-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The first thermodynamic textbook was written in 1859 by <a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">William Rankine</a>, originally trained as a physicist and a civil and mechanical engineering professor at the <a href="/wiki/University_of_Glasgow" title="University of Glasgow">University of Glasgow</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>, and <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">William Thomson</a> (Lord Kelvin). The foundations of statistical thermodynamics were set out by physicists such as <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>, <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a>, <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>, <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> and <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">J. Willard Gibbs</a>. </p><p>Clausius, who first stated the basic ideas of the second law in his paper "On the Moving Force of Heat",<sup id="cite_ref-Theory_of_Heat_3-1" class="reference"><a href="#cite_note-Theory_of_Heat-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> published in 1850, and is called "one of the founding fathers of thermodynamics",<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> introduced the concept of <a href="/wiki/Entropy" title="Entropy">entropy</a> in 1865. </p><p>During the years 1873–76 the American mathematical physicist <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Josiah Willard Gibbs</a> published a series of three papers, the most famous being <i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a></i>,<sup id="cite_ref-Gibbs_1876_15-0" class="reference"><a href="#cite_note-Gibbs_1876-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> in which he showed how <a href="/wiki/Thermodynamic_processes" class="mw-redirect" title="Thermodynamic processes">thermodynamic processes</a>, including <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>, could be graphically analyzed, by studying the <a href="/wiki/Energy" title="Energy">energy</a>, <a href="/wiki/Entropy" title="Entropy">entropy</a>, <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>, <a href="/wiki/Temperature" title="Temperature">temperature</a> and <a href="/wiki/Pressure" title="Pressure">pressure</a> of the <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a> in such a manner, one can determine if a process would occur spontaneously.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Also <a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Pierre Duhem</a> in the 19th century wrote about chemical thermodynamics.<sup id="cite_ref-Duhem_1886_17-0" class="reference"><a href="#cite_note-Duhem_1886-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> During the early 20th century, chemists such as <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a>, <a href="/wiki/Merle_Randall" title="Merle Randall">Merle Randall</a>,<sup id="cite_ref-Lewis_Randall_1923_18-0" class="reference"><a href="#cite_note-Lewis_Randall_1923-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/E._A._Guggenheim" class="mw-redirect" title="E. A. Guggenheim">E. A. Guggenheim</a><sup id="cite_ref-Guggenheim_1933_19-0" class="reference"><a href="#cite_note-Guggenheim_1933-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Guggenheim_1949/1967_20-0" class="reference"><a href="#cite_note-Guggenheim_1949/1967-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> applied the mathematical methods of Gibbs to the analysis of chemical processes. </p> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2></div> <p><i>Thermodynamics</i> has an intricate etymology.<sup id="cite_ref-eoht_21-0" class="reference"><a href="#cite_note-eoht-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>By a surface-level analysis, the word consists of two parts that can be traced back to Ancient Greek. Firstly, <i lang="en"><a href="https://en.wiktionary.org/wiki/thermo-#English" class="extiw" title="wikt:thermo-">thermo-</a></i> ("of heat"; used in words such as <i><a href="/wiki/Thermometer" title="Thermometer">thermometer</a></i>) can be traced back to the root <a href="https://en.wiktionary.org/wiki/%CE%B8%CE%AD%CF%81%CE%BC%CE%B7" class="extiw" title="wikt:θέρμη">θέρμη</a> <i>therme</i>, meaning "heat". Secondly, the word <i lang="en"><a href="https://en.wiktionary.org/wiki/dynamics#English" class="extiw" title="wikt:dynamics">dynamics</a></i> ("science of force [or power]")<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> can be traced back to the root <a href="https://en.wiktionary.org/wiki/%CE%B4%CF%8D%CE%BD%CE%B1%CE%BC%CE%B9%CF%82" class="extiw" title="wikt:δύναμις">δύναμις</a> <i>dynamis</i>, meaning "power".<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>In 1849, the adjective <i>thermo-dynamic</i> is used by William Thomson.<sup id="cite_ref-kelvin1849_24-0" class="reference"><a href="#cite_note-kelvin1849-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smith77_25-0" class="reference"><a href="#cite_note-smith77-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>In 1854, the noun <i>thermo-dynamics</i> is used by Thomson and William Rankine to represent the science of generalized heat engines.<sup id="cite_ref-smith77_25-1" class="reference"><a href="#cite_note-smith77-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-eoht_21-1" class="reference"><a href="#cite_note-eoht-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Pierre Perrot claims that the term <i>thermodynamics</i> was coined by <a href="/wiki/James_Joule" class="mw-redirect" title="James Joule">James Joule</a> in 1858 to designate the science of relations between heat and power,<sup id="cite_ref-Perrot_12-1" class="reference"><a href="#cite_note-Perrot-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> however, Joule never used that term, but used instead the term <i>perfect thermo-dynamic engine</i> in reference to Thomson's 1849<sup id="cite_ref-kelvin1849_24-1" class="reference"><a href="#cite_note-kelvin1849-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> phraseology.<sup id="cite_ref-eoht_21-2" class="reference"><a href="#cite_note-eoht-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Branches_of_thermodynamics">Branches of thermodynamics</h2></div> <p>The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems. </p> <div class="mw-heading mw-heading3"><h3 id="Classical_thermodynamics">Classical thermodynamics</h3></div> <p>Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>. The qualifier <i>classical</i> reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of <i>statistical mechanics</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Statistical_mechanics">Statistical mechanics</h3></div> <p><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a>, also known as statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum theory</a> at the microscopic level. </p> <div class="mw-heading mw-heading3"><h3 id="Chemical_thermodynamics">Chemical thermodynamics</h3></div> <p><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a> is the study of the interrelation of <a href="/wiki/Energy" title="Energy">energy</a> with <a href="/wiki/Chemical_reactions" class="mw-redirect" title="Chemical reactions">chemical reactions</a> or with a physical change of <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">state</a> within the confines of the <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>. The primary objective of chemical thermodynamics is determining the spontaneity of a given transformation.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Equilibrium_thermodynamics">Equilibrium thermodynamics</h3></div> <p><a href="/wiki/Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium thermodynamics</a> is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings. </p> <div class="mw-heading mw-heading3"><h3 id="Non-equilibrium_thermodynamics">Non-equilibrium thermodynamics</h3></div> <p><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium thermodynamics</a> is a branch of thermodynamics that deals with systems that are not in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods. </p> <div class="mw-heading mw-heading2"><h2 id="Laws_of_thermodynamics">Laws of thermodynamics</h2></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws of thermodynamics</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Carnot_engine_(hot_body_-_working_body_-_cold_body).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Carnot_engine_%28hot_body_-_working_body_-_cold_body%29.jpg/300px-Carnot_engine_%28hot_body_-_working_body_-_cold_body%29.jpg" decoding="async" width="300" height="320" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/c7/Carnot_engine_%28hot_body_-_working_body_-_cold_body%29.jpg 1.5x" data-file-width="400" data-file-height="427" /></a><figcaption>Annotated color version of the original 1824 <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a> showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a></figcaption></figure> <p>Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following. </p> <div class="mw-heading mw-heading3"><h3 id="Zeroth_law">Zeroth law</h3></div> <p>The <a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">zeroth law of thermodynamics</a> states: <i>If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.</i> </p><p>This statement implies that thermal equilibrium is an <a href="/wiki/Equivalence_relation" title="Equivalence relation">equivalence relation</a> on the set of <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic systems</a> under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. <a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a>) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same <a href="/wiki/Temperature" title="Temperature">temperature</a>, it is not necessary to bring them into contact and measure any changes of their observable properties in time.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers. </p><p>The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the <i>zeroth law</i>. </p> <div class="mw-heading mw-heading3"><h3 id="First_law">First law</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg/170px-Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg" decoding="async" width="170" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg/255px-Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg/340px-Kurzzeitfotografie_sektkorken_06-19-s02_2017-09-03_01_hinnerk-ruemenapf_exif.jpg 2x" data-file-width="2653" data-file-height="4053" /></a><figcaption>Opening a bottle of <a href="/wiki/Sparkling_wine" title="Sparkling wine">sparkling wine</a> (<a href="/wiki/High-speed_photography" title="High-speed photography">high-speed photography</a>). The sudden drop of pressure causes a huge drop of temperature. The moisture in the air freezes, creating a smoke of tiny ice crystals.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a> states: <i>In a process without transfer of matter, the change in <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a>,</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 \Delta U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4716a2c49bbbe155e8b399117ca78342e802cbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.718ex; height:2.176ex;" alt="{\displaystyle \Delta U}"></span><i>, of a <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a> is equal to the energy gained as heat,</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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span><i>, less the thermodynamic work,</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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span><i>, done by the system on its surroundings.</i><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>nb 1<span class="cite-bracket">]</span></a></sup> </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 \Delta U=Q-W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mo>−</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q-W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e02cf059e743ecc2291c2fe20291b44cc977ccde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.931ex; height:2.509ex;" alt="{\displaystyle \Delta U=Q-W}"></span>.</dd></dl> <p>where <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 U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4716a2c49bbbe155e8b399117ca78342e802cbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.718ex; height:2.176ex;" alt="{\displaystyle \Delta U}"></span> denotes the change in the internal energy of a <a href="/wiki/Thermodynamic_system#Closed_system" title="Thermodynamic system">closed system</a> (for which heat or work through the system boundary are possible, but matter transfer is not possible), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> denotes the quantity of energy supplied <i>to</i> the system as heat, and <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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> denotes the amount of thermodynamic work done <i>by</i> the system <i>on</i> its surroundings. An equivalent statement is that <a href="/wiki/Perpetual_motion_machines" class="mw-redirect" title="Perpetual motion machines">perpetual motion machines</a> of the first kind are impossible; work <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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> done by a system on its surrounding requires that the system's internal energy <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> decrease or be consumed, so that the amount of internal energy lost by that work must be resupplied as heat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> by an external energy source or as work by an external machine acting on the system (so that <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> is recovered) to make the system work continuously. </p><p>For processes that include transfer of matter, a further statement is needed: <i>With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then</i> </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 U_{0}=U_{1}+U_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{0}=U_{1}+U_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b308bd0e9e4b5c9fe1b75b343bb265a10a66f4cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.864ex; height:2.509ex;" alt="{\displaystyle U_{0}=U_{1}+U_{2}}"></span>,</dd></dl> <p><i>where</i> <span class="texhtml"><i>U</i><sub>0</sub></span> <i>denotes the internal energy of the combined system, and</i> <span class="texhtml"><i>U</i><sub>1</sub></span> <i>and</i> <span class="texhtml"><i>U</i><sub>2</sub></span> <i>denote the internal energies of the respective separated systems.</i> </p><p>Adapted for thermodynamics, this law is an expression of the principle of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>Internal energy is a principal property of the <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">thermodynamic state</a>, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a <a href="/wiki/State_function" title="State function">function of state</a>, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state. </p> <div class="mw-heading mw-heading3"><h3 id="Second_law">Second law</h3></div> <p>A traditional version of the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a> states: <i>Heat does not spontaneously flow from a colder body to a hotter body.</i> </p><p>The second law refers to a system of matter and radiation, initially with inhomogeneities in temperature, pressure, chemical potential, and other <a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">intensive properties</a>, that are due to internal 'constraints', or impermeable rigid walls, within it, or to externally imposed forces. The law observes that, when the system is isolated from the outside world and from those forces, there is a definite thermodynamic quantity, its <a href="/wiki/Entropy" title="Entropy">entropy</a>, that increases as the constraints are removed, eventually reaching a maximum value at thermodynamic equilibrium, when the inhomogeneities practically vanish. For systems that are initially far from thermodynamic equilibrium, though several have been proposed, there is known no general physical principle that determines the rates of approach to thermodynamic equilibrium, and thermodynamics does not deal with such rates. The many versions of the second law all express the general <a href="/wiki/Irreversibility" class="mw-redirect" title="Irreversibility">irreversibility</a> of the transitions involved in systems approaching thermodynamic equilibrium. </p><p>In macroscopic thermodynamics, the second law is a basic observation applicable to any actual thermodynamic process; in statistical thermodynamics, the second law is postulated to be a consequence of molecular chaos. </p> <div class="mw-heading mw-heading3"><h3 id="Third_law">Third law</h3></div> <p>The <a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">third law of thermodynamics</a> states: <i>As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.</i> </p><p>This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching <a href="/wiki/Absolute_zero" title="Absolute zero">absolute zero</a> of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes". </p><p>Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15 °C (degrees Celsius), or −459.67 °F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees <a href="/wiki/Rankine_scale" title="Rankine scale">Rankine</a>). </p> <div class="mw-heading mw-heading2"><h2 id="System_models">System models</h2></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:System_boundary.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/System_boundary.svg/200px-System_boundary.svg.png" decoding="async" width="200" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/System_boundary.svg/300px-System_boundary.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/System_boundary.svg/400px-System_boundary.svg.png 2x" data-file-width="931" data-file-height="818" /></a><figcaption>A diagram of a generic thermodynamic system</figcaption></figure> <p>An important concept in thermodynamics is the <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a>, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the <a href="/wiki/Environment_(systems)" title="Environment (systems)"><i>surroundings</i></a>. A system is separated from the remainder of the universe by a <a href="/wiki/Boundary_(thermodynamic)" class="mw-redirect" title="Boundary (thermodynamic)"><i>boundary</i></a> which may be a physical or notional, but serve to confine the system to a finite volume. Segments of the <i>boundary</i> are often described as <i>walls</i>; they have respective defined 'permeabilities'. Transfers of energy as <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, or as <a href="/wiki/Heat" title="Heat">heat</a>, or of <a href="/wiki/Matter" title="Matter">matter</a>, between the system and the surroundings, take place through the walls, according to their respective permeabilities. </p><p>Matter or energy that pass across the boundary so as to effect a change in the internal energy of the system need to be accounted for in the energy balance equation. The volume contained by the walls can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a <a href="/wiki/Steam_engine" title="Steam engine">steam engine</a>, such as Sadi Carnot defined in 1824. The system could also be just one <a href="/wiki/Nuclide" title="Nuclide">nuclide</a> (i.e. a system of <a href="/wiki/Quark" title="Quark">quarks</a>) as hypothesized in <a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">quantum thermodynamics</a>. When a looser viewpoint is adopted, and the requirement of thermodynamic equilibrium is dropped, the system can be the body of a <a href="/wiki/Tropical_cyclone" title="Tropical cyclone">tropical cyclone</a>, such as <a href="/wiki/Kerry_Emanuel" title="Kerry Emanuel">Kerry Emanuel</a> theorized in 1986 in the field of <a href="/wiki/Atmospheric_thermodynamics" title="Atmospheric thermodynamics">atmospheric thermodynamics</a>, or the <a href="/wiki/Event_horizon" title="Event horizon">event horizon</a> of a <a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">black hole</a>. </p><p>Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle. </p><p>Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries: </p> <table class="wikitable" style="text-align: center;"> <caption>Interactions of thermodynamic systems </caption> <tbody><tr> <th>Type of system </th> <th><a href="/wiki/Mass_flow_rate" title="Mass flow rate">Mass flow</a> </th> <th><a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">Work</a> </th> <th><a href="/wiki/Heat" title="Heat">Heat</a> </th></tr> <tr> <td><a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">Open</a> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td></tr> <tr> <td><a href="/wiki/Thermodynamic_system#Closed_system" title="Thermodynamic system">Closed</a> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td></tr> <tr> <td><a href="/wiki/Thermally_isolated_system" title="Thermally isolated system">Thermally isolated</a> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td></tr> <tr> <td><a href="/wiki/Mechanically_isolated_system" title="Mechanically isolated system">Mechanically isolated</a> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Green tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/13px-Green_check.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/20px-Green_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Green_check.svg/26px-Green_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display:none">Y</span> </td></tr> <tr> <td><a href="/wiki/Isolated_system" title="Isolated system">Isolated</a> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td> <td><span typeof="mw:File"><span><img alt="Red X" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/13px-Red_x.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/20px-Red_x.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Red_x.svg/26px-Red_x.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><span style="display: none;">N</span> </td></tr></tbody></table> <p>As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a <a href="/wiki/State_(thermodynamic)" class="mw-redirect" title="State (thermodynamic)">state</a> of <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. </p><p>Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be <a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">reversible processes</a>. </p> <div class="mw-heading mw-heading2"><h2 id="States_and_processes">States and processes</h2></div> <p>When a system is at equilibrium under a given set of conditions, it is said to be in a definite <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">thermodynamic state</a>. The state of the system can be described by a number of <a href="/wiki/State_function" title="State function">state quantities</a> that do not depend on the process by which the system arrived at its state. They are called <a href="/wiki/Intensive_variable" class="mw-redirect" title="Intensive variable">intensive variables</a> or <a href="/wiki/Extensive_variable" class="mw-redirect" title="Extensive variable">extensive variables</a> according to how they change when the size of the system changes. The properties of the system can be described by an <a href="/wiki/Equation_of_state" title="Equation of state">equation of state</a> which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant. </p><p>A <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">thermodynamic process</a> may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by <a href="/wiki/Process_function" title="Process function">process quantities</a>. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">conjugate</a> pair. </p><p>Several commonly studied thermodynamic processes are: </p> <ul><li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic process</a>: occurs without loss or gain of energy by <a href="/wiki/Heat" title="Heat">heat</a></li> <li><a href="/wiki/Isenthalpic_process" title="Isenthalpic process">Isenthalpic process</a>: occurs at a constant <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a></li> <li><a href="/wiki/Isentropic_process" title="Isentropic process">Isentropic process</a>: a reversible adiabatic process, occurs at a constant <a href="/wiki/Entropy" title="Entropy">entropy</a></li> <li><a href="/wiki/Isobaric_process" title="Isobaric process">Isobaric process</a>: occurs at constant <a href="/wiki/Pressure" title="Pressure">pressure</a></li> <li><a href="/wiki/Isochoric_process" title="Isochoric process">Isochoric process</a>: occurs at constant <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a> (also called isometric/isovolumetric)</li> <li><a href="/wiki/Isothermal_process" title="Isothermal process">Isothermal process</a>: occurs at a constant <a href="/wiki/Temperature" title="Temperature">temperature</a></li> <li><a href="/wiki/Steady_state" title="Steady state">Steady state process</a>: occurs without a change in the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Instrumentation">Instrumentation</h2></div> <p>There are two types of <a href="/wiki/Thermodynamic_instruments" title="Thermodynamic instruments">thermodynamic instruments</a>, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a>. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the <a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">zeroth law</a> states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Maxwell</a> in 1872, asserts that it is possible to measure temperature. An idealized <a href="/wiki/Thermometer" title="Thermometer">thermometer</a> is a sample of an ideal gas at constant pressure. From the <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a> <i>pV=nRT</i>, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a <a href="/wiki/Barometer" title="Barometer">barometer</a> may also be constructed from a sample of an ideal gas held at a constant temperature. A <a href="/wiki/Calorimeter" title="Calorimeter">calorimeter</a> is a device which is used to measure and define the internal energy of a system. </p><p>A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. The ocean can act as temperature reservoir when used to cool power plants. </p> <div class="mw-heading mw-heading2"><h2 id="Conjugate_variables">Conjugate variables</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a></div> <p>The central concept of thermodynamics is that of <a href="/wiki/Energy" title="Energy">energy</a>, the ability to do <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>. By the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First Law</a>, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, for example, energy transfer equals the product of the force applied to a body and the resulting displacement. </p><p><a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a>, the second being akin to the resulting "displacement", and the product of the two equaling the amount of energy transferred. The common conjugate variables are: </p> <ul><li><a href="/wiki/Pressure" title="Pressure">Pressure</a>-<a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a> (the <a href="/wiki/Mechanics" title="Mechanics">mechanical</a> parameters);</li> <li><a href="/wiki/Temperature" title="Temperature">Temperature</a>-<a href="/wiki/Entropy" title="Entropy">entropy</a> (thermal parameters);</li> <li><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a>-<a href="/wiki/Particle_number" title="Particle number">particle number</a> (material parameters).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Potentials">Potentials</h2></div> <p><a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">Thermodynamic potentials</a> are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively. Thermodynamic potentials cannot be measured in laboratories, but can be computed using molecular thermodynamics.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>The five most well known potentials are: </p> <table class="wikitable"> <tbody><tr> <th>Name </th> <th>Symbol </th> <th>Formula </th> <th>Natural variables </th></tr> <tr> <td><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a> </td> <td style="text-align:center;"><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> </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 \int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf642ff95cbe71aacf0082c0cdab27c96089311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:31.296ex; height:7.509ex;" alt="{\displaystyle \int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)}"></span> </td> <td style="text-align:center;"><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,V,\{N_{i}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S,V,\{N_{i}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f5040c18acf7c4b9078e23be03181584fd2a043" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.345ex; height:2.843ex;" alt="{\displaystyle S,V,\{N_{i}\}}"></span> </td></tr> <tr> <td><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8358d6aaeb8a833c863c47da5aaeb392e379da7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.758ex; height:2.343ex;" alt="{\displaystyle U-TS}"></span> </td> <td style="text-align:center;"><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,V,\{N_{i}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T,V,\{N_{i}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a5b26f6395cbc33a906c4732b51ab323b7eb9bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.482ex; height:2.843ex;" alt="{\displaystyle T,V,\{N_{i}\}}"></span> </td></tr> <tr> <td><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a> </td> <td style="text-align:center;"><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> </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 U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8e077195ce5861be98320e9ef98978335d34433" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.58ex; height:2.509ex;" alt="{\displaystyle U+pV}"></span> </td> <td style="text-align:center;"><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,p,\{N_{i}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S,p,\{N_{i}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53ce76f7fbf9bd41d6b694f5ebc4f54398843860" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.727ex; height:2.843ex;" alt="{\displaystyle S,p,\{N_{i}\}}"></span> </td></tr> <tr> <td><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U+pV-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U+pV-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3802c0bf0302bb5b9854b57f9e81154b7043bb22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.556ex; height:2.509ex;" alt="{\displaystyle U+pV-TS}"></span> </td> <td style="text-align:center;"><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,p,\{N_{i}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T,p,\{N_{i}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82008ddebd791da96f2a6e9138ee38d5387d61ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.864ex; height:2.843ex;" alt="{\displaystyle T,p,\{N_{i}\}}"></span> </td></tr> <tr> <td><a href="/wiki/Grand_potential" title="Grand potential">Landau potential, or <br />grand potential</a> </td> <td style="text-align:center;"><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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></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 \Phi _{\text{G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{\text{G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0226578737e0aaa90a4e31f17d906a5787bf0f82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.2ex; height:2.509ex;" alt="{\displaystyle \Phi _{\text{G}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U-TS-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U-TS-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8833665cc5e0872196dec6a80f233fb751b131bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.567ex; height:2.343ex;" alt="{\displaystyle U-TS-}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69f671f4400a9759635c041ddd93cd2c02d8299f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:3.742ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\,}"></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 \mu _{i}N_{i}}"> <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> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}N_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/858d9c67f6b7cdb725d730ff6ec685afa8ec7c08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.867ex; height:2.676ex;" alt="{\displaystyle \mu _{i}N_{i}}"></span> </td> <td style="text-align:center;"><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,V,\{\mu _{i}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T,V,\{\mu _{i}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c0ffc858a2f9b88367920d66d6e26bca6fffbd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.018ex; height:2.843ex;" alt="{\displaystyle T,V,\{\mu _{i}\}}"></span> </td></tr></tbody></table> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> is the <a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">temperature</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 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> the <a href="/wiki/Entropy" title="Entropy">entropy</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> the <a href="/wiki/Pressure" title="Pressure">pressure</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> the <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> the number of particles in the system, and <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/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> is the count of particles types in the system. </p><p>Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through <a href="/wiki/Legendre_transformation" title="Legendre transformation">Legendre transformation</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Axiomatic_thermodynamics">Axiomatic thermodynamics</h2></div> <p>Axiomatic thermodynamics is a <a href="/wiki/Mathematical_discipline" class="mw-redirect" title="Mathematical discipline">mathematical discipline</a> that aims to describe thermodynamics in terms of rigorous <a href="/wiki/Axiom" title="Axiom">axioms</a>, for example by finding a mathematically rigorous way to express the familiar <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>. </p><p>The first attempt at an axiomatic theory of thermodynamics was <a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a>'s 1909 work <i>Investigations on the Foundations of Thermodynamics</i>, which made use of <a href="/wiki/Integrability_conditions_for_differential_systems" title="Integrability conditions for differential systems">Pfaffian systems</a> and the concept of <a href="/wiki/Adiabatic_accessibility" title="Adiabatic accessibility">adiabatic accessibility</a>, a notion that was introduced by Carathéodory himself.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-frankel_38-0" class="reference"><a href="#cite_note-frankel-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> In this formulation, thermodynamic concepts such as <a href="/wiki/Heat" title="Heat">heat</a>, <a href="/wiki/Entropy" title="Entropy">entropy</a>, and <a href="/wiki/Temperature" title="Temperature">temperature</a> are derived from quantities that are more directly measurable.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Theories that came after, differed in the sense that they made assumptions regarding <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">thermodynamic processes</a> with arbitrary initial and final states, as opposed to considering only neighboring states. </p> <div class="mw-heading mw-heading2"><h2 id="Applied_fields">Applied fields</h2></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Atmospheric_thermodynamics" title="Atmospheric thermodynamics">Atmospheric thermodynamics</a></li> <li><a href="/wiki/Biological_thermodynamics" title="Biological thermodynamics">Biological thermodynamics</a></li> <li><a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">Black hole thermodynamics</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li> <li><a href="/wiki/Classical_thermodynamics" class="mw-redirect" title="Classical thermodynamics">Classical thermodynamics</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium thermodynamics</a></li> <li><a href="/wiki/Industrial_ecology" title="Industrial ecology">Industrial ecology</a> (re: <a href="/wiki/Exergy" title="Exergy">Exergy</a>)</li> <li><a href="/wiki/Maximum_entropy_thermodynamics" title="Maximum entropy thermodynamics">Maximum entropy thermodynamics</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium thermodynamics</a></li> <li><a href="/wiki/Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy of thermal and statistical physics</a></li> <li><a href="/wiki/Psychrometrics" title="Psychrometrics">Psychrometrics</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li> <li><a href="/wiki/Statistical_thermodynamics" class="mw-redirect" title="Statistical thermodynamics">Statistical thermodynamics</a>, i.e. Statistical mechanics</li> <li><a href="/wiki/Thermoeconomics" title="Thermoeconomics">Thermoeconomics</a></li> <li><a href="/wiki/Polymer_chemistry" title="Polymer chemistry">Polymer chemistry</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a 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<ul><li><a href="/wiki/Thermodynamic_process_path" class="mw-redirect" title="Thermodynamic process path">Thermodynamic process path</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Lists_and_timelines">Lists and timelines</h3></div> <ul><li><a href="/wiki/List_of_important_publications_in_physics#Thermodynamics" title="List of important publications in physics">List of important publications in thermodynamics</a><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/MOS:BROKENSECTIONLINKS" class="mw-redirect" title="MOS:BROKENSECTIONLINKS"><span title="The anchor (Thermodynamics) has been deleted. (2024-06-17)">broken anchor</span></a></i>]</sup></li> <li><a href="/wiki/List_of_textbooks_in_statistical_mechanics" class="mw-redirect" title="List of textbooks in statistical mechanics">List of textbooks on thermodynamics and statistical mechanics</a></li> <li><a href="/wiki/List_of_thermal_conductivities" title="List of thermal conductivities">List of thermal conductivities</a></li> <li><a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">List of thermodynamic properties</a></li> <li><a href="/wiki/Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></li> <li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">Timeline of thermodynamics</a></li> <li><a href="/wiki/Thermodynamic_equations" title="Thermodynamic equations">Thermodynamic equations</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">The sign convention (Q is heat supplied <i>to</i> the system as, W is work done <i>by</i> the system) is that of <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>. The opposite sign convention is customary in chemical thermodynamics.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFClausius1850" class="citation book cs1">Clausius, Rudolf (1850). <i>On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat</i>. Poggendorff's Annalen der Physik, LXXIX (Dover Reprint). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-59065-3" title="Special:BookSources/978-0-486-59065-3"><bdi>978-0-486-59065-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+Motive+Power+of+Heat%2C+and+on+the+Laws+which+can+be+deduced+from+it+for+the+Theory+of+Heat&rft.pub=Poggendorff%27s+Annalen+der+Physik%2C+LXXIX+%28Dover+Reprint%29&rft.date=1850&rft.isbn=978-0-486-59065-3&rft.aulast=Clausius&rft.aufirst=Rudolf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-kelvin1854-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-kelvin1854_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliam_Thomson,_LL.D._D.C.L.,_F.R.S.1882" class="citation book cs1">William Thomson, LL.D. D.C.L., F.R.S. (1882). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100"><i>Mathematical and Physical Papers</i></a>. Vol. 1. London, Cambridge: C.J. Clay, M.A. & Son, Cambridge University Press. p. 232. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-598-96004-7" title="Special:BookSources/978-0-598-96004-7"><bdi>978-0-598-96004-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210418220146/https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100">Archived</a> from the original on 18 April 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">2 November</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+and+Physical+Papers&rft.place=London%2C+Cambridge&rft.pages=232&rft.pub=C.J.+Clay%2C+M.A.+%26+Son%2C+Cambridge+University+Press&rft.date=1882&rft.isbn=978-0-598-96004-7&rft.au=William+Thomson%2C+LL.D.+D.C.L.%2C+F.R.S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnWMSAAAAIAAJ%26q%3DOn%2Ban%2BAbsolute%2BThermometric%2BScale%2BFounded%2Bon%2BCarnot%25E2%2580%2599s%2BTheory%26pg%3DPA100&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-Theory_of_Heat-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Theory_of_Heat_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Theory_of_Heat_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1867" class="citation book cs1">Clausius, R. (1867). <a rel="nofollow" class="external text" href="https://archive.org/details/mechanicaltheor04claugoog"><i>The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies</i></a>. London: John van Voorst<span class="reference-accessdate">. Retrieved <span class="nowrap">19 June</span> 2012</span>. <q>editions:PwR_Sbkwa8IC.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mechanical+Theory+of+Heat+%E2%80%93+with+its+Applications+to+the+Steam+Engine+and+to+Physical+Properties+of+Bodies&rft.place=London&rft.pub=John+van+Voorst&rft.date=1867&rft.aulast=Clausius&rft.aufirst=R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmechanicaltheor04claugoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> Contains English translations of many of his other works.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1870" class="citation journal cs1">Clausius, RJE (1870). "On a Mechanical Theorem Applicable to Heat". <i>Philosophical Magazine</i>. 4th Series. <b>40</b>: 122–127.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=On+a+Mechanical+Theorem+Applicable+to+Heat&rft.volume=40&rft.pages=122-127&rft.date=1870&rft.aulast=Clausius&rft.aufirst=RJE&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVan_Ness,_H.C.1983" class="citation book cs1">Van Ness, H.C. (1983) [1969]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/understandingthe00vann"><i>Understanding Thermodynamics</i></a></span>. Dover Publications, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486632773" title="Special:BookSources/9780486632773"><bdi>9780486632773</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/8846081">8846081</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+Thermodynamics&rft.pub=Dover+Publications%2C+Inc.&rft.date=1983&rft_id=info%3Aoclcnum%2F8846081&rft.isbn=9780486632773&rft.au=Van+Ness%2C+H.C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Funderstandingthe00vann&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDugdale,_J.S.1998" class="citation book cs1">Dugdale, J.S. (1998). <i>Entropy and its Physical Meaning</i>. Taylor and Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7484-0569-5" title="Special:BookSources/978-0-7484-0569-5"><bdi>978-0-7484-0569-5</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/36457809">36457809</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Entropy+and+its+Physical+Meaning&rft.pub=Taylor+and+Francis&rft.date=1998&rft_id=info%3Aoclcnum%2F36457809&rft.isbn=978-0-7484-0569-5&rft.au=Dugdale%2C+J.S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmithVan_NessAbbott2005" class="citation book cs1">Smith, J.M.; Van Ness, H.C.; Abbott, M.M. (2005). <a rel="nofollow" class="external text" href="http://www3.ub.tu-berlin.de/ihv/000471510.pdf"><i>Introduction to Chemical Engineering Thermodynamics</i></a> <span class="cs1-format">(PDF)</span>. Vol. 27 (7th ed.). p. 584. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1950JChEd..27..584S">1950JChEd..27..584S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed027p584.3">10.1021/ed027p584.3</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-310445-4" title="Special:BookSources/978-0-07-310445-4"><bdi>978-0-07-310445-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/56491111">56491111</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Chemical+Engineering+Thermodynamics&rft.pages=584&rft.edition=7th&rft.date=2005&rft_id=info%3Aoclcnum%2F56491111&rft_id=info%3Adoi%2F10.1021%2Fed027p584.3&rft_id=info%3Abibcode%2F1950JChEd..27..584S&rft.isbn=978-0-07-310445-4&rft.aulast=Smith&rft.aufirst=J.M.&rft.au=Van+Ness%2C+H.C.&rft.au=Abbott%2C+M.M.&rft_id=http%3A%2F%2Fwww3.ub.tu-berlin.de%2Fihv%2F000471510.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaynie,_Donald_T.2001" class="citation book cs1">Haynie, Donald T. (2001). <i>Biological Thermodynamics</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-79549-4" title="Special:BookSources/978-0-521-79549-4"><bdi>978-0-521-79549-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/43993556">43993556</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biological+Thermodynamics&rft.pub=Cambridge+University+Press&rft.date=2001&rft_id=info%3Aoclcnum%2F43993556&rft.isbn=978-0-521-79549-4&rft.au=Haynie%2C+Donald+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-auto-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-auto_9-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.eoht.info/page/Schools+of+thermodynamics">Schools of thermodynamics</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171207151102/http://www.eoht.info/page/Schools+of+thermodynamics">Archived</a> 7 December 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – EoHT.info.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPartington,_J.R.1989" class="citation book cs1"><a href="/wiki/J._R._Partington" title="J. R. Partington">Partington, J.R.</a> (1989). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/shorthistoryofch0000part_q6h4"><i>A Short History of Chemistry</i></a></span>. Dover. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/19353301">19353301</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Short+History+of+Chemistry&rft.pub=Dover&rft.date=1989&rft_id=info%3Aoclcnum%2F19353301&rft.au=Partington%2C+J.R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fshorthistoryofch0000part_q6h4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</span> </li> <li id="cite_note-Perrot-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Perrot_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Perrot_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPerrot,_Pierre1998" class="citation book cs1">Perrot, Pierre (1998). <i>A to Z of Thermodynamics</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856552-9" title="Special:BookSources/978-0-19-856552-9"><bdi>978-0-19-856552-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/123283342">123283342</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+to+Z+of+Thermodynamics&rft.pub=Oxford+University+Press&rft.date=1998&rft_id=info%3Aoclcnum%2F123283342&rft.isbn=978-0-19-856552-9&rft.au=Perrot%2C+Pierre&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCengel,_Yunus_A.Boles,_Michael_A.2005" class="citation book cs1">Cengel, Yunus A.; Boles, Michael A. (2005). <i>Thermodynamics – an Engineering Approach</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-310768-4" title="Special:BookSources/978-0-07-310768-4"><bdi>978-0-07-310768-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+%E2%80%93+an+Engineering+Approach&rft.pub=McGraw-Hill&rft.date=2005&rft.isbn=978-0-07-310768-4&rft.au=Cengel%2C+Yunus+A.&rft.au=Boles%2C+Michael+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCardwell,_D.S.L.1971" class="citation cs2">Cardwell, D.S.L. (1971), <i>From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age</i>, London: Heinemann, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-435-54150-7" title="Special:BookSources/978-0-435-54150-7"><bdi>978-0-435-54150-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Watt+to+Clausius%3A+The+Rise+of+Thermodynamics+in+the+Early+Industrial+Age&rft.place=London&rft.pub=Heinemann&rft.date=1971&rft.isbn=978-0-435-54150-7&rft.au=Cardwell%2C+D.S.L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-Gibbs_1876-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gibbs_1876_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs,_Willard,_J.1874–1878" class="citation book cs1">Gibbs, Willard, J. (1874–1878). <a rel="nofollow" class="external text" href="https://archive.org/details/transactions03conn"><i>Transactions of the Connecticut Academy of Arts and Sciences</i></a>. Vol. III. New Haven. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/transactions03conn/page/108">108</a>–248, 343–524.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transactions+of+the+Connecticut+Academy+of+Arts+and+Sciences&rft.pages=108-248%2C+343-524&rft.pub=New+Haven&rft.date=1874%2F1878&rft.au=Gibbs%2C+Willard%2C+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftransactions03conn&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs,_Willard1993" class="citation book cs1">Gibbs, Willard (1993). <i>The Scientific Papers of J. 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Ox Bow Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-918024-77-0" title="Special:BookSources/978-0-918024-77-0"><bdi>978-0-918024-77-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/27974820">27974820</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Scientific+Papers+of+J.+Willard+Gibbs%2C+Volume+One%3A+Thermodynamics&rft.pub=Ox+Bow+Press&rft.date=1993&rft_id=info%3Aoclcnum%2F27974820&rft.isbn=978-0-918024-77-0&rft.au=Gibbs%2C+Willard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-Duhem_1886-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Duhem_1886_17-0">^</a></b></span> <span class="reference-text">Duhem, P.M.M. (1886). <i>Le Potential Thermodynamique et ses Applications</i>, Hermann, Paris.</span> </li> <li id="cite_note-Lewis_Randall_1923-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lewis_Randall_1923_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewisRandall1923" class="citation book cs1">Lewis, Gilbert N.; Randall, Merle (1923). <a rel="nofollow" class="external text" href="https://archive.org/details/thermodynamicsfr00gnle"><i>Thermodynamics and the Free Energy of Chemical Substances</i></a>. McGraw-Hill Book Co. Inc.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+and+the+Free+Energy+of+Chemical+Substances&rft.pub=McGraw-Hill+Book+Co.+Inc.&rft.date=1923&rft.aulast=Lewis&rft.aufirst=Gilbert+N.&rft.au=Randall%2C+Merle&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fthermodynamicsfr00gnle&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-Guggenheim_1933-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Guggenheim_1933_19-0">^</a></b></span> <span class="reference-text">Guggenheim, E.A. (1933). <i>Modern Thermodynamics by the Methods of J.W. Gibbs</i>, Methuen, London.</span> </li> <li id="cite_note-Guggenheim_1949/1967-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Guggenheim_1949/1967_20-0">^</a></b></span> <span class="reference-text">Guggenheim, E.A. (1949/1967). <i>Thermodynamics. An Advanced Treatment for Chemists and Physicists</i>, 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</span> </li> <li id="cite_note-eoht-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-eoht_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-eoht_21-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-eoht_21-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.eoht.info/page/Thermodynamics+(etymology)">"Thermodynamics (etymology)"</a>. EoHT.info. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231029004136/https://www.eoht.info/page/Thermodynamics%20(etymology)">Archived</a> from the original on 29 October 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">29 October</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Thermodynamics+%28etymology%29&rft.pub=EoHT.info&rft_id=https%3A%2F%2Fwww.eoht.info%2Fpage%2FThermodynamics%2B%28etymology%29&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThompson1910" class="citation book cs1">Thompson, Silvanus (1910). <a rel="nofollow" class="external text" href="https://archive.org/details/b31360403_0001"><i>The Life of William Thomson, Baron Kelvin of Largs</i></a>. Vol. 1. MacMillan and Co., Limited. p. <a rel="nofollow" class="external text" href="https://archive.org/details/b31360403_0001/page/241">241</a>. <q>the fundamental subject of Natural Philosophy is Dynamics, or the <i>science of force</i> .... Every phenomenon in nature is a manifestation of force.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Life+of+William+Thomson%2C+Baron+Kelvin+of+Largs&rft.pages=241&rft.pub=MacMillan+and+Co.%2C+Limited&rft.date=1910&rft.aulast=Thompson&rft.aufirst=Silvanus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fb31360403_0001&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDonald_T._Haynie2008" class="citation book cs1">Donald T. 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Cambridge University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/biologicalthermo0000hayn/page/26">26</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biological+Thermodynamics&rft.pages=26&rft.edition=2&rft.pub=Cambridge+University+Press&rft.date=2008&rft.au=Donald+T.+Haynie&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbiologicalthermo0000hayn&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-kelvin1849-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-kelvin1849_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-kelvin1849_24-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." <i>Transactions of the Edinburg Royal Society, XVI. 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(1977). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41133471">"William Thomson and the Creation of Thermodynamics: 1840-1855"</a>. <i>Archive for History of Exact Sciences</i>. <b>16</b> (3): 231–288. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00328156">10.1007/BF00328156</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0003-9519">0003-9519</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41133471">41133471</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:36609995">36609995</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=William+Thomson+and+the+Creation+of+Thermodynamics%3A+1840-1855&rft.volume=16&rft.issue=3&rft.pages=231-288&rft.date=1977&rft.issn=0003-9519&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A36609995%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41133471%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1007%2FBF00328156&rft.aulast=Smith&rft.aufirst=Crosbie+W.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41133471&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlotz2008" class="citation book cs1">Klotz, Irving (2008). <i>Chemical Thermodynamics: Basic Theory and Methods</i>. 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IOP Publishing, Bristol, UK. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020tcsp.book.....P">2020tcsp.book.....P</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+of+Complex+Systems%3A+Principles+and+applications.&rft.pub=IOP+Publishing%2C+Bristol%2C+UK.&rft.date=2020&rft_id=info%3Abibcode%2F2020tcsp.book.....P&rft.aulast=Pokrovskii&rft.aufirst=Vladimir&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">Moran, Michael J. and Howard N. Shapiro, 2008. <i>Fundamentals of Engineering Thermodynamics</i>. 6th ed. Wiley and Sons: 16.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.chemistryviews.org/details/ezine/889289/Sparkling_Wine_Champagne__Co__Part_2/">"Sparkling Wine, Champagne & Co - Part 2"</a>. <i>Sparkling Wine, Champagne & Co</i>. Chemistry Europe (chemistryviews.org). 17 December 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">17 April</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Sparkling+Wine%2C+Champagne+%26+Co&rft.atitle=Sparkling+Wine%2C+Champagne+%26+Co+-+Part+2&rft.date=2010-12-17&rft_id=https%3A%2F%2Fwww.chemistryviews.org%2Fdetails%2Fezine%2F889289%2FSparkling_Wine_Champagne__Co__Part_2%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">Klaus Roth: <i>Sekt, Champagner & Co. So prickelnd kann Chemie sein</i> in <i>Chemie unserer Zeit</i> 8. Dezember 2009: Vol. 43, Issue 6, S. 418-432 <a href="//doi.org/10.1002/ciuz.200900520" class="extiw" title="doi:10.1002/ciuz.200900520">doi:10.1002/ciuz.200900520</a></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">Klaus Roth: <i>Chemische Köstlichkeiten</i>, Wiley-VCH Verlag GmbH & Co. KGaA, 2010, ISBN 978-3527327522, S. 47</span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text">Bailyn, M. (1994). <i>A Survey of Thermodynamics</i>, American Institute of Physics, AIP Press, Woodbury NY, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0883187973" title="Special:BookSources/0883187973">0883187973</a>, p. 79.</span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">Callen, H.B. (1960/1985).<i>Thermodynamics and an Introduction to Thermostatistics</i>, second edition, John Wiley & Sons, Hoboken NY, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780471862567" title="Special:BookSources/9780471862567">9780471862567</a>, pp. 11–13.</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrabenRay1993" class="citation journal cs1">Graben, H.W.; Ray, John R. (10 December 1993). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1080/00268979300102971">"Eight physical systems of thermodynamics, statistical mechanics, and computer simulations"</a>. <i>Molecular Physics</i>. <b>80</b> (5): 1183–1193. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993MolPh..80.1183G">1993MolPh..80.1183G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00268979300102971">10.1080/00268979300102971</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0026-8976">0026-8976</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Molecular+Physics&rft.atitle=Eight+physical+systems+of+thermodynamics%2C+statistical+mechanics%2C+and+computer+simulations&rft.volume=80&rft.issue=5&rft.pages=1183-1193&rft.date=1993-12-10&rft.issn=0026-8976&rft_id=info%3Adoi%2F10.1080%2F00268979300102971&rft_id=info%3Abibcode%2F1993MolPh..80.1183G&rft.aulast=Graben&rft.aufirst=H.W.&rft.au=Ray%2C+John+R.&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1080%2F00268979300102971&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNitzkeStephanVrabec2024" class="citation journal cs1">Nitzke, Isabel; Stephan, Simon; Vrabec, Jadran (3 June 2024). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1063/5.0207592">"Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null"</a>. <i>The Journal of Chemical Physics</i>. <b>160</b> (21). <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2024JChPh.160u4104N">2024JChPh.160u4104N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F5.0207592">10.1063/5.0207592</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-9606">0021-9606</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/38828811">38828811</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Chemical+Physics&rft.atitle=Topology+of+thermodynamic+potentials+using+physical+models%3A+Helmholtz%2C+Gibbs%2C+Grand%2C+and+Null&rft.volume=160&rft.issue=21&rft.date=2024-06-03&rft_id=info%3Adoi%2F10.1063%2F5.0207592&rft.issn=0021-9606&rft_id=info%3Apmid%2F38828811&rft_id=info%3Abibcode%2F2024JChPh.160u4104N&rft.aulast=Nitzke&rft.aufirst=Isabel&rft.au=Stephan%2C+Simon&rft.au=Vrabec%2C+Jadran&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1063%2F5.0207592&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1909" class="citation journal cs1 cs1-prop-foreign-lang-source">Carathéodory, C. (1909). <a rel="nofollow" class="external text" href="http://link.springer.com/10.1007/BF01450409">"Untersuchungen über die Grundlagen der Thermodynamik"</a>. <i><a href="/wiki/Mathematische_Annalen" title="Mathematische Annalen">Mathematische Annalen</a></i> (in German). <b>67</b> (3): 355–386. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01450409">10.1007/BF01450409</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0025-5831">0025-5831</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118230148">118230148</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=Untersuchungen+%C3%BCber+die+Grundlagen+der+Thermodynamik&rft.volume=67&rft.issue=3&rft.pages=355-386&rft.date=1909&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118230148%23id-name%3DS2CID&rft.issn=0025-5831&rft_id=info%3Adoi%2F10.1007%2FBF01450409&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.&rft_id=http%3A%2F%2Flink.springer.com%2F10.1007%2FBF01450409&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-frankel-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-frankel_38-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrankel2004" class="citation book cs1">Frankel, Theodore (2004). <i>The Geometry of Physics: An Introduction</i> (second ed.). Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521539272" title="Special:BookSources/9780521539272"><bdi>9780521539272</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Geometry+of+Physics%3A+An+Introduction&rft.edition=second&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=9780521539272&rft.aulast=Frankel&rft.aufirst=Theodore&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRastall1970" class="citation journal cs1">Rastall, Peter (1 October 1970). <a rel="nofollow" class="external text" href="https://aip.scitation.org/doi/10.1063/1.1665080">"Classical Thermodynamics Simplified"</a>. <i><a href="/wiki/Journal_of_Mathematical_Physics" title="Journal of Mathematical Physics">Journal of Mathematical Physics</a></i>. <b>11</b> (10): 2955–2965. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1970JMP....11.2955R">1970JMP....11.2955R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1665080">10.1063/1.1665080</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-2488">0022-2488</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Mathematical+Physics&rft.atitle=Classical+Thermodynamics+Simplified&rft.volume=11&rft.issue=10&rft.pages=2955-2965&rft.date=1970-10-01&rft.issn=0022-2488&rft_id=info%3Adoi%2F10.1063%2F1.1665080&rft_id=info%3Abibcode%2F1970JMP....11.2955R&rft.aulast=Rastall&rft.aufirst=Peter&rft_id=https%3A%2F%2Faip.scitation.org%2Fdoi%2F10.1063%2F1.1665080&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldstein,_MartinInge_F.1993" class="citation book cs1">Goldstein, Martin & Inge F. (1993). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/refrigeratoruniv0000gold"><i>The Refrigerator and the Universe</i></a></span>. Harvard University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-674-75325-9" title="Special:BookSources/978-0-674-75325-9"><bdi>978-0-674-75325-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/32826343">32826343</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Refrigerator+and+the+Universe&rft.pub=Harvard+University+Press&rft.date=1993&rft_id=info%3Aoclcnum%2F32826343&rft.isbn=978-0-674-75325-9&rft.au=Goldstein%2C+Martin&rft.au=Inge+F.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Frefrigeratoruniv0000gold&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> A nontechnical introduction, good on historical and interpretive matters.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKazakovMuznyChiricoDiky2008" class="citation journal cs1">Kazakov, Andrei; Muzny, Chris D.; Chirico, Robert D.; Diky, Vladimir V.; Frenkel, Michael (2008). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4651616">"Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables"</a>. <i>Journal of Research of the National Institute of Standards and Technology</i>. <b>113</b> (4): 209–220. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.6028%2Fjres.113.016">10.6028/jres.113.016</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1044-677X">1044-677X</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4651616">4651616</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27096122">27096122</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Research+of+the+National+Institute+of+Standards+and+Technology&rft.atitle=Web+Thermo+Tables+%E2%80%93+an+On-Line+Version+of+the+TRC+Thermodynamic+Tables&rft.volume=113&rft.issue=4&rft.pages=209-220&rft.date=2008&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4651616%23id-name%3DPMC&rft.issn=1044-677X&rft_id=info%3Apmid%2F27096122&rft_id=info%3Adoi%2F10.6028%2Fjres.113.016&rft.aulast=Kazakov&rft.aufirst=Andrei&rft.au=Muzny%2C+Chris+D.&rft.au=Chirico%2C+Robert+D.&rft.au=Diky%2C+Vladimir+V.&rft.au=Frenkel%2C+Michael&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4651616&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs_J.W.1928" class="citation book cs1">Gibbs J.W. (1928). <i>The Collected Works of J. Willard Gibbs Thermodynamics</i>. New York: Longmans, Green and Co.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Collected+Works+of+J.+Willard+Gibbs+Thermodynamics.&rft.place=New+York&rft.pub=Longmans%2C+Green+and+Co.&rft.date=1928&rft.au=Gibbs+J.W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> Vol. 1, pp. 55–349.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuggenheim_E.A.1933" class="citation book cs1">Guggenheim E.A. (1933). <i>Modern thermodynamics by the methods of Willard Gibbs</i>. London: Methuen & co. ltd.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+thermodynamics+by+the+methods+of+Willard+Gibbs&rft.place=London&rft.pub=Methuen+%26+co.+ltd.&rft.date=1933&rft.au=Guggenheim+E.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDenbigh_K.1981" class="citation book cs1">Denbigh K. (1981). <i>The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering</i>. London: Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principles+of+Chemical+Equilibrium%3A+With+Applications+in+Chemistry+and+Chemical+Engineering.&rft.place=London&rft.pub=Cambridge+University+Press&rft.date=1981&rft.au=Denbigh+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStull,_D.R.,_Westrum_Jr.,_E.F._and_Sinke,_G.C.1969" class="citation book cs1">Stull, D.R., Westrum Jr., E.F. and Sinke, G.C. (1969). <i>The Chemical Thermodynamics of Organic Compounds</i>. London: John Wiley and Sons, Inc.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Chemical+Thermodynamics+of+Organic+Compounds.&rft.place=London&rft.pub=John+Wiley+and+Sons%2C+Inc.&rft.date=1969&rft.au=Stull%2C+D.R.%2C+Westrum+Jr.%2C+E.F.+and+Sinke%2C+G.C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBazarov_I.P.2010" class="citation book cs1">Bazarov I.P. (2010). <i>Thermodynamics: Textbook</i>. St. Petersburg: Lan publishing house. p. 384. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-5-8114-1003-3" title="Special:BookSources/978-5-8114-1003-3"><bdi>978-5-8114-1003-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3A+Textbook.&rft.place=St.+Petersburg&rft.pages=384&rft.pub=Lan+publishing+house&rft.date=2010&rft.isbn=978-5-8114-1003-3&rft.au=Bazarov+I.P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> 5th ed. (in Russian)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBawendi_Moungi_G.,_Alberty_Robert_A._and_Silbey_Robert_J.2004" class="citation book cs1">Bawendi Moungi G., Alberty Robert A. and Silbey Robert J. (2004). <i>Physical Chemistry</i>. J. Wiley & Sons, Incorporated.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physical+Chemistry&rft.pub=J.+Wiley+%26+Sons%2C+Incorporated&rft.date=2004&rft.au=Bawendi+Moungi+G.%2C+Alberty+Robert+A.+and+Silbey+Robert+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlberty_Robert_A.2003" class="citation book cs1">Alberty Robert A. (2003). <i>Thermodynamics of Biochemical Reactions</i>. Wiley-Interscience.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+of+Biochemical+Reactions&rft.pub=Wiley-Interscience&rft.date=2003&rft.au=Alberty+Robert+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlberty_Robert_A.2006" class="citation book cs1">Alberty Robert A. (2006). <i>Biochemical Thermodynamics: Applications of Mathematica</i>. Vol. 48. John Wiley & Sons, Inc. pp. 1–458. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-75798-6" title="Special:BookSources/978-0-471-75798-6"><bdi>978-0-471-75798-6</bdi></a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16878778">16878778</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biochemical+Thermodynamics%3A+Applications+of+Mathematica&rft.pages=1-458&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2006&rft_id=info%3Apmid%2F16878778&rft.isbn=978-0-471-75798-6&rft.au=Alberty+Robert+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDill_Ken_A.,_Bromberg_Sarina2011" class="citation book cs1">Dill Ken A., Bromberg Sarina (2011). <i>Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience</i>. Garland Science. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8153-4430-8" title="Special:BookSources/978-0-8153-4430-8"><bdi>978-0-8153-4430-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Driving+Forces%3A+Statistical+Thermodynamics+in+Biology%2C+Chemistry%2C+Physics%2C+and+Nanoscience&rft.pub=Garland+Science&rft.date=2011&rft.isbn=978-0-8153-4430-8&rft.au=Dill+Ken+A.%2C+Bromberg+Sarina&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM._Scott_Shell2015" class="citation book cs1">M. Scott Shell (2015). <i>Thermodynamics and Statistical Mechanics: An Integrated Approach</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1107656789" title="Special:BookSources/978-1107656789"><bdi>978-1107656789</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+and+Statistical+Mechanics%3A+An+Integrated+Approach&rft.pub=Cambridge+University+Press&rft.date=2015&rft.isbn=978-1107656789&rft.au=M.+Scott+Shell&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDouglas_E._Barrick2018" class="citation book cs1">Douglas E. Barrick (2018). <i>Biomolecular Thermodynamics: From Theory to Applications</i>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4398-0019-5" title="Special:BookSources/978-1-4398-0019-5"><bdi>978-1-4398-0019-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biomolecular+Thermodynamics%3A+From+Theory+to+Applications&rft.pub=CRC+Press&rft.date=2018&rft.isbn=978-1-4398-0019-5&rft.au=Douglas+E.+Barrick&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li></ul> <p>The following titles are more technical: </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBejan2016" class="citation book cs1">Bejan, Adrian (2016). <i>Advanced Engineering Thermodynamics</i> (4 ed.). Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-05209-8" title="Special:BookSources/978-1-119-05209-8"><bdi>978-1-119-05209-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Engineering+Thermodynamics&rft.edition=4&rft.pub=Wiley&rft.date=2016&rft.isbn=978-1-119-05209-8&rft.aulast=Bejan&rft.aufirst=Adrian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCengel,_Yunus_A.,_&_Boles,_Michael_A.2002" class="citation book cs1">Cengel, Yunus A., & Boles, Michael A. (2002). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/thermodynamicsen00ceng_0"><i>Thermodynamics – an Engineering Approach</i></a></span>. McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-238332-4" title="Special:BookSources/978-0-07-238332-4"><bdi>978-0-07-238332-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/45791449">45791449</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+%E2%80%93+an+Engineering+Approach&rft.pub=McGraw+Hill&rft.date=2002&rft_id=info%3Aoclcnum%2F45791449&rft.isbn=978-0-07-238332-4&rft.au=Cengel%2C+Yunus+A.%2C+%26+Boles%2C+Michael+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fthermodynamicsen00ceng_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunning-Davies,_Jeremy1997" class="citation book cs1">Dunning-Davies, Jeremy (1997). <i>Concise Thermodynamics: Principles and Applications</i>. Horwood Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-8985-6315-0" title="Special:BookSources/978-1-8985-6315-0"><bdi>978-1-8985-6315-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/36025958">36025958</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Concise+Thermodynamics%3A+Principles+and+Applications&rft.pub=Horwood+Publishing&rft.date=1997&rft_id=info%3Aoclcnum%2F36025958&rft.isbn=978-1-8985-6315-0&rft.au=Dunning-Davies%2C+Jeremy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKroemer,_HerbertKittel,_Charles1980" class="citation book cs1">Kroemer, Herbert & Kittel, Charles (1980). <i>Thermal Physics</i>. W.H. Freeman Company. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-1088-2" title="Special:BookSources/978-0-7167-1088-2"><bdi>978-0-7167-1088-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/32932988">32932988</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermal+Physics&rft.pub=W.H.+Freeman+Company&rft.date=1980&rft_id=info%3Aoclcnum%2F32932988&rft.isbn=978-0-7167-1088-2&rft.au=Kroemer%2C+Herbert&rft.au=Kittel%2C+Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" 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<i><b><a href="https://en.wikiquote.org/wiki/Thermodynamics" class="extiw" title="q:Thermodynamics">Thermodynamics</a></b></i>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCallendar1911" class="citation encyclopaedia cs1">Callendar, Hugh Longbourne (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Thermodynamics"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Thermodynamics">"Thermodynamics" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 26 (11th ed.). pp. 808–814.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Thermodynamics&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=808-814&rft.edition=11th&rft.date=1911&rft.aulast=Callendar&rft.aufirst=Hugh+Longbourne&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermodynamics" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html">Thermodynamics Data & Property Calculation Websites</a></li> <li><a rel="nofollow" class="external text" href="http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html">Thermodynamics Educational Websites</a></li> <li><a rel="nofollow" class="external text" href="http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm">Biochemistry Thermodynamics</a></li> <li><a rel="nofollow" class="external text" href="http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html">Thermodynamics and Statistical Mechanics</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/">Engineering Thermodynamics – A Graphical Approach</a></li> <li><a rel="nofollow" class="external text" href="http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf">Thermodynamics and Statistical Mechanics</a> by Richard Fitzpatrick</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output 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scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_physics" title="Template talk:Branches of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_physics" title="Special:EditPage/Template:Branches of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_branches_of_physics" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a class="mw-selflink selflink">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General</a></li></ul></li> <li><a href="/wiki/Nuclear_physics" 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style="width:1%"><a href="/wiki/Category:Applied_and_interdisciplinary_physics" title="Category:Applied and interdisciplinary physics">Interdisciplinary</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysics" title="Astrophysics">Astrophysics</a></li> <li><a href="/wiki/Atmospheric_physics" title="Atmospheric physics">Atmospheric physics</a></li> <li><a href="/wiki/Biophysics" title="Biophysics">Biophysics</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Medical_physics" title="Medical physics">Medical physics</a></li> <li><a href="/wiki/Physical_oceanography" title="Physical oceanography">Ocean physics</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_physics" title="History of physics">History of physics</a></li> <li><a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Physics_education" title="Physics education">Physics education</a></li> <li><a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">Timeline of physics discoveries</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Heating,_ventilation,_and_air_conditioning" style="vertical-align: middle;;padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:HVAC" title="Template:HVAC"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:HVAC" title="Template talk:HVAC"><abbr 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title="Convection">Convection</a></li> <li><a href="/wiki/Dilution_(equation)" title="Dilution (equation)">Dilution</a></li> <li><a href="/wiki/Domestic_energy_consumption" title="Domestic energy consumption">Domestic energy consumption</a></li> <li><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">Gas compressor</a></li> <li><a href="/wiki/Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Heat pump and refrigeration cycle</a></li> <li><a href="/wiki/Heat_transfer" title="Heat transfer">Heat transfer</a></li> <li><a href="/wiki/Humidity" title="Humidity">Humidity</a></li> <li><a href="/wiki/Infiltration_(HVAC)" title="Infiltration (HVAC)">Infiltration</a></li> <li><a href="/wiki/Latent_heat" title="Latent heat">Latent heat</a></li> <li><a href="/wiki/Noise_control" title="Noise control">Noise control</a></li> <li><a href="/wiki/Outgassing" title="Outgassing">Outgassing</a></li> <li><a href="/wiki/Particulates" title="Particulates">Particulates</a></li> <li><a href="/wiki/Psychrometrics" title="Psychrometrics">Psychrometrics</a></li> <li><a href="/wiki/Sensible_heat" title="Sensible heat">Sensible heat</a></li> <li><a href="/wiki/Stack_effect" title="Stack effect">Stack effect</a></li> <li><a href="/wiki/Thermal_comfort" title="Thermal comfort">Thermal comfort</a></li> <li><a href="/wiki/Thermal_destratification" title="Thermal destratification">Thermal destratification</a></li> <li><a href="/wiki/Thermal_mass" title="Thermal mass">Thermal mass</a></li> <li><a class="mw-selflink selflink">Thermodynamics</a></li> <li><a href="/wiki/Vapour_pressure_of_water" title="Vapour pressure of water">Vapour pressure of water</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technology</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absorption-compression_heat_pump" title="Absorption-compression heat pump">Absorption-compression heat pump</a></li> <li><a href="/wiki/Absorption_refrigerator" title="Absorption refrigerator">Absorption refrigerator</a></li> <li><a href="/wiki/Air_barrier" title="Air barrier">Air barrier</a></li> <li><a href="/wiki/Air_conditioning" title="Air conditioning">Air conditioning</a></li> <li><a href="/wiki/Antifreeze" title="Antifreeze">Antifreeze</a></li> <li><a href="/wiki/Automobile_air_conditioning" class="mw-redirect" title="Automobile air conditioning">Automobile air conditioning</a></li> <li><a href="/wiki/Autonomous_building" title="Autonomous building">Autonomous building</a></li> <li><a href="/wiki/Building_insulation_material" title="Building insulation material">Building insulation materials</a></li> <li><a href="/wiki/Central_heating" title="Central heating">Central heating</a></li> <li><a href="/wiki/Central_solar_heating" title="Central solar heating">Central solar heating</a></li> <li><a href="/wiki/Chilled_beam" title="Chilled beam">Chilled beam</a></li> <li><a href="/wiki/Chilled_water" title="Chilled water">Chilled water</a></li> <li><a href="/wiki/Constant_air_volume" title="Constant air volume">Constant air volume</a> (CAV)</li> <li><a href="/wiki/Coolant" title="Coolant">Coolant</a></li> <li><a href="/wiki/Cross_ventilation" title="Cross ventilation">Cross ventilation</a></li> <li><a href="/wiki/Dedicated_outdoor_air_system" title="Dedicated outdoor air system">Dedicated outdoor air system</a> (DOAS)</li> <li><a href="/wiki/Deep_water_source_cooling" title="Deep water source cooling">Deep water source cooling</a></li> <li><a href="/wiki/Demand_controlled_ventilation" title="Demand controlled ventilation">Demand controlled ventilation</a> (DCV)</li> <li><a href="/wiki/Displacement_ventilation" title="Displacement ventilation">Displacement ventilation</a></li> <li><a href="/wiki/District_cooling" title="District cooling">District cooling</a></li> <li><a href="/wiki/District_heating" title="District heating">District heating</a></li> <li><a href="/wiki/Electric_heating" title="Electric heating">Electric heating</a></li> <li><a href="/wiki/Energy_recovery_ventilation" class="mw-redirect" title="Energy recovery ventilation">Energy recovery ventilation</a> (ERV)</li> <li><a href="/wiki/Firestop" title="Firestop">Firestop</a></li> <li><a href="/wiki/Forced-air" title="Forced-air">Forced-air</a></li> <li><a href="/wiki/Forced-air_gas" title="Forced-air gas">Forced-air gas</a></li> <li><a href="/wiki/Free_cooling" title="Free cooling">Free cooling</a></li> <li><a href="/wiki/Heat_recovery_ventilation" title="Heat recovery ventilation">Heat recovery ventilation</a> (HRV)</li> <li><a href="/wiki/Hybrid_heat" title="Hybrid heat">Hybrid heat</a></li> <li><a href="/wiki/Hydronics" title="Hydronics">Hydronics</a></li> <li><a href="/wiki/Ice_storage_air_conditioning" title="Ice storage air conditioning">Ice storage air conditioning</a></li> <li><a href="/wiki/Kitchen_ventilation" title="Kitchen ventilation">Kitchen ventilation</a></li> <li><a href="/wiki/Mixed-mode_ventilation" title="Mixed-mode ventilation">Mixed-mode ventilation</a></li> <li><a href="/wiki/Microgeneration" title="Microgeneration">Microgeneration</a></li> <li><a href="/wiki/Passive_cooling" title="Passive cooling">Passive cooling</a></li> <li><a href="/wiki/Passive_daytime_radiative_cooling" title="Passive daytime radiative cooling">Passive daytime radiative cooling</a></li> <li><a href="/wiki/Passive_house" title="Passive house">Passive house</a></li> <li><a href="/wiki/Passive_ventilation" title="Passive ventilation">Passive ventilation</a></li> <li><a href="/wiki/Radiant_heating_and_cooling" title="Radiant heating and cooling">Radiant heating and cooling</a></li> <li><a href="/wiki/Radiant_cooling" class="mw-redirect" title="Radiant cooling">Radiant cooling</a></li> <li><a href="/wiki/Radiant_heating" class="mw-redirect" title="Radiant heating">Radiant heating</a></li> <li><a href="/wiki/Radon_mitigation" title="Radon mitigation">Radon mitigation</a></li> <li><a href="/wiki/Refrigeration" title="Refrigeration">Refrigeration</a></li> <li><a href="/wiki/Renewable_heat" title="Renewable heat">Renewable heat</a></li> <li><a href="/wiki/Room_air_distribution" title="Room air distribution">Room air distribution</a></li> <li><a href="/wiki/Solar_air_heat" title="Solar air heat">Solar air heat</a></li> <li><a href="/wiki/Solar_combisystem" title="Solar combisystem">Solar combisystem</a></li> <li><a href="/wiki/Solar_cooling" class="mw-redirect" title="Solar cooling">Solar cooling</a></li> <li><a href="/wiki/Solar_heating" class="mw-redirect" title="Solar heating">Solar heating</a></li> <li><a href="/wiki/Thermal_insulation" title="Thermal insulation">Thermal insulation</a></li> <li><a href="/wiki/Thermosiphon" title="Thermosiphon">Thermosiphon</a></li> <li><a href="/wiki/Underfloor_air_distribution" title="Underfloor air distribution">Underfloor air distribution</a></li> <li><a href="/wiki/Underfloor_heating" title="Underfloor heating">Underfloor heating</a></li> <li><a href="/wiki/Vapor_barrier" title="Vapor barrier">Vapor barrier</a></li> <li><a href="/wiki/Vapor-compression_refrigeration" title="Vapor-compression refrigeration">Vapor-compression refrigeration</a> (VCRS)</li> <li><a href="/wiki/Variable_air_volume" title="Variable air volume">Variable air volume</a> (VAV)</li> <li><a href="/wiki/Variable_refrigerant_flow" title="Variable refrigerant flow">Variable refrigerant flow</a> (VRF)</li> <li><a href="/wiki/Ventilation_(architecture)" title="Ventilation (architecture)">Ventilation</a></li> <li><a href="/wiki/Water_heat_recycling" title="Water heat recycling">Water heat recycling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_conditioner_inverter" class="mw-redirect" title="Air conditioner inverter">Air conditioner inverter</a></li> <li><a href="/wiki/Air_door" title="Air door">Air door</a></li> <li><a href="/wiki/Air_filter" title="Air filter">Air filter</a></li> <li><a href="/wiki/Air_handler" title="Air handler">Air handler</a></li> <li><a href="/wiki/Air_ioniser" title="Air ioniser">Air ionizer</a></li> <li><a href="/wiki/Air-mixing_plenum" title="Air-mixing plenum">Air-mixing plenum</a></li> <li><a href="/wiki/Air_purifier" title="Air purifier">Air purifier</a></li> <li><a href="/wiki/Air_source_heat_pump" title="Air source heat pump">Air source heat pump</a></li> <li><a href="/wiki/Attic_fan" title="Attic fan">Attic fan</a></li> <li><a href="/wiki/Automatic_balancing_valve" title="Automatic balancing valve">Automatic balancing valve</a></li> <li><a href="/wiki/Back_boiler" title="Back boiler">Back boiler</a></li> <li><a href="/wiki/Barrier_pipe" title="Barrier pipe">Barrier pipe</a></li> <li><a href="/wiki/Blast_damper" title="Blast damper">Blast damper</a></li> <li><a href="/wiki/Boiler" title="Boiler">Boiler</a></li> <li><a href="/wiki/Centrifugal_fan" title="Centrifugal fan">Centrifugal fan</a></li> <li><a href="/wiki/Ceramic_heater" title="Ceramic heater">Ceramic heater</a></li> <li><a href="/wiki/Chiller" title="Chiller">Chiller</a></li> <li><a href="/wiki/Condensate_pump" title="Condensate pump">Condensate pump</a></li> <li><a href="/wiki/Condenser_(heat_transfer)" title="Condenser (heat transfer)">Condenser</a></li> <li><a href="/wiki/Condensing_boiler" title="Condensing boiler">Condensing boiler</a></li> <li><a href="/wiki/Convection_heater" title="Convection heater">Convection heater</a></li> <li><a href="/wiki/Compressor" title="Compressor">Compressor</a></li> <li><a href="/wiki/Cooling_tower" title="Cooling tower">Cooling tower</a></li> <li><a href="/wiki/Damper_(flow)" title="Damper (flow)">Damper</a></li> <li><a href="/wiki/Dehumidifier" title="Dehumidifier">Dehumidifier</a></li> <li><a href="/wiki/Duct_(flow)" title="Duct (flow)">Duct</a></li> <li><a href="/wiki/Economizer" title="Economizer">Economizer</a></li> <li><a href="/wiki/Electrostatic_precipitator" title="Electrostatic precipitator">Electrostatic precipitator</a></li> <li><a href="/wiki/Evaporative_cooler" title="Evaporative cooler">Evaporative cooler</a></li> <li><a href="/wiki/Evaporator" title="Evaporator">Evaporator</a></li> <li><a href="/wiki/Exhaust_hood" class="mw-redirect" title="Exhaust hood">Exhaust hood</a></li> <li><a href="/wiki/Expansion_tank" title="Expansion tank">Expansion tank</a></li> <li><a href="/wiki/Fan_(machine)" title="Fan (machine)">Fan</a></li> <li><a href="/wiki/Fan_coil_unit" title="Fan coil unit">Fan coil unit</a></li> <li><a href="/wiki/Fan_filter_unit" title="Fan filter unit">Fan filter unit</a></li> <li><a href="/wiki/Fan_heater" title="Fan heater">Fan heater</a></li> <li><a href="/wiki/Fire_damper" title="Fire damper">Fire damper</a></li> <li><a href="/wiki/Fireplace" title="Fireplace">Fireplace</a></li> <li><a href="/wiki/Fireplace_insert" title="Fireplace insert">Fireplace insert</a></li> <li><a href="/wiki/Freeze_stat" title="Freeze stat">Freeze stat</a></li> <li><a href="/wiki/Flue" title="Flue">Flue</a></li> <li><a href="/wiki/Freon" title="Freon">Freon</a></li> <li><a href="/wiki/Fume_hood" title="Fume hood">Fume hood</a></li> <li><a href="/wiki/Furnace_(house_heating)" class="mw-redirect" title="Furnace (house heating)">Furnace</a></li> <li><a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">Gas compressor</a></li> <li><a href="/wiki/Gas_heater" title="Gas heater">Gas heater</a></li> <li><a href="/wiki/Gasoline_heater" title="Gasoline heater">Gasoline heater</a></li> <li><a href="/wiki/Grease_duct" title="Grease duct">Grease duct</a></li> <li><a href="/wiki/Grille_(architecture)" title="Grille (architecture)">Grille</a></li> <li><a href="/wiki/Ground-coupled_heat_exchanger" title="Ground-coupled heat exchanger">Ground-coupled heat exchanger</a></li> <li><a href="/wiki/Ground_source_heat_pump" title="Ground source heat pump">Ground source heat pump</a></li> <li><a href="/wiki/Heat_exchanger" title="Heat exchanger">Heat exchanger</a></li> <li><a href="/wiki/Heat_pipe" title="Heat pipe">Heat pipe</a></li> <li><a href="/wiki/Heat_pump" title="Heat pump">Heat pump</a></li> <li><a href="/wiki/Heating_film" title="Heating film">Heating film</a></li> <li><a href="/wiki/Heating_system" title="Heating system">Heating system</a></li> <li><a href="/wiki/HEPA" title="HEPA">HEPA</a></li> <li><a href="/wiki/High_efficiency_glandless_circulating_pump" title="High efficiency glandless circulating pump">High efficiency glandless circulating pump</a></li> <li><a href="/wiki/High-pressure_cut-off_switch" class="mw-redirect" title="High-pressure cut-off switch">High-pressure cut-off switch</a></li> <li><a href="/wiki/Humidifier" title="Humidifier">Humidifier</a></li> <li><a href="/wiki/Infrared_heater" title="Infrared heater">Infrared heater</a></li> <li><a href="/wiki/Inverter_compressor" title="Inverter compressor">Inverter compressor</a></li> <li><a href="/wiki/Kerosene_heater" title="Kerosene heater">Kerosene heater</a></li> <li><a href="/wiki/Louver" title="Louver">Louver</a></li> <li><a href="/wiki/Mechanical_room" title="Mechanical room">Mechanical room</a></li> <li><a href="/wiki/Oil_heater" title="Oil heater">Oil heater</a></li> <li><a href="/wiki/Packaged_terminal_air_conditioner" title="Packaged terminal air conditioner">Packaged terminal air conditioner</a></li> <li><a href="/wiki/Plenum_space" title="Plenum space">Plenum space</a></li> <li><a href="/wiki/Pressurisation_ductwork" title="Pressurisation ductwork">Pressurisation ductwork</a></li> <li><a href="/wiki/Process_duct_work" title="Process duct work">Process duct work</a></li> <li><a href="/wiki/Radiator_(heating)" title="Radiator (heating)">Radiator</a></li> <li><a href="/wiki/Radiator_reflector" title="Radiator reflector">Radiator reflector</a></li> <li><a href="/wiki/Recuperator" title="Recuperator">Recuperator</a></li> <li><a href="/wiki/Refrigerant" title="Refrigerant">Refrigerant</a></li> <li><a href="/wiki/Register_(air_and_heating)" title="Register (air and heating)">Register</a></li> <li><a href="/wiki/Reversing_valve" title="Reversing valve">Reversing valve</a></li> <li><a href="/wiki/Run-around_coil" title="Run-around coil">Run-around coil</a></li> <li><a href="/wiki/Sail_switch" title="Sail switch">Sail switch</a></li> <li><a href="/wiki/Scroll_compressor" title="Scroll compressor">Scroll compressor</a></li> <li><a href="/wiki/Solar_chimney" title="Solar chimney">Solar chimney</a></li> <li><a href="/wiki/Solar-assisted_heat_pump" title="Solar-assisted heat pump">Solar-assisted heat pump</a></li> <li><a href="/wiki/Space_heater" title="Space heater">Space heater</a></li> <li><a href="/wiki/Smoke_canopy" title="Smoke canopy">Smoke canopy</a></li> <li><a href="/wiki/Smoke_damper" title="Smoke damper">Smoke damper</a></li> <li><a href="/wiki/Smoke_exhaust_ductwork" title="Smoke exhaust ductwork">Smoke exhaust ductwork</a></li> <li><a href="/wiki/Thermal_expansion_valve" title="Thermal expansion valve">Thermal expansion valve</a></li> <li><a href="/wiki/Thermal_wheel" title="Thermal wheel">Thermal wheel</a></li> <li><a href="/wiki/Thermostatic_radiator_valve" title="Thermostatic radiator valve">Thermostatic radiator valve</a></li> <li><a href="/wiki/Trickle_vent" title="Trickle vent">Trickle vent</a></li> <li><a href="/wiki/Trombe_wall" title="Trombe wall">Trombe wall</a></li> <li><a href="/wiki/TurboSwing" title="TurboSwing">TurboSwing</a></li> <li><a href="/wiki/Turning_vanes_(HVAC)" title="Turning vanes (HVAC)">Turning vanes</a></li> <li><a href="/wiki/Ultra-low_particulate_air" title="Ultra-low particulate air">Ultra-low particulate air</a> (ULPA)</li> <li><a href="/wiki/Whole-house_fan" title="Whole-house fan">Whole-house fan</a></li> <li><a href="/wiki/Windcatcher" title="Windcatcher">Windcatcher</a></li> <li><a href="/wiki/Wood-burning_stove" title="Wood-burning stove">Wood-burning stove</a></li> <li><a href="/wiki/Zone_valve" title="Zone valve">Zone valve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement<br />and control</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_flow_meter" title="Air flow meter">Air flow meter</a></li> <li><a href="/wiki/Aquastat" title="Aquastat">Aquastat</a></li> <li><a href="/wiki/BACnet" title="BACnet">BACnet</a></li> <li><a href="/wiki/Blower_door" title="Blower door">Blower door</a></li> <li><a href="/wiki/Building_automation" title="Building automation">Building automation</a></li> <li><a href="/wiki/Carbon_dioxide_sensor" title="Carbon dioxide sensor">Carbon dioxide sensor</a></li> <li><a href="/wiki/Clean_air_delivery_rate" title="Clean air delivery rate">Clean air delivery rate</a> (CADR)</li> <li><a href="/wiki/Control_valve" title="Control valve">Control valve</a></li> <li><a href="/wiki/Gas_detector" title="Gas detector">Gas detector</a></li> <li><a href="/wiki/Home_energy_monitor" title="Home energy monitor">Home energy monitor</a></li> <li><a href="/wiki/Humidistat" title="Humidistat">Humidistat</a></li> <li><a href="/wiki/HVAC_control_system" title="HVAC control system">HVAC control system</a></li> <li><a href="/wiki/Infrared_thermometer" title="Infrared thermometer">Infrared thermometer</a></li> <li><a href="/wiki/Intelligent_buildings" class="mw-redirect" title="Intelligent buildings">Intelligent buildings</a></li> <li><a href="/wiki/LonWorks" title="LonWorks">LonWorks</a></li> <li><a href="/wiki/Minimum_efficiency_reporting_value" title="Minimum efficiency reporting value">Minimum efficiency reporting value</a> (MERV)</li> <li><a href="/wiki/Normal_temperature_and_pressure" class="mw-redirect" title="Normal temperature and pressure">Normal temperature and pressure</a> (NTP)</li> <li><a href="/wiki/OpenTherm" title="OpenTherm">OpenTherm</a></li> <li><a href="/wiki/Programmable_communicating_thermostat" title="Programmable communicating thermostat">Programmable communicating thermostat</a></li> <li><a href="/wiki/Programmable_thermostat" title="Programmable thermostat">Programmable thermostat</a></li> <li><a href="/wiki/Psychrometrics" title="Psychrometrics">Psychrometrics</a></li> <li><a href="/wiki/Room_temperature" title="Room temperature">Room temperature</a></li> <li><a href="/wiki/Smart_thermostat" title="Smart thermostat">Smart thermostat</a></li> <li><a href="/wiki/Standard_temperature_and_pressure" title="Standard temperature and pressure">Standard temperature and pressure</a> (STP)</li> <li><a href="/wiki/Thermographic_camera" class="mw-redirect" title="Thermographic camera">Thermographic camera</a></li> <li><a href="/wiki/Thermostat" title="Thermostat">Thermostat</a></li> <li><a href="/wiki/Thermostatic_radiator_valve" title="Thermostatic radiator valve">Thermostatic radiator valve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Professions,<br />trades,<br />and services</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Architectural_acoustics" title="Architectural acoustics">Architectural acoustics</a></li> <li><a href="/wiki/Architectural_engineering" title="Architectural engineering">Architectural engineering</a></li> <li><a href="/wiki/Architectural_technologist" title="Architectural technologist">Architectural technologist</a></li> <li><a href="/wiki/Building_services_engineering" title="Building services engineering">Building services engineering</a></li> <li><a href="/wiki/Building_information_modeling" title="Building information modeling">Building information modeling</a> (BIM)</li> <li><a href="/wiki/Deep_energy_retrofit" title="Deep energy retrofit">Deep energy retrofit</a></li> <li><a href="/wiki/Duct_cleaning" class="mw-redirect" title="Duct cleaning">Duct cleaning</a></li> <li><a href="/wiki/Duct_leakage_testing" title="Duct leakage testing">Duct leakage testing</a></li> <li><a href="/wiki/Environmental_engineering" title="Environmental engineering">Environmental engineering</a></li> <li><a href="/wiki/Hydronic_balancing" title="Hydronic balancing">Hydronic balancing</a></li> <li><a href="/wiki/Kitchen_exhaust_cleaning" title="Kitchen exhaust cleaning">Kitchen exhaust cleaning</a></li> <li><a href="/wiki/Mechanical_engineering" title="Mechanical engineering">Mechanical engineering</a></li> <li><a href="/wiki/Mechanical,_electrical,_and_plumbing" title="Mechanical, electrical, and plumbing">Mechanical, electrical, and plumbing</a></li> <li><a href="/wiki/Mold_growth,_assessment,_and_remediation" class="mw-redirect" title="Mold growth, assessment, and remediation">Mold growth, assessment, and remediation</a></li> <li><a href="/wiki/Refrigerant_reclamation" title="Refrigerant reclamation">Refrigerant reclamation</a></li> <li><a href="/wiki/Testing,_adjusting,_balancing" title="Testing, adjusting, balancing">Testing, adjusting, balancing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Industry <br />organizations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_Conditioning,_Heating_and_Refrigeration_Institute" title="Air Conditioning, Heating and Refrigeration Institute">AHRI</a></li> <li><a href="/wiki/Air_Movement_and_Control_Association" title="Air Movement and Control Association">AMCA</a></li> <li><a href="/wiki/ASHRAE" title="ASHRAE">ASHRAE</a></li> <li><a href="/wiki/ASTM_International" title="ASTM International">ASTM International</a></li> <li><a href="/wiki/Building_Research_Establishment" title="Building Research Establishment">BRE</a></li> <li><a href="/wiki/BSRIA" title="BSRIA">BSRIA</a></li> <li><a href="/wiki/Chartered_Institution_of_Building_Services_Engineers" title="Chartered Institution of Building Services Engineers">CIBSE</a></li> <li><a href="/wiki/Institute_of_Refrigeration" title="Institute of Refrigeration">Institute of Refrigeration</a></li> <li><a href="/wiki/International_Institute_of_Refrigeration" title="International Institute of Refrigeration">IIR</a></li> <li><a href="/wiki/Leadership_in_Energy_and_Environmental_Design" class="mw-redirect" title="Leadership in Energy and Environmental Design">LEED</a></li> <li><a href="/wiki/Sheet_Metal_and_Air_Conditioning_Contractors%27_National_Association" title="Sheet Metal and Air Conditioning Contractors' National Association">SMACNA</a></li> <li><a href="/wiki/Uniform_Mechanical_Code" title="Uniform Mechanical Code">UMC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Health and safety</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indoor_air_quality" title="Indoor air quality">Indoor air quality</a> (IAQ)</li> <li><a href="/wiki/Passive_smoking" title="Passive smoking">Passive smoking</a></li> <li><a href="/wiki/Sick_building_syndrome" title="Sick building syndrome">Sick building syndrome</a> (SBS)</li> <li><a href="/wiki/Volatile_organic_compound" title="Volatile organic compound">Volatile organic compound</a> (VOC)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ASHRAE_Handbook" title="ASHRAE Handbook">ASHRAE Handbook</a></li> <li><a href="/wiki/Building_science" title="Building science">Building science</a></li> <li><a href="/wiki/Fireproofing" title="Fireproofing">Fireproofing</a></li> <li><a href="/wiki/Glossary_of_HVAC_terms" title="Glossary of HVAC terms">Glossary of HVAC terms</a></li> <li><a href="/wiki/Warm_Spaces" title="Warm Spaces">Warm Spaces</a></li> <li><a href="/wiki/World_Refrigeration_Day" title="World Refrigeration Day">World Refrigeration Day</a></li> <li><a href="/wiki/Template:Home_automation" title="Template:Home automation">Template:Home automation</a></li> <li><a href="/wiki/Template:Solar_energy" title="Template:Solar energy">Template:Solar energy</a></li></ul> </div></td></tr></tbody></table></div> <div 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