Gibbs free energy - Wikipedia

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id="toc-Homogeneous_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Homogeneous_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Homogeneous systems</span> </div> </a> <ul id="toc-Homogeneous_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gibbs_free_energy_of_reactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gibbs_free_energy_of_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Gibbs free energy of reactions</span> </div> </a> <button aria-controls="toc-Gibbs_free_energy_of_reactions-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 Gibbs free energy of reactions subsection</span> </button> <ul id="toc-Gibbs_free_energy_of_reactions-sublist" class="vector-toc-list"> <li id="toc-In_electrochemical_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_electrochemical_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>In electrochemical thermodynamics</span> </div> </a> <ul id="toc-In_electrochemical_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Useful_identities_to_derive_the_Nernst_equation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Useful_identities_to_derive_the_Nernst_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Useful identities to derive the Nernst equation</span> </div> </a> <ul id="toc-Useful_identities_to_derive_the_Nernst_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standard_Gibbs_energy_change_of_formation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Standard_Gibbs_energy_change_of_formation"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Standard Gibbs energy change of formation</span> </div> </a> <ul id="toc-Standard_Gibbs_energy_change_of_formation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Graphical_interpretation_by_Gibbs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Graphical_interpretation_by_Gibbs"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Graphical interpretation by Gibbs</span> </div> </a> <ul id="toc-Graphical_interpretation_by_Gibbs-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">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_and_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_and_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Notes and references</span> </div> </a> <ul id="toc-Notes_and_references-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">11</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">Gibbs free energy</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 54 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-54" 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">54 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%A7%D9%82%D8%A9_%D8%BA%D9%8A%D8%A8%D8%B3_%D8%A7%D9%84%D8%AD%D8%B1%D8%A9" title="طاقة غيبس الحرة – Arabic" lang="ar" hreflang="ar" data-title="طاقة غيبس الحرة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Enerx%C3%ADa_de_Gibbs" title="Enerxía de Gibbs – Asturian" lang="ast" hreflang="ast" data-title="Enerxía de Gibbs" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Gibbs_enerjisi" title="Gibbs enerjisi – Azerbaijani" lang="az" hreflang="az" data-title="Gibbs enerjisi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%BF%E0%A6%AC%E0%A6%B8_%E0%A6%AE%E0%A7%81%E0%A6%95%E0%A7%8D%E0%A6%A4_%E0%A6%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF" title="গিবস মুক্ত শক্তি – Bangla" lang="bn" hreflang="bn" data-title="গিবস মুক্ত শক্তি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%93%D0%B8%D0%B1%D1%81" title="Свободна енергия на Гибс – Bulgarian" lang="bg" hreflang="bg" data-title="Свободна енергия на Гибс" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Gibbsova_slobodna_energija" title="Gibbsova slobodna energija – Bosnian" lang="bs" hreflang="bs" data-title="Gibbsova slobodna energija" 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/Energia_de_Gibbs" title="Energia de Gibbs – Catalan" lang="ca" hreflang="ca" data-title="Energia de Gibbs" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Gibbsova_voln%C3%A1_energie" title="Gibbsova volná energie – Czech" lang="cs" hreflang="cs" data-title="Gibbsova volná energie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Gibbs_fri_energi" title="Gibbs fri energi – Danish" lang="da" hreflang="da" data-title="Gibbs fri energi" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gibbs-Energie" title="Gibbs-Energie – German" lang="de" hreflang="de" data-title="Gibbs-Energie" 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/Gibbsi_vabaenergia" title="Gibbsi vabaenergia – Estonian" lang="et" hreflang="et" data-title="Gibbsi vabaenergia" 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%95%CE%BB%CE%B5%CF%8D%CE%B8%CE%B5%CF%81%CE%B7_%CE%B5%CE%BD%CE%AD%CF%81%CE%B3%CE%B5%CE%B9%CE%B1_%CE%93%CE%BA%CE%B9%CE%BC%CF%80%CF%82" title="Ελεύθερη ενέργεια Γκιμπς – Greek" lang="el" hreflang="el" data-title="Ελεύθερη ενέργεια Γκιμπς" 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/Energ%C3%ADa_de_Gibbs" title="Energía de Gibbs – Spanish" lang="es" hreflang="es" data-title="Energía de Gibbs" 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/Gibsa_libera_energio" title="Gibsa libera energio – Esperanto" lang="eo" hreflang="eo" data-title="Gibsa libera energio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Gibbsen_energia" title="Gibbsen energia – Basque" lang="eu" hreflang="eu" data-title="Gibbsen energia" 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%A7%D9%86%D8%B1%DA%98%DB%8C_%D8%A2%D8%B2%D8%A7%D8%AF_%DA%AF%DB%8C%D8%A8%D8%B3" title="انرژی آزاد گیبس – Persian" lang="fa" hreflang="fa" data-title="انرژی آزاد گیبس" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Enthalpie_libre" title="Enthalpie libre – French" lang="fr" hreflang="fr" data-title="Enthalpie libre" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Enerx%C3%ADa_libre_de_Gibbs" title="Enerxía libre de Gibbs – Galician" lang="gl" hreflang="gl" data-title="Enerxía libre de Gibbs" 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/%EA%B9%81%EC%8A%A4_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" title="깁스 자유 에너지 – Korean" lang="ko" hreflang="ko" data-title="깁스 자유 에너지" 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/%D4%B3%D5%AB%D5%A2%D5%BD%D5%AB_%D5%A7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1" title="Գիբսի էներգիա – Armenian" lang="hy" hreflang="hy" data-title="Գիբսի էներգիա" 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%97%E0%A4%BF%E0%A4%AC%E0%A5%8D%E0%A4%B8_%E0%A4%AE%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%A4_%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE" title="गिब्स मुक्त ऊर्जा – Hindi" lang="hi" hreflang="hi" data-title="गिब्स मुक्त ऊर्जा" 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/Gibbsova_slobodna_energija" title="Gibbsova slobodna energija – Croatian" lang="hr" hreflang="hr" data-title="Gibbsova slobodna energija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Energi_bebas_Gibbs" title="Energi bebas Gibbs – Indonesian" lang="id" hreflang="id" data-title="Energi bebas Gibbs" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Energia_libera_di_Gibbs" title="Energia libera di Gibbs – Italian" lang="it" hreflang="it" data-title="Energia libera di Gibbs" 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%90%D7%A0%D7%A8%D7%92%D7%99%D7%94_%D7%97%D7%95%D7%A4%D7%A9%D7%99%D7%AA_%D7%A9%D7%9C_%D7%92%D7%99%D7%91%D7%A1" title="אנרגיה חופשית של גיבס – Hebrew" lang="he" hreflang="he" data-title="אנרגיה חופשית של גיבס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B8%D0%B1%D0%B1%D1%81_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8B" title="Гиббс потенциалы – Kazakh" lang="kk" hreflang="kk" data-title="Гиббс потенциалы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B8%D0%B1%D1%81%D1%81_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D1%81%D1%8B" title="Гибсс энергиясы – Kyrgyz" lang="ky" hreflang="ky" data-title="Гибсс энергиясы" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Gibso_laisvoji_energija" title="Gibso laisvoji energija – Lithuanian" lang="lt" hreflang="lt" data-title="Gibso laisvoji energija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szabadentalpia" title="Szabadentalpia – Hungarian" lang="hu" hreflang="hu" data-title="Szabadentalpia" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B4%BF%E0%B4%AC%E0%B5%8D%E0%B4%B8%E0%B5%8D_%E0%B4%AB%E0%B5%8D%E0%B4%B0%E0%B5%80_%E0%B4%8E%E0%B4%A8%E0%B5%BC%E0%B4%9C%E0%B4%BF" title="ഗിബ്സ് ഫ്രീ എനർജി – Malayalam" lang="ml" hreflang="ml" data-title="ഗിബ്സ് ഫ്രീ എനർജി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tenaga_bebas_Gibbs" title="Tenaga bebas Gibbs – Malay" lang="ms" hreflang="ms" data-title="Tenaga bebas Gibbs" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Gibbs_vrije_energie" title="Gibbs vrije energie – Dutch" lang="nl" hreflang="nl" data-title="Gibbs vrije energie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja badge-Q70894304 mw-list-item" title=""><a href="https://ja.wikipedia.org/wiki/%E3%82%AE%E3%83%96%E3%82%BA%E8%87%AA%E7%94%B1%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="ギブズ自由エネルギー – Japanese" lang="ja" hreflang="ja" data-title="ギブズ自由エネルギー" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Gibbs_fri_energi" title="Gibbs fri energi – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Gibbs fri energi" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Entalpia_swobodna" title="Entalpia swobodna – Polish" lang="pl" hreflang="pl" data-title="Entalpia swobodna" 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/Energia_livre_de_Gibbs" title="Energia livre de Gibbs – Portuguese" lang="pt" hreflang="pt" data-title="Energia livre de Gibbs" 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/Entalpie_liber%C4%83" title="Entalpie liberă – Romanian" lang="ro" hreflang="ro" data-title="Entalpie liberă" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D0%93%D0%B8%D0%B1%D0%B1%D1%81%D0%B0" title="Энергия Гиббса – Russian" lang="ru" hreflang="ru" data-title="Энергия Гиббса" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B7%92%E0%B6%B6%E0%B7%8A%E0%B7%83%E0%B7%8A_%E0%B7%81%E0%B6%9A%E0%B7%8A%E0%B6%AD%E0%B7%92%E0%B6%BA" title="ගිබ්ස් ශක්තිය – Sinhala" lang="si" hreflang="si" data-title="ගිබ්ස් ශක්තිය" 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/Gibbs_free_energy" title="Gibbs free energy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Gibbs free energy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Gibbsova_vo%C4%BEn%C3%A1_energia" title="Gibbsova voľná energia – Slovak" lang="sk" hreflang="sk" data-title="Gibbsova voľná energia" 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/Prosta_entalpija" title="Prosta entalpija – Slovenian" lang="sl" hreflang="sl" data-title="Prosta entalpija" 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/%D9%88%D8%B2%DB%95%DB%8C_%DA%95%DB%95%DA%BE%D8%A7%DB%8C_%DA%AF%DB%8C%D8%A8%D8%B3" title="وزەی ڕەھای گیبس – Central Kurdish" lang="ckb" hreflang="ckb" data-title="وزەی ڕەھای گیبس" 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/Gibsova_slobodna_energija" title="Gibsova slobodna energija – Serbian" lang="sr" hreflang="sr" data-title="Gibsova slobodna energija" 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/Gibsova_slobodna_energija" title="Gibsova slobodna energija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Gibsova slobodna energija" 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/Gibbsin_energia" title="Gibbsin energia – Finnish" lang="fi" hreflang="fi" data-title="Gibbsin energia" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Gibbs_fria_energi" title="Gibbs fria energi – Swedish" lang="sv" hreflang="sv" data-title="Gibbs fria energi" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%9A%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%86%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D" title="கிப்சின் ஆற்றல் – Tamil" lang="ta" hreflang="ta" data-title="கிப்சின் ஆற்றல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%87%E0%B8%B2%E0%B8%99%E0%B9%80%E0%B8%AA%E0%B8%A3%E0%B8%B5%E0%B8%81%E0%B8%B4%E0%B8%9A%E0%B8%AA%E0%B9%8C" title="พลังงานเสรีกิบส์ – Thai" lang="th" hreflang="th" data-title="พลังงานเสรีกิบส์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Gibbs_serbest_enerjisi" title="Gibbs serbest enerjisi – Turkish" lang="tr" hreflang="tr" data-title="Gibbs serbest enerjisi" 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%92%D1%96%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F_%D0%93%D1%96%D0%B1%D0%B1%D0%B7%D0%B0" title="Вільна енергія Гіббза – Ukrainian" lang="uk" hreflang="uk" data-title="Вільна енергія Гіббза" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/N%C4%83ng_l%C6%B0%E1%BB%A3ng_Gibbs" title="Năng lượng Gibbs – Vietnamese" lang="vi" hreflang="vi" data-title="Năng lượng Gibbs" 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-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%90%89%E5%B8%83%E5%A3%AB%E8%87%AA%E7%94%B1%E8%83%BD" title="吉布士自由能 – Cantonese" lang="yue" hreflang="yue" data-title="吉布士自由能" 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-zh mw-list-item"><a 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href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a href="/wiki/Thermodynamics" title="Thermodynamics">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 href="/wiki/Thermodynamics" title="Thermodynamics">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 class="mw-selflink selflink">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>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, the <b>Gibbs free energy</b> (or <b>Gibbs energy</b> as the recommended name; symbol <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>) is a <a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">thermodynamic potential</a> that can be used to calculate the <a href="/wiki/Maximum" class="mw-redirect" title="Maximum">maximum</a> amount of <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, other than <a href="/wiki/Work_(thermodynamics)#Pressure–volume_work" title="Work (thermodynamics)">pressure-volume work</a>, that may be performed by a <a href="/wiki/Closed_system" title="Closed system">thermodynamically closed system</a> at constant <a href="/wiki/Temperature" title="Temperature">temperature</a> and <a href="/wiki/Pressure" title="Pressure">pressure</a>. It also provides a necessary condition for processes such as <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> that may occur under these conditions. The Gibbs free energy is expressed as<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(p,T)=U+pV-TS=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(p,T)=U+pV-TS=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5fdd62bf765e32447cc4e69238c277cdd396537" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.268ex; height:2.843ex;" alt="{\displaystyle G(p,T)=U+pV-TS=H-TS}"></span>Where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/087a7d8a39fe35012cbf2f561879f9e975cb4555" 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="{\textstyle U}"></span> is the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of the system</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2435ce1b360a5f6f5a0ab5acbb3c672bf229dac7" 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="{\textstyle H}"></span> is the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> of the system</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e10a3c52d186162ec8910ebc0288ce982aef842f" 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="{\textstyle S}"></span> is the <a href="/wiki/Entropy" title="Entropy">entropy</a> of the system</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db299e88e5485f250f4ba15530469c8c6080a8cb" 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="{\textstyle T}"></span> is the temperature of the system</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d67b50b7ba03a56fea637093cf80e12807852d19" 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="{\textstyle V}"></span> is the <a href="/wiki/Volume" title="Volume">volume</a> of the system</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad87bd7009e2a5c52bd0fb5a9bda9d8c1c23a79b" 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="{\textstyle p}"></span> is the pressure of the system (which must be equal to that of the surroundings for mechanical equilibrium).</li></ul> <p>The Gibbs free energy change <span class="nowrap">(<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 G=\Delta H-T\Delta S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>G</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi mathvariant="normal">Δ</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G=\Delta H-T\Delta S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/062377921bd620d44f679e76b7fc687d07ce2c79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.772ex; height:2.343ex;" alt="{\displaystyle \Delta G=\Delta H-T\Delta S}"></span></span>, measured in <a href="/wiki/Joule" title="Joule">joules</a> in <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a>) is the <i>maximum</i> amount of non-volume expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely <a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">reversible process</a>. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the <a href="/wiki/Pressure" title="Pressure">pressure</a> forces.<sup id="cite_ref-Perrot_1-0" class="reference"><a href="#cite_note-Perrot-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The Gibbs energy is the thermodynamic potential that is minimized when a system reaches <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">chemical equilibrium</a> at constant pressure and temperature when not driven by an applied electrolytic voltage. Its derivative with respect to the reaction coordinate of the system then vanishes at the equilibrium point. As such, a reduction in <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> is necessary for a reaction to be <a href="/wiki/Spontaneous_process" title="Spontaneous process">spontaneous</a> under these conditions. </p><p>The concept of Gibbs free energy, originally called <i>available energy</i>, was developed in the 1870s by the American scientist <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Josiah Willard Gibbs</a>. In 1873, Gibbs described this "available energy" as<sup id="cite_ref-Gibbs1873_2-0" class="reference"><a href="#cite_note-Gibbs1873-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 400">: 400 </span></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a> or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.</p></blockquote> <p>The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of <a href="/wiki/Dissipated_energy" class="mw-redirect" title="Dissipated energy">dissipated energy</a> by <a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">reversible processes</a>". In his 1876 <a href="/wiki/Masterpiece" title="Masterpiece">magnum opus</a> <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>, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical-free energy in full. </p><p>If the reactants and products are all in their thermodynamic <a href="/wiki/Standard_state" title="Standard state">standard states</a>, then the defining equation is written as <span class="nowrap"><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 G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <mi>T</mi> <mi mathvariant="normal">Δ</mi> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ad050dba0fa6a434943a52d4f854863e18bde92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:21.997ex; height:2.509ex;" alt="{\displaystyle \Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }}"></span></span>, where <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 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></i> is <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</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 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 <a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">absolute temperature</a>, and <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 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></i> is <a href="/wiki/Entropy" title="Entropy">entropy</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Diamond.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/36/Diamond.jpg" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a><figcaption>The reaction C<sub>(s)</sub><sup>diamond</sup> → C<sub>(s)</sub><sup>graphite</sup> has a negative change in Gibbs free energy and is therefore thermodynamically favorable at 25 °C and 1 atm. However, the reaction is too slow to be observed, because of its very high <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a>. Whether a reaction is thermodynamically favorable does not determine its rate.</figcaption></figure> <p>According to the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, for systems reacting at fixed temperature and pressure without input of non-<i>Pressure Volume</i> (pV) <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, there is a general natural tendency to achieve a minimum of the Gibbs free energy. </p><p>A quantitative measure of the favorability of a given reaction under these conditions is the change Δ<i>G</i> (sometimes written "delta <i>G</i>" or "d<i>G</i>") in Gibbs free energy that is (or would be) caused by the reaction. As a necessary condition for the reaction to occur at constant temperature and pressure, Δ<i>G</i> must be smaller than the non-pressure-volume (non-<i>pV</i>, e.g. electrical) work, which is often equal to zero (then Δ<i>G</i> must be negative). Δ<i>G</i> equals the maximum amount of non-<i>pV</i> work that can be performed as a result of the chemical reaction for the case of a reversible process. If analysis indicates a positive Δ<i>G</i> for a reaction, then energy — in the form of electrical or other non-<i>pV</i> work — would have to be added to the reacting system for Δ<i>G</i> to be smaller than the non-<i>pV</i> work and make it possible for the reaction to occur.<sup id="cite_ref-AtkinsJones2007_3-0" class="reference"><a href="#cite_note-AtkinsJones2007-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 298–299">: 298–299 </span></sup> </p><p>One can think of ∆G as the amount of "free" or "useful" energy available to do non-<i>pV</i> work at constant temperature and pressure. The equation can be also seen from the perspective of the system taken together with its surroundings (the rest of the universe). First, one assumes that the given reaction at constant temperature and pressure is the only one that is occurring. Then the <a href="/wiki/Entropy" title="Entropy">entropy</a> released or absorbed by the system equals the entropy that the environment must absorb or release, respectively. The reaction will only be allowed if the total entropy change of the universe is zero or positive. This is reflected in a negative Δ<i>G</i>, and the reaction is called an <a href="/wiki/Exergonic_process" title="Exergonic process">exergonic process</a>. </p><p>If two chemical reactions are coupled, then an otherwise <a href="/wiki/Endergonic_reaction" title="Endergonic reaction">endergonic reaction</a> (one with positive Δ<i>G</i>) can be made to happen. The input of heat into an inherently endergonic reaction, such as the <a href="/wiki/Elimination_reaction" title="Elimination reaction">elimination</a> of <a href="/wiki/Cyclohexanol" title="Cyclohexanol">cyclohexanol</a> to <a href="/wiki/Cyclohexene" title="Cyclohexene">cyclohexene</a>, can be seen as coupling an unfavorable reaction (elimination) to a favorable one (burning of coal or other provision of heat) such that the total entropy change of the universe is greater than or equal to zero, making the <i>total</i> Gibbs free energy change of the coupled reactions negative. </p><p>In traditional use, the term "free" was included in "Gibbs free energy" to mean "available in the form of useful work".<sup id="cite_ref-Perrot_1-1" class="reference"><a href="#cite_note-Perrot-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The characterization becomes more precise if we add the qualification that it is the energy available for non-pressure-volume work.<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> (An analogous, but slightly different, meaning of "free" applies in conjunction with the <a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a>, for systems at constant temperature). However, an increasing number of books and journal articles do not include the attachment "free", referring to <i>G</i> as simply "Gibbs energy". This is the result of a 1988 <a href="/wiki/IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a> meeting to set unified terminologies for the international scientific community, in which the removal of the adjective "free" was recommended.<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><sup id="cite_ref-GoldBook_6-0" class="reference"><a href="#cite_note-GoldBook-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><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> This standard, however, has not yet been universally adopted. </p><p>The name "free <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a>" was also used for <i>G</i> in the past.<sup id="cite_ref-GoldBook_6-1" class="reference"><a href="#cite_note-GoldBook-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">See also: <a href="/wiki/Thermodynamic_free_energy#History" title="Thermodynamic free energy">Thermodynamic free energy</a></div> <p>The quantity called "free energy" is a more advanced and accurate replacement for the outdated term <i>affinity</i>, which was used by chemists in the earlier years of physical chemistry to describe the <i>force</i> that caused <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>. </p><p>In 1873, <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Josiah Willard Gibbs</a> published <i>A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces</i>, in which he sketched the principles of his new equation that was able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies composed of part solid, part liquid, and part vapor, and by using a three-dimensional <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>-<a href="/wiki/Entropy" title="Entropy">entropy</a>-<a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes would ensue. Further, Gibbs stated:<sup id="cite_ref-Gibbs1873_2-1" class="reference"><a href="#cite_note-Gibbs1873-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>If we wish to express in a single equation the necessary and sufficient condition of <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a> for a substance when surrounded by a medium of constant <a href="/wiki/Pressure" title="Pressure">pressure</a> <i>p</i> and <a href="/wiki/Temperature" title="Temperature">temperature</a> <i>T</i>, this equation may be written: <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style></p><div class="block-indent"><span class="nowrap"><i>δ</i>(<i>ε</i> − <i>Tη</i> + <i>pν</i>) = 0</span></div><p> when <i>δ</i> refers to the variation produced by any variations in the <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">state</a> of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum.</p></blockquote> <p>In this description, as used by Gibbs, <i>ε</i> refers to the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of the body, <i>η</i> refers to the <a href="/wiki/Entropy" title="Entropy">entropy</a> of the body, and <i>ν</i> is the <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a> of the body... </p><p>Thereafter, in 1882, the German scientist <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> characterized the affinity as the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (<i>Gibbs free energy</i> <i>G</i> at <i>T</i> = constant, <i>P</i> = constant or <i>Helmholtz free energy</i> <i>F</i> at <i>T</i> = constant, <i>V</i> = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (<a href="/wiki/Internal_energy" title="Internal energy">internal energy</a>). Thus, <i>G</i> or <i>F</i> is the amount of energy "free" for work under the given conditions. </p><p>Until this point, the general view had been such that: "all chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanish". Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian Henry Leicester, the influential 1923 textbook <i>Thermodynamics and the Free Energy of Chemical Substances</i> by <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> and <a href="/wiki/Merle_Randall" title="Merle Randall">Merle Randall</a> led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.<sup id="cite_ref-Leicester1971_8-0" class="reference"><a href="#cite_note-Leicester1971-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 206">: 206 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=3" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wykres_Gibbsa.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/220px-Wykres_Gibbsa.svg.png" decoding="async" width="220" height="253" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/330px-Wykres_Gibbsa.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/440px-Wykres_Gibbsa.svg.png 2x" data-file-width="695" data-file-height="800" /></a><figcaption><a href="/wiki/Willard_Gibbs" class="mw-redirect" title="Willard Gibbs">Willard Gibbs</a>' 1873 <b>available energy</b> (free energy) graph, which shows a plane perpendicular to the axis of <i>v</i> (<a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>) and passing through point A, which represents the initial state of the body. MN is the section of the surface of <a href="/wiki/Dissipated_energy" class="mw-redirect" title="Dissipated energy">dissipated energy</a>. Q<i>ε</i> and Q<i>η</i> are sections of the planes <i>η</i> = 0 and <i>ε</i> = 0, and therefore parallel to the axes of <i>ε</i> (<a href="/wiki/Internal_energy" title="Internal energy">internal energy</a>) and <i>η</i> (<a href="/wiki/Entropy" title="Entropy">entropy</a>), respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its <i>available energy</i> (Gibbs free energy) and its <i>capacity for entropy</i> (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume), respectively.</figcaption></figure> <p>The Gibbs free energy is defined as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(p,T)=U+pV-TS,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(p,T)=U+pV-TS,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03d8e77a3812b88eb0386eed25051b0178581585" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.776ex; height:2.843ex;" alt="{\displaystyle G(p,T)=U+pV-TS,}"></span> </p><p>which is the same as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(p,T)=H-TS,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(p,T)=H-TS,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e72beaddce40a3040fecb565a686009e0ad53e6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.26ex; height:2.843ex;" alt="{\displaystyle G(p,T)=H-TS,}"></span> </p><p>where: </p> <ul><li><i>U</i> is the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> (SI unit: <a href="/wiki/Joule" title="Joule">joule</a>),</li> <li><i>p</i> is <a href="/wiki/Pressure" title="Pressure">pressure</a> (SI unit: <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a>),</li> <li><i>V</i> is <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a> (SI unit: m<sup>3</sup>),</li> <li><i>T</i> is the <a href="/wiki/Temperature" title="Temperature">temperature</a> (SI unit: <a href="/wiki/Kelvin" title="Kelvin">kelvin</a>),</li> <li><i>S</i> is the <a href="/wiki/Entropy" title="Entropy">entropy</a> (SI unit: joule per kelvin),</li> <li><i>H</i> is the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> (SI unit: joule).</li></ul> <p><span typeof="mw:File/Frameless"><a href="/wiki/File:Gibbs-Helmholtz_equation.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Gibbs-Helmholtz_equation.png/364px-Gibbs-Helmholtz_equation.png" decoding="async" width="364" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Gibbs-Helmholtz_equation.png/546px-Gibbs-Helmholtz_equation.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Gibbs-Helmholtz_equation.png/728px-Gibbs-Helmholtz_equation.png 2x" data-file-width="847" data-file-height="494" /></a></span> </p><p>The expression for the infinitesimal reversible change in the Gibbs free energy as a function of its <a href="/wiki/Thermodynamic_potential#Natural_variables" title="Thermodynamic potential">"natural variables"</a> <i>p</i> and <i>T</i>, for an <a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">open system</a>, subjected to the operation of external forces (for instance, electrical or magnetic) <i>X<sub>i</sub></i>, which cause the external parameters of the system <i>a<sub>i</sub></i> to change by an amount d<i>a<sub>i</sub></i>, can be derived as follows from the first law for reversible processes: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}T\,\mathrm {d} S&=\mathrm {d} U+p\,\mathrm {d} V-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (TS)-S\,\mathrm {d} T&=\mathrm {d} U+\mathrm {d} (pV)-V\,\mathrm {d} p-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (U-TS+pV)&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} G&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</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> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <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> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mi>S</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mi>V</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <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> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">(</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <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> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <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> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}T\,\mathrm {d} S&=\mathrm {d} U+p\,\mathrm {d} V-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (TS)-S\,\mathrm {d} T&=\mathrm {d} U+\mathrm {d} (pV)-V\,\mathrm {d} p-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (U-TS+pV)&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} G&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57be97e60af321086d4db464dff710f88c708c01" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -14.122ex; margin-bottom: -0.216ex; width:71.666ex; height:29.843ex;" alt="{\displaystyle {\begin{aligned}T\,\mathrm {d} S&=\mathrm {d} U+p\,\mathrm {d} V-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (TS)-S\,\mathrm {d} T&=\mathrm {d} U+\mathrm {d} (pV)-V\,\mathrm {d} p-\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}+\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} (U-TS+pV)&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \\\mathrm {d} G&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots \end{aligned}}}"></span> </p><p>where: </p> <ul><li><i>μ</i><sub><i>i</i></sub> is the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a> of the <i>i</i>-th <a href="/wiki/Chemical_species" title="Chemical species">chemical component</a>. (SI unit: joules per particle<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> or joules per mole<sup id="cite_ref-Perrot_1-2" class="reference"><a href="#cite_note-Perrot-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>)</li> <li><i>N</i><sub><i>i</i></sub> is the <a href="/wiki/Particle_number" title="Particle number">number of particles</a> (or number of moles) composing the <i>i</i>-th chemical component.</li></ul> <p>This is one form of the <b>Gibbs fundamental equation</b>.<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> In the infinitesimal expression, the term involving the chemical potential accounts for changes in Gibbs free energy resulting from an influx or outflux of particles. In other words, it holds for an <a href="/wiki/Open_system_(systems_theory)" title="Open system (systems theory)">open system</a> or for a <a href="/wiki/Closed_system" title="Closed system">closed</a>, chemically reacting system where the <i>N<sub>i</sub></i> are changing. For a closed, non-reacting system, this term may be dropped. </p><p>Any number of extra terms may be added, depending on the particular system being considered. Aside from <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">mechanical work</a>, a system may, in addition, perform numerous other types of work. For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber that shortens by an amount −d<i>l</i> under a force <i>f</i> would result in a term <i>f</i> d<i>l</i> being added. If a quantity of charge −d<i>e</i> is acquired by a system at an electrical potential Ψ, the electrical work associated with this is −Ψ d<i>e</i>, which would be included in the infinitesimal expression. Other work terms are added on per system requirements.<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> </p><p>Each quantity in the equations above can be divided by the amount of substance, measured in <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a>, to form <i>molar Gibbs free energy</i>. The Gibbs free energy is one of the most important thermodynamic functions for the characterization of a system. It is a factor in determining outcomes such as the <a href="/wiki/Voltage" title="Voltage">voltage</a> of an <a href="/wiki/Electrochemical_cell" title="Electrochemical cell">electrochemical cell</a>, and the <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> for a <a href="/wiki/Reversible_reaction" title="Reversible reaction">reversible reaction</a>. In isothermal, isobaric systems, Gibbs free energy can be thought of as a "dynamic" quantity, in that it is a representative measure of the competing effects of the enthalpic<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="What is enthalpic force? No reference to it in Wikipedia's enthalpy article. (March 2015)">clarification needed</span></a></i>]</sup> and entropic driving forces involved in a thermodynamic process. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Thermodynamics_Gibbs_E0_Ecell_pH.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/b/b2/Thermodynamics_Gibbs_E0_Ecell_pH.png/420px-Thermodynamics_Gibbs_E0_Ecell_pH.png" decoding="async" width="420" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b2/Thermodynamics_Gibbs_E0_Ecell_pH.png/630px-Thermodynamics_Gibbs_E0_Ecell_pH.png 1.5x, //upload.wikimedia.org/wikipedia/en/b/b2/Thermodynamics_Gibbs_E0_Ecell_pH.png 2x" data-file-width="716" data-file-height="286" /></a><figcaption>Relation to other relevant parameters</figcaption></figure> <p>The temperature dependence of the Gibbs energy for an <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gas</a> is given by the <a href="/wiki/Gibbs%E2%80%93Helmholtz_equation" title="Gibbs–Helmholtz equation">Gibbs–Helmholtz equation</a>, and its pressure dependence is given by<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {G}{N}}={\frac {G^{\circ }}{N}}+kT\ln {\frac {p}{p^{\circ }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>G</mi> <mi>N</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>N</mi> </mfrac> </mrow> <mo>+</mo> <mi>k</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {G}{N}}={\frac {G^{\circ }}{N}}+kT\ln {\frac {p}{p^{\circ }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83ebe33d6239d9fd66c244758a28f15529031b22" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.823ex; height:5.843ex;" alt="{\displaystyle {\frac {G}{N}}={\frac {G^{\circ }}{N}}+kT\ln {\frac {p}{p^{\circ }}}.}"></span> </p><p>or more conveniently as its <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {G}{N}}=\mu =\mu ^{\circ }+kT\ln {\frac {p}{p^{\circ }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>G</mi> <mi>N</mi> </mfrac> </mrow> <mo>=</mo> <mi>μ</mi> <mo>=</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>+</mo> <mi>k</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {G}{N}}=\mu =\mu ^{\circ }+kT\ln {\frac {p}{p^{\circ }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16ab65239af4b0142354505a89b3143ea71993c2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.062ex; height:5.843ex;" alt="{\displaystyle {\frac {G}{N}}=\mu =\mu ^{\circ }+kT\ln {\frac {p}{p^{\circ }}}.}"></span> </p><p>In non-ideal systems, <a href="/wiki/Fugacity" title="Fugacity">fugacity</a> comes into play. </p> <div class="mw-heading mw-heading2"><h2 id="Derivation">Derivation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=4" title="Edit section: Derivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Gibbs free energy <a href="/wiki/Total_differential" class="mw-redirect" title="Total differential">total differential</a> with respect to <a href="/wiki/Thermodynamic_potential#Natural_variables" title="Thermodynamic potential">natural variables</a> may be derived by <a href="/wiki/Legendre_transformation" title="Legendre transformation">Legendre transforms</a> of the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a>. </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 \mathrm {d} U=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <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> <mspace width="thinmathspace" /> <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> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c547ae16b2e1e8762072c50621e71e41c3dacac8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.242ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} U=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.}"></span></dd></dl> <p>The definition of <i>G</i> from above is </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 G=U+pV-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <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 G=U+pV-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3124fecdfd2403dd038dd3ee30a018011e302228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.481ex; height:2.509ex;" alt="{\displaystyle G=U+pV-TS}"></span>.</dd></dl> <p>Taking the total differential, we have </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 \mathrm {d} G=\mathrm {d} U+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</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> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G=\mathrm {d} U+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec480ca32c77c2b3fcea8a086622c636acba5317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:40.204ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} G=\mathrm {d} U+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T.}"></span></dd></dl> <p>Replacing d<i>U</i> with the result from the first law gives<sup id="cite_ref-Salzman2001_13-0" class="reference"><a href="#cite_note-Salzman2001-13"><span class="cite-bracket">[</span>13<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 {\begin{aligned}\mathrm {d} G&=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T\\&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <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> <mspace width="thinmathspace" /> <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> <mo>+</mo> <mi>p</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</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> <mspace width="thinmathspace" /> <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> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\mathrm {d} G&=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T\\&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0ff0b3eee913c1c3d9df761ff290f34042c0023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:62.655ex; height:11.176ex;" alt="{\displaystyle {\begin{aligned}\mathrm {d} G&=T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}+p\,\mathrm {d} V+V\,\mathrm {d} p-T\,\mathrm {d} S-S\,\mathrm {d} T\\&=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}.\end{aligned}}}"></span></dd></dl> <p>The natural variables of <i>G</i> are then <i>p</i>, <i>T</i>, and {<i>N</i><sub><i>i</i></sub>}. </p> <div class="mw-heading mw-heading3"><h3 id="Homogeneous_systems">Homogeneous systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=5" title="Edit section: Homogeneous systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because <i>S</i>, <i>V</i>, and <i>N</i><sub><i>i</i></sub> are <a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">extensive variables</a>, an <a href="/wiki/Thermodynamic_potentials#Euler_relations" class="mw-redirect" title="Thermodynamic potentials">Euler relation</a> allows easy integration of d<i>U</i>:<sup id="cite_ref-Salzman2001_13-1" class="reference"><a href="#cite_note-Salzman2001-13"><span class="cite-bracket">[</span>13<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 U=TS-pV+\sum _{i}\mu _{i}N_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mi>V</mi> <mo>+</mo> <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> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=TS-pV+\sum _{i}\mu _{i}N_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8b9af8ad20da89bf31cd23f188baa81e9e452d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.91ex; height:5.509ex;" alt="{\displaystyle U=TS-pV+\sum _{i}\mu _{i}N_{i}.}"></span></dd></dl> <p>Because some of the natural variables of <i>G</i> are intensive, d<i>G</i> may not be integrated using Euler relations as is the case with internal energy. However, simply substituting the above integrated result for <i>U</i> into the definition of <i>G</i> gives a standard expression for <i>G</i>:<sup id="cite_ref-Salzman2001_13-2" class="reference"><a href="#cite_note-Salzman2001-13"><span class="cite-bracket">[</span>13<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 {\begin{aligned}G&=U+pV-TS\\&=\left(TS-pV+\sum _{i}\mu _{i}N_{i}\right)+pV-TS\\&=\sum _{i}\mu _{i}N_{i}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>T</mi> <mi>S</mi> <mo>−</mo> <mi>p</mi> <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> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>p</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></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> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}G&=U+pV-TS\\&=\left(TS-pV+\sum _{i}\mu _{i}N_{i}\right)+pV-TS\\&=\sum _{i}\mu _{i}N_{i}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/809687c0917d217c0acf30d8cbad88b95f8883ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.255ex; margin-bottom: -0.25ex; width:41.513ex; height:16.176ex;" alt="{\displaystyle {\begin{aligned}G&=U+pV-TS\\&=\left(TS-pV+\sum _{i}\mu _{i}N_{i}\right)+pV-TS\\&=\sum _{i}\mu _{i}N_{i}.\end{aligned}}}"></span></dd></dl> <p>This result shows that the chemical potential of a substance <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 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></i> is its (partial) mol(ecul)ar Gibbs free energy. It applies to homogeneous, macroscopic systems, but not to all thermodynamic systems.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Gibbs_free_energy_of_reactions">Gibbs free energy of reactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=6" title="Edit section: Gibbs free energy of reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The system under consideration is held at constant temperature and pressure, and is closed (no matter can come in or out). The Gibbs energy of any system is <span class="nowrap">⁠<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G=U+pV-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <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 G=U+pV-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3124fecdfd2403dd038dd3ee30a018011e302228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.481ex; height:2.509ex;" alt="{\displaystyle G=U+pV-TS}"></span>⁠</span> and an infinitesimal change in <i>G</i>, at constant temperature and pressure, yields </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 dG=dU+pdV-TdS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mi>d</mi> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>d</mi> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG=dU+pdV-TdS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42c816201cf07ef0808a6fa5f176c983fb4d82e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.344ex; height:2.509ex;" alt="{\displaystyle dG=dU+pdV-TdS}"></span>.</dd></dl> <p>By the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a>, a change in the internal energy <i>U</i> is given by </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 dU=\delta Q+\delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>+</mo> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=\delta Q+\delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f10c787cb18695b396842ebeb02fa681e67b9756" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.308ex; height:2.676ex;" alt="{\displaystyle dU=\delta Q+\delta W}"></span></dd></dl> <p>where <span class="texhtml"><i>δQ</i></span> is energy added as heat, and <span class="texhtml"><i>δW</i></span> is energy added as work. The work done on the system may be written as <span class="texhtml"><i>δW</i> = −<i>pdV</i> + <i>δW<sub>x</sub></i></span>, where <span class="texhtml">−<i>pdV</i></span> is the mechanical work of compression/expansion done on or by the system and <span class="texhtml"><i>δW<sub>x</sub></i></span> is all other forms of work, which may include electrical, magnetic, etc. Then </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 dU=\delta Q-pdV+\delta W_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>p</mi> <mi>d</mi> <mi>V</mi> <mo>+</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=\delta Q-pdV+\delta W_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfad00a80d08605ab1e0a3326a31249dd6dc54e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.252ex; height:2.676ex;" alt="{\displaystyle dU=\delta Q-pdV+\delta W_{x}}"></span></dd></dl> <p>and the infinitesimal change in <i>G</i> is </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 dG=\delta Q-TdS+\delta W_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>+</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG=\delta Q-TdS+\delta W_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05b998538c67974f01c41d3d714a7877b96fce2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.475ex; height:2.676ex;" alt="{\displaystyle dG=\delta Q-TdS+\delta W_{x}}"></span>.</dd></dl> <p>The <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a> states that for a closed system at constant temperature (in a heat bath), <span class="nowrap"><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 TdS\geq \delta Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>≥</mo> <mi>δ</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TdS\geq \delta Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31ad1ad35067060565db4924295e4730c374db46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.676ex;" alt="{\displaystyle TdS\geq \delta Q}"></span>,</span> and so it follows that </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 dG\leq \delta W_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>≤</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG\leq \delta W_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc45958a22f726be633105b059bcdec4d57e0a77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.556ex; height:2.676ex;" alt="{\displaystyle dG\leq \delta W_{x}}"></span></dd></dl> <p>Assuming that only mechanical work is done, this simplifies to </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 dG\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cd3f1fc2b37828367d6f9f96526485393070a13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.304ex; height:2.343ex;" alt="{\displaystyle dG\leq 0}"></span></dd></dl> <p>This means that for such a system when not in equilibrium, the Gibbs energy will always be decreasing, and in equilibrium, the infinitesimal change <i>dG</i> will be zero. In particular, this will be true if the system is experiencing any number of internal chemical reactions on its path to equilibrium. </p> <div class="mw-heading mw-heading3"><h3 id="In_electrochemical_thermodynamics">In electrochemical thermodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=7" title="Edit section: In electrochemical thermodynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When electric charge <i>dQ</i><sub>ele</sub> is passed between the electrodes of an electrochemical cell generating an <a href="/wiki/Electromotive_force" title="Electromotive force">emf</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 {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}"></span>, an electrical work term appears in the expression for the change in Gibbs energy: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dG=-SdT+Vdp+{\mathcal {E}}dQ_{ele},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mi>d</mi> <mi>T</mi> <mo>+</mo> <mi>V</mi> <mi>d</mi> <mi>p</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mi>d</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG=-SdT+Vdp+{\mathcal {E}}dQ_{ele},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1aa68ab59810b9eb0cfdb7c6c70982550dfbddb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.421ex; height:2.509ex;" alt="{\displaystyle dG=-SdT+Vdp+{\mathcal {E}}dQ_{ele},}"></span> where <i>S</i> is the <a href="/wiki/Entropy" title="Entropy">entropy</a>, <i>V</i> is the system volume, <i>p</i> is its pressure and <i>T</i> is its <a href="/wiki/Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a>. </p><p>The combination (<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 {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}"></span>, <i>Q<sub>ele</sub></i>) is an example of a <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">conjugate pair of variables</a>. At constant pressure the above equation produces a <a href="/wiki/Maxwell_relation" class="mw-redirect" title="Maxwell relation">Maxwell relation</a> that links the change in open cell voltage with temperature <i>T</i> (a measurable quantity) to the change in entropy <i>S</i> when charge is passed <a href="/wiki/Isothermally" class="mw-redirect" title="Isothermally">isothermally</a> and <a href="/wiki/Isobarically" class="mw-redirect" title="Isobarically">isobarically</a>. The latter is closely related to the reaction <a href="/wiki/Entropy" title="Entropy">entropy</a> of the electrochemical reaction that lends the battery its power. This Maxwell relation is:<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <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 \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q_{ele},p}=-\left({\frac {\partial S}{\partial Q_{ele}}}\right)_{T,p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q_{ele},p}=-\left({\frac {\partial S}{\partial Q_{ele}}}\right)_{T,p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbddddef40f1134fce175d3bbf2f9006b603ac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:29.083ex; height:6.676ex;" alt="{\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q_{ele},p}=-\left({\frac {\partial S}{\partial Q_{ele}}}\right)_{T,p}}"></span></dd></dl> <p>If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is </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 Q_{ele}=-n_{0}F_{0}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta Q_{ele}=-n_{0}F_{0}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e94c6dbf78b9941d37f8be10df10d293605de5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.967ex; height:2.509ex;" alt="{\displaystyle \Delta Q_{ele}=-n_{0}F_{0}\,,}"></span></dd></dl> <p>where <i>n</i><sub>0</sub> is the number of electrons/ion, and <i>F</i><sub>0</sub> is the <a href="/wiki/Faraday_constant" title="Faraday constant">Faraday constant</a> and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by </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 H=-n_{0}F_{0}\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{dT}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H=-n_{0}F_{0}\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{dT}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dac47a34d0922f346d81a6cb431271393605c42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.222ex; height:6.176ex;" alt="{\displaystyle \Delta H=-n_{0}F_{0}\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{dT}}\right),}"></span></dd></dl> <p>where Δ<i>H</i> is the <a href="/wiki/Standard_enthalpy_of_reaction" title="Standard enthalpy of reaction">enthalpy of reaction</a>. The quantities on the right are all directly measurable. </p> <div class="mw-heading mw-heading2"><h2 id="Useful_identities_to_derive_the_Nernst_equation">Useful identities to derive the Nernst equation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=8" title="Edit section: Useful identities to derive the Nernst equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Confusing plainlinks metadata ambox ambox-style ambox-confusing" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may be <a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness">confusing or unclear</a> to readers</b>. In particular, the physical situation is not explained. Also, the circle notation is not well explained (even in the one case where it is attempted). It's just bare equations.<span class="hide-when-compact"> Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the section</a>. There might be a discussion about this on <a href="/wiki/Talk:Gibbs_free_energy" title="Talk:Gibbs free energy">the talk page</a>.</span> <span class="date-container"><i>(<span class="date">March 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>During a reversible electrochemical reaction at constant temperature and pressure, the following equations involving the Gibbs free energy hold: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\text{r}}G=\Delta _{\text{r}}G^{\circ }+RT\ln Q_{\text{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>G</mi> <mo>=</mo> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{r}}G=\Delta _{\text{r}}G^{\circ }+RT\ln Q_{\text{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/278bd241cc763e9fff1236921ff1f5b004a8c05d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.101ex; height:2.676ex;" alt="{\displaystyle \Delta _{\text{r}}G=\Delta _{\text{r}}G^{\circ }+RT\ln Q_{\text{r}}}"></span> (see <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">chemical equilibrium</a>),</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\text{r}}G^{\circ }=-RT\ln K_{\text{eq}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{r}}G^{\circ }=-RT\ln K_{\text{eq}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32c40e2f2f23078e83bbde7638a6f336e3fd83fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.517ex; height:3.009ex;" alt="{\displaystyle \Delta _{\text{r}}G^{\circ }=-RT\ln K_{\text{eq}}}"></span> (for a system at chemical equilibrium),</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\text{r}}G=w_{\text{elec,rev}}=-nF{\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>G</mi> <mo>=</mo> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>elec,rev</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>n</mi> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{r}}G=w_{\text{elec,rev}}=-nF{\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8266076baf4f50bcbe1ea8af6ff84c078dd22e27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.335ex; height:2.843ex;" alt="{\displaystyle \Delta _{\text{r}}G=w_{\text{elec,rev}}=-nF{\mathcal {E}}}"></span> (for a reversible electrochemical process at constant temperature and pressure),</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\text{r}}G^{\circ }=-nF{\mathcal {E}}^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mi>n</mi> <mi>F</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{r}}G^{\circ }=-nF{\mathcal {E}}^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8dd0038ca8ff8fc6592e969950fef60608a0ad2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.126ex; height:2.676ex;" alt="{\displaystyle \Delta _{\text{r}}G^{\circ }=-nF{\mathcal {E}}^{\circ }}"></span> (definition of <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 {\mathcal {E}}^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f86ccfa3068286e87abfcd8b35b456bd40be6f91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.391ex; height:2.343ex;" alt="{\displaystyle {\mathcal {E}}^{\circ }}"></span>),</li></ul> <p>and rearranging gives <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}nF{\mathcal {E}}^{\circ }&=RT\ln K_{\text{eq}},\\nF{\mathcal {E}}&=nF{\mathcal {E}}^{\circ }-RT\ln Q_{\text{r}},\\{\mathcal {E}}&={\mathcal {E}}^{\circ }-{\frac {RT}{nF}}\ln Q_{\text{r}},\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>n</mi> <mi>F</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>n</mi> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>n</mi> <mi>F</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>T</mi> </mrow> <mrow> <mi>n</mi> <mi>F</mi> </mrow> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}nF{\mathcal {E}}^{\circ }&=RT\ln K_{\text{eq}},\\nF{\mathcal {E}}&=nF{\mathcal {E}}^{\circ }-RT\ln Q_{\text{r}},\\{\mathcal {E}}&={\mathcal {E}}^{\circ }-{\frac {RT}{nF}}\ln Q_{\text{r}},\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf275994d7ec5f025021ba8f424c4c205ab7275d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:27.218ex; height:11.509ex;" alt="{\displaystyle {\begin{aligned}nF{\mathcal {E}}^{\circ }&=RT\ln K_{\text{eq}},\\nF{\mathcal {E}}&=nF{\mathcal {E}}^{\circ }-RT\ln Q_{\text{r}},\\{\mathcal {E}}&={\mathcal {E}}^{\circ }-{\frac {RT}{nF}}\ln Q_{\text{r}},\end{aligned}}}"></span> </p><p>which relates the cell potential resulting from the reaction to the equilibrium constant and <a href="/wiki/Reaction_quotient" title="Reaction quotient">reaction quotient</a> for that reaction (<a href="/wiki/Nernst_equation" title="Nernst equation">Nernst equation</a>), </p><p>where </p> <ul><li><span class="texhtml">Δ<sub>r</sub><i>G</i></span>, Gibbs free energy change per mole of reaction,</li> <li><span class="texhtml">Δ<sub>r</sub><i>G°</i></span>, Gibbs free energy change per mole of reaction for unmixed reactants and products at standard conditions (i.e. 298<span class="nowrap"> </span>K, 100<span class="nowrap"> </span>kPa, 1<span class="nowrap"> </span>M of each reactant and product),</li> <li><span class="texhtml"><i>R</i></span>, <a href="/wiki/Gas_constant" title="Gas constant">gas constant</a>,</li> <li><span class="texhtml"><i>T</i></span>, absolute <a href="/wiki/Temperature" title="Temperature">temperature</a>,</li> <li><span class="texhtml">ln</span>, <a href="/wiki/Natural_logarithm" title="Natural logarithm">natural logarithm</a>,</li> <li><span class="texhtml"><i>Q</i><sub>r</sub></span>, <a href="/wiki/Reaction_quotient" title="Reaction quotient">reaction quotient</a> (unitless),</li> <li><span class="texhtml"><i>K</i><sub>eq</sub></span>, <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> (unitless),</li> <li><span class="texhtml"><i>w</i><sub>elec,rev</sub></span>, <a href="/wiki/Work_(electrical)" class="mw-redirect" title="Work (electrical)">electrical work</a> in a reversible process (chemistry sign convention),</li> <li><span class="texhtml"><i>n</i></span>, number of <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> of <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> transferred in the reaction,</li> <li><span class="texhtml"><i>F</i> = <i>N</i><sub>A</sub><i>e</i> ≈ 96485<span class="nowrap"> </span>C/mol</span>, <a href="/wiki/Faraday_constant" title="Faraday constant">Faraday constant</a> (charge per <a href="/wiki/Mole_(unit)" title="Mole (unit)">mole</a> of electrons),</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}"></span>, <a href="/wiki/Electrode_potential" title="Electrode potential">cell potential</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {E}}^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f86ccfa3068286e87abfcd8b35b456bd40be6f91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.391ex; height:2.343ex;" alt="{\displaystyle {\mathcal {E}}^{\circ }}"></span>, <a href="/wiki/Standard_electrode_potential" title="Standard electrode potential">standard cell potential</a>.</li></ul> <p>Moreover, we also have <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}K_{\text{eq}}&=e^{-{\frac {\Delta _{\text{r}}G^{\circ }}{RT}}},\\\Delta _{\text{r}}G^{\circ }&=-RT\left(\ln K_{\text{eq}}\right)=-2.303\,RT\left(\log _{10}K_{\text{eq}}\right),\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mi>R</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>2.303</mn> <mspace width="thinmathspace" /> <mi>R</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}K_{\text{eq}}&=e^{-{\frac {\Delta _{\text{r}}G^{\circ }}{RT}}},\\\Delta _{\text{r}}G^{\circ }&=-RT\left(\ln K_{\text{eq}}\right)=-2.303\,RT\left(\log _{10}K_{\text{eq}}\right),\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80eb4f2bfadad2778e356e0ad06e909a19daa8cc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:49.337ex; height:7.843ex;" alt="{\displaystyle {\begin{aligned}K_{\text{eq}}&=e^{-{\frac {\Delta _{\text{r}}G^{\circ }}{RT}}},\\\Delta _{\text{r}}G^{\circ }&=-RT\left(\ln K_{\text{eq}}\right)=-2.303\,RT\left(\log _{10}K_{\text{eq}}\right),\end{aligned}}}"></span> </p><p>which relates the equilibrium constant with Gibbs free energy. This implies that at equilibrium <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{\text{r}}=K_{\text{eq}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{\text{r}}=K_{\text{eq}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c5813ca0bc70cce86df58857d5372018079a674" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.617ex; height:2.843ex;" alt="{\displaystyle Q_{\text{r}}=K_{\text{eq}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\text{r}}G=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>G</mi> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{r}}G=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ffdf926fb7a01c42f67b5a01d00f316ca5bb4f0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.547ex; height:2.509ex;" alt="{\displaystyle \Delta _{\text{r}}G=0.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Standard_Gibbs_energy_change_of_formation">Standard Gibbs energy change of formation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=9" title="Edit section: Standard Gibbs energy change of formation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable floatright" style="text-align:right"> <caption>Table of selected substances<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> </caption> <tbody><tr> <th rowspan="2">Substance <br />(state) </th> <th colspan="2">Δ<sub><i>f</i></sub><i>G°</i> </th></tr> <tr> <th>(<a href="/wiki/Joule_(unit)" class="mw-redirect" title="Joule (unit)">kJ</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>) </th> <th>(<a href="/wiki/Kilocalorie" class="mw-redirect" title="Kilocalorie">kcal</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>) </th></tr> <tr> <td>NO(g) </td> <td>87.6 </td> <td>20.9<span class="nowrap"> </span> </td></tr> <tr> <td>NO<sub>2</sub>(g) </td> <td>51.3 </td> <td>12.3<span class="nowrap"> </span> </td></tr> <tr> <td>N<sub>2</sub>O(g) </td> <td>103.7 </td> <td>24.78 </td></tr> <tr> <td>H<sub>2</sub>O(g) </td> <td>−228.6 </td> <td>−54.64 </td></tr> <tr> <td>H<sub>2</sub>O(l) </td> <td>−237.1 </td> <td>−56.67 </td></tr> <tr> <td>CO<sub>2</sub>(g) </td> <td>−394.4 </td> <td>−94.26 </td></tr> <tr> <td>CO(g) </td> <td>−137.2 </td> <td>−32.79 </td></tr> <tr> <td>CH<sub>4</sub>(g) </td> <td>−50.5 </td> <td>−12.1<span class="nowrap"> </span> </td></tr> <tr> <td>C<sub>2</sub>H<sub>6</sub>(g) </td> <td>−32.0 </td> <td>−7.65 </td></tr> <tr> <td>C<sub>3</sub>H<sub>8</sub>(g) </td> <td>−23.4 </td> <td>−5.59 </td></tr> <tr> <td>C<sub>6</sub>H<sub>6</sub>(g) </td> <td>129.7 </td> <td>29.76 </td></tr> <tr> <td>C<sub>6</sub>H<sub>6</sub>(l) </td> <td>124.5 </td> <td>31.00 </td></tr></tbody></table> <p>The <a href="/wiki/Standard_Gibbs_free_energy_of_formation" title="Standard Gibbs free energy of formation">standard Gibbs free energy of formation</a> of a compound is the change of Gibbs free energy that accompanies the formation of 1 <a href="/wiki/Mole_(unit)" title="Mole (unit)">mole</a> of that substance from its component elements, in their <a href="/wiki/Standard_state" title="Standard state">standard states</a> (the most stable form of the element at 25 °C and 100 <a href="/wiki/Kilopascal" class="mw-redirect" title="Kilopascal">kPa</a>). Its symbol is Δ<sub><i>f</i></sub><i>G</i>˚. </p><p>All elements in their standard states (diatomic <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> gas, <a href="/wiki/Graphite" title="Graphite">graphite</a>, etc.) have standard Gibbs free energy change of formation equal to zero, as there is no change involved. </p> <dl><dd>Δ<sub>f</sub><i>G</i> = Δ<sub><i>f</i></sub><i>G</i>˚ + <i>RT</i> ln <i>Q<sub>f</sub></i>,</dd></dl> <p>where <i>Q<sub>f</sub></i> is the <a href="/wiki/Reaction_quotient" title="Reaction quotient">reaction quotient</a>. </p><p>At equilibrium, Δ<sub><i>f</i></sub><i>G</i> = 0, and <i>Q<sub>f</sub></i> = <i>K</i>, so the equation becomes </p> <dl><dd>Δ<sub><i>f</i></sub><i>G</i>˚ = −<i>RT</i> ln <i>K</i>,</dd></dl> <p>where <i>K</i> is the <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> of the formation reaction of the substance from the elements in their standard states. </p> <div class="mw-heading mw-heading2"><h2 id="Graphical_interpretation_by_Gibbs">Graphical interpretation by Gibbs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=10" title="Edit section: Graphical interpretation by Gibbs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gibbs free energy was originally defined graphically. In 1873, American scientist <a href="/wiki/Willard_Gibbs" class="mw-redirect" title="Willard Gibbs">Willard Gibbs</a> published his first thermodynamics paper, "Graphical Methods in the Thermodynamics of Fluids", in which Gibbs used the two coordinates of the entropy and volume to represent the state of the body. In his second follow-up paper, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", published later that year, Gibbs added in the third coordinate of the energy of the body, defined on three figures. In 1874, Scottish physicist <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> used Gibbs' figures to make a 3D energy-entropy-volume <a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">thermodynamic surface</a> of a fictitious water-like substance.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Thus, in order to understand the concept of Gibbs free energy, it may help to understand its interpretation by Gibbs as section AB on his figure 3, and as Maxwell sculpted that section on his <a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">3D surface figure</a>. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Gibbs-Maxwell_surfaces.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Gibbs-Maxwell_surfaces.png/750px-Gibbs-Maxwell_surfaces.png" decoding="async" width="750" height="291" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/40/Gibbs-Maxwell_surfaces.png 1.5x" data-file-width="993" data-file-height="385" /></a><figcaption>American scientist <a href="/wiki/Willard_Gibbs" class="mw-redirect" title="Willard Gibbs">Willard Gibbs</a>' 1873 figures two and three (above left and middle) used by Scottish physicist <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> in 1874 to create a three-dimensional <a href="/wiki/Entropy" title="Entropy">entropy</a>, <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>, <a href="/wiki/Energy" title="Energy">energy</a> <b><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">thermodynamic surface</a></b> diagram for a fictitious water-like substance, transposed the two figures of Gibbs (above right) onto the volume-entropy coordinates (transposed to bottom of cube) and energy-entropy coordinates (flipped upside down and transposed to back of cube), respectively, of a three-dimensional <a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a>; the region AB being the first-ever three-dimensional representation of Gibbs free energy, or what Gibbs called "available energy"; the region AC being its capacity for <a href="/wiki/Entropy" title="Entropy">entropy</a>, what Gibbs defined as "the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bioenergetics" title="Bioenergetics">Bioenergetics</a></li> <li><a href="/wiki/Calphad" class="mw-redirect" title="Calphad">Calphad</a> (CALculation of PHAse Diagrams)</li> <li><a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">Critical point (thermodynamics)</a></li> <li><a href="/wiki/Electron_equivalent" class="mw-redirect" title="Electron equivalent">Electron equivalent</a></li> <li><a href="/wiki/Enthalpy-entropy_compensation" class="mw-redirect" title="Enthalpy-entropy compensation">Enthalpy-entropy compensation</a></li> <li><a href="/wiki/Free_entropy" title="Free entropy">Free entropy</a></li> <li><a href="/wiki/Gibbs%E2%80%93Helmholtz_equation" title="Gibbs–Helmholtz equation">Gibbs–Helmholtz equation</a></li> <li><a href="/wiki/Grand_potential" title="Grand potential">Grand potential</a></li> <li><a href="/wiki/Non-random_two-liquid_model" title="Non-random two-liquid model">Non-random two-liquid model</a> (NRTL model) – Gibbs energy of excess and mixing calculation and activity coefficients</li> <li><a href="/wiki/Spinodal" title="Spinodal">Spinodal</a> – Spinodal Curves (Hessian matrix)</li> <li><a href="/wiki/Standard_molar_entropy" title="Standard molar entropy">Standard molar entropy</a></li> <li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Thermodynamic free energy</a></li> <li><a href="/wiki/UNIQUAC" title="UNIQUAC">UNIQUAC</a> model – Gibbs energy of excess and mixing calculation and activity coefficients</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_and_references">Notes and references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=12" title="Edit section: Notes and references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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 reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-Perrot-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Perrot_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Perrot_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Perrot_1-2"><sup><i><b>c</b></i></sup></a></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="CITEREFPerrot1998" 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/0-19-856552-6" title="Special:BookSources/0-19-856552-6"><bdi>0-19-856552-6</bdi></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.isbn=0-19-856552-6&rft.aulast=Perrot&rft.aufirst=Pierre&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-Gibbs1873-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gibbs1873_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gibbs1873_2-1"><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="CITEREFGibbs1873" class="citation journal cs1"><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs, Josiah Willard</a> (December 1873). <a rel="nofollow" class="external text" href="https://www3.nd.edu/~powers/ame.20231/gibbs1873b.pdf">"A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces"</a> <span class="cs1-format">(PDF)</span>. <i>Transactions of the Connecticut Academy of Arts and Sciences</i>. <b>2</b>: 382–404.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Connecticut+Academy+of+Arts+and+Sciences&rft.atitle=A+Method+of+Geometrical+Representation+of+the+Thermodynamic+Properties+of+Substances+by+Means+of+Surfaces&rft.volume=2&rft.pages=382-404&rft.date=1873-12&rft.aulast=Gibbs&rft.aufirst=Josiah+Willard&rft_id=https%3A%2F%2Fwww3.nd.edu%2F~powers%2Fame.20231%2Fgibbs1873b.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-AtkinsJones2007-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-AtkinsJones2007_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeter_AtkinsLoretta_Jones2007" class="citation book cs1">Peter Atkins; Loretta Jones (1 August 2007). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/chemicalprincipl0004unse"><i>Chemical Principles: The Quest for Insight</i></a></span>. W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4292-0965-6" title="Special:BookSources/978-1-4292-0965-6"><bdi>978-1-4292-0965-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Principles%3A+The+Quest+for+Insight&rft.pub=W.+H.+Freeman&rft.date=2007-08-01&rft.isbn=978-1-4292-0965-6&rft.au=Peter+Atkins&rft.au=Loretta+Jones&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fchemicalprincipl0004unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></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="CITEREFReiss1965" class="citation book cs1">Reiss, Howard (1965). <i>Methods of Thermodynamics</i>. Dover Publications. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-69445-3" title="Special:BookSources/0-486-69445-3"><bdi>0-486-69445-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Methods+of+Thermodynamics&rft.pub=Dover+Publications&rft.date=1965&rft.isbn=0-486-69445-3&rft.aulast=Reiss&rft.aufirst=Howard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" 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="CITEREFCalvert1990" class="citation journal cs1">Calvert, J. G. (1 January 1990). <a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac199062112167">"Glossary of atmospheric chemistry terms (Recommendations 1990)"</a>. <i>Pure and Applied Chemistry</i>. <b>62</b> (11): 2167–2219. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac199062112167">10.1351/pac199062112167</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pure+and+Applied+Chemistry&rft.atitle=Glossary+of+atmospheric+chemistry+terms+%28Recommendations+1990%29&rft.volume=62&rft.issue=11&rft.pages=2167-2219&rft.date=1990-01-01&rft_id=info%3Adoi%2F10.1351%2Fpac199062112167&rft.aulast=Calvert&rft.aufirst=J.+G.&rft_id=https%3A%2F%2Fdoi.org%2F10.1351%252Fpac199062112167&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-GoldBook-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-GoldBook_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-GoldBook_6-1"><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 class="citation journal cs1"><a rel="nofollow" class="external text" href="http://goldbook.iupac.org/terms/view/G02629">"Gibbs energy (function), G"</a>. <i>IUPAC Gold Book (Compendium of Chemical Technology)</i>. IUPAC (International Union of Pure and Applied Chemistry). 2008. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.G02629">10.1351/goldbook.G02629</a></span><span class="reference-accessdate">. Retrieved <span class="nowrap">24 December</span> 2020</span>. <q>It was formerly called free energy or free enthalpy.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IUPAC+Gold+Book+%28Compendium+of+Chemical+Technology%29&rft.atitle=Gibbs+energy+%28function%29%2C+G&rft.date=2008&rft_id=info%3Adoi%2F10.1351%2Fgoldbook.G02629&rft_id=http%3A%2F%2Fgoldbook.iupac.org%2Fterms%2Fview%2FG02629&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" 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="CITEREFLehmannFuentes-ArderiuBertello1996" class="citation journal cs1">Lehmann, H. P.; Fuentes-Arderiu, X.; Bertello, L. F. (1 January 1996). <a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac199668040957">"Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)"</a>. <i>Pure and Applied Chemistry</i>. <b>68</b> (4): 957–1000. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac199668040957">10.1351/pac199668040957</a></span>. <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:95196393">95196393</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pure+and+Applied+Chemistry&rft.atitle=Glossary+of+terms+in+quantities+and+units+in+Clinical+Chemistry+%28IUPAC-IFCC+Recommendations+1996%29&rft.volume=68&rft.issue=4&rft.pages=957-1000&rft.date=1996-01-01&rft_id=info%3Adoi%2F10.1351%2Fpac199668040957&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A95196393%23id-name%3DS2CID&rft.aulast=Lehmann&rft.aufirst=H.+P.&rft.au=Fuentes-Arderiu%2C+X.&rft.au=Bertello%2C+L.+F.&rft_id=https%3A%2F%2Fdoi.org%2F10.1351%252Fpac199668040957&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-Leicester1971-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Leicester1971_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenry_Marshall_Leicester1971" class="citation book cs1">Henry Marshall Leicester (1971). <i>The Historical Background of Chemistry</i>. Courier Corporation. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-61053-5" title="Special:BookSources/978-0-486-61053-5"><bdi>978-0-486-61053-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Historical+Background+of+Chemistry&rft.pub=Courier+Corporation&rft.date=1971&rft.isbn=978-0-486-61053-5&rft.au=Henry+Marshall+Leicester&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://goldbook.iupac.org/C01032.html">Chemical Potential</a>, IUPAC Gold Book.</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="CITEREFMüller2007" class="citation book cs1">Müller, Ingo (2007). <i>A History of Thermodynamics – the Doctrine of Energy and Entropy</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-46226-2" title="Special:BookSources/978-3-540-46226-2"><bdi>978-3-540-46226-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Thermodynamics+%E2%80%93+the+Doctrine+of+Energy+and+Entropy&rft.pub=Springer&rft.date=2007&rft.isbn=978-3-540-46226-2&rft.aulast=M%C3%BCller&rft.aufirst=Ingo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatchalskyCurran,_Peter_F.1965" class="citation book cs1">Katchalsky, A.; Curran, Peter F. (1965). <i>Nonequilibrium Thermodynamics in Biophysics</i>. <a href="/wiki/Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>. CCN 65-22045.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nonequilibrium+Thermodynamics+in+Biophysics&rft.pub=Harvard+University+Press&rft.date=1965&rft.aulast=Katchalsky&rft.aufirst=A.&rft.au=Curran%2C+Peter+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtkinsde_Paula2006" class="citation book cs1">Atkins, Peter; de Paula, Julio (2006). <i>Atkins' Physical Chemistry</i> (8th ed.). W. H. Freeman. p. 109. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-8759-8" title="Special:BookSources/0-7167-8759-8"><bdi>0-7167-8759-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atkins%27+Physical+Chemistry&rft.pages=109&rft.edition=8th&rft.pub=W.+H.+Freeman&rft.date=2006&rft.isbn=0-7167-8759-8&rft.aulast=Atkins&rft.aufirst=Peter&rft.au=de+Paula%2C+Julio&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-Salzman2001-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Salzman2001_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Salzman2001_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Salzman2001_13-2"><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 id="CITEREFSalzman2001" class="citation web cs1">Salzman, William R. (2001-08-21). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070707224025/http://www.chem.arizona.edu/~salzmanr/480a/480ants/opensys/opensys.html">"Open Systems"</a>. <i>Chemical Thermodynamics</i>. <a href="/wiki/University_of_Arizona" title="University of Arizona">University of Arizona</a>. Archived from <a rel="nofollow" class="external text" href="http://www.chem.arizona.edu/~salzmanr/480a/480ants/opensys/opensys.html">the original</a> on 2007-07-07<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-10-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Chemical+Thermodynamics&rft.atitle=Open+Systems&rft.date=2001-08-21&rft.aulast=Salzman&rft.aufirst=William+R.&rft_id=http%3A%2F%2Fwww.chem.arizona.edu%2F~salzmanr%2F480a%2F480ants%2Fopensys%2Fopensys.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" 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="CITEREFBrachman1954" class="citation journal cs1">Brachman, M. K. (1954). "Fermi Level, Chemical Potential, and Gibbs Free Energy". <i>The Journal of Chemical Physics</i>. <b>22</b> (6): 1152. <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/1954JChPh..22.1152B">1954JChPh..22.1152B</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%2F1.1740312">10.1063/1.1740312</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=Fermi+Level%2C+Chemical+Potential%2C+and+Gibbs+Free+Energy&rft.volume=22&rft.issue=6&rft.pages=1152&rft.date=1954&rft_id=info%3Adoi%2F10.1063%2F1.1740312&rft_id=info%3Abibcode%2F1954JChPh..22.1152B&rft.aulast=Brachman&rft.aufirst=M.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGibbs+free+energy" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">H. S. Harned, B. B. Owen, The Physical Chemistry of Electrolytic Solutions, third edition, Reinhold Publishing Corporation, N.Y.,1958, p. 2-6</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">CRC Handbook of Chemistry and Physics, 2009, pp. 5-4–5-42, 90th ed., Lide.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">James Clerk Maxwell, <a href="/wiki/Elizabeth_Garber" title="Elizabeth Garber">Elizabeth Garber</a>, Stephen G. Brush, and C. W. Francis Everitt (1995), <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=hA-oIDR0eXkC&pg=PA248">Maxwell on heat and statistical mechanics: on "avoiding all personal enquiries" of molecules</a></i>, Lehigh University Press, <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/0-934223-34-3" title="Special:BookSources/0-934223-34-3">0-934223-34-3</a>, p. 248.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gibbs_free_energy&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" 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Gibbs free energy - Wikipedia