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class="vector-toc-link" href="#Propiedades_de_la_energía_de_Helmholtz"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Propiedades de la energía de Helmholtz</span> </div> </a> <ul id="toc-Propiedades_de_la_energía_de_Helmholtz-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Otros_datos_importantes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Otros_datos_importantes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Otros datos importantes</span> </div> </a> <ul id="toc-Otros_datos_importantes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" 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class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contenidos" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Energía de Helmholtz</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="Ir a un artículo en otro idioma. Disponible en 34 idiomas" > <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-34" 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">34 idiomas</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_%D9%87%D9%84%D9%85%D9%87%D9%88%D9%84%D8%AA%D8%B2_%D8%A7%D9%84%D8%AD%D8%B1%D8%A9" title="طاقة هلمهولتز الحرة (árabe)" lang="ar" hreflang="ar" data-title="طاقة هلمهولتز الحرة" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%B2%D0%B0%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86%D0%B0" title="Свабодная энергія Гельмгольца (bielorruso)" lang="be" hreflang="be" data-title="Свабодная энергія Гельмгольца" data-language-autonym="Беларуская" data-language-local-name="bielorruso" class="interlanguage-link-target"><span>Беларуская</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%A5%D0%B5%D0%BB%D0%BC%D1%85%D0%BE%D0%BB%D1%86" title="Свободна енергия на Хелмхолц (búlgaro)" lang="bg" hreflang="bg" data-title="Свободна енергия на Хелмхолц" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Energia_lliure_de_Helmholtz" title="Energia lliure de Helmholtz (catalán)" lang="ca" hreflang="ca" data-title="Energia lliure de Helmholtz" data-language-autonym="Català" data-language-local-name="catalán" 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/Helmholtzova_voln%C3%A1_energie" title="Helmholtzova volná energie (checo)" lang="cs" hreflang="cs" data-title="Helmholtzova volná energie" data-language-autonym="Čeština" data-language-local-name="checo" 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/Helmholtz_fri_energi" title="Helmholtz fri energi (danés)" lang="da" hreflang="da" data-title="Helmholtz fri energi" data-language-autonym="Dansk" data-language-local-name="danés" 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/Freie_Energie" title="Freie Energie (alemán)" lang="de" hreflang="de" data-title="Freie Energie" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Helmholtz_free_energy" title="Helmholtz free energy (inglés)" lang="en" hreflang="en" data-title="Helmholtz free energy" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Helmholca_libera_energio" title="Helmholca libera energio (esperanto)" lang="eo" hreflang="eo" data-title="Helmholca 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-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Helmholtzi_vabaenergia" title="Helmholtzi vabaenergia (estonio)" lang="et" hreflang="et" data-title="Helmholtzi vabaenergia" data-language-autonym="Eesti" data-language-local-name="estonio" class="interlanguage-link-target"><span>Eesti</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_%D9%87%D9%84%D9%85%D9%88%D9%84%D8%AA%D8%B2" title="انرژی آزاد هلمولتز (persa)" lang="fa" hreflang="fa" data-title="انرژی آزاد هلمولتز" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Helmholtzin_energia" title="Helmholtzin energia (finés)" lang="fi" hreflang="fi" data-title="Helmholtzin energia" data-language-autonym="Suomi" data-language-local-name="finés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89nergie_libre" title="Énergie libre (francés)" lang="fr" hreflang="fr" data-title="Énergie libre" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</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%94%D7%9C%D7%9E%D7%94%D7%95%D7%9C%D7%A5" title="אנרגיה חופשית של הלמהולץ (hebreo)" lang="he" hreflang="he" data-title="אנרגיה חופשית של הלמהולץ" data-language-autonym="עברית" data-language-local-name="hebreo" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D5%AC%D5%B4%D5%B0%D5%B8%D5%AC%D6%81%D5%AB_%D5%A1%D5%A6%D5%A1%D5%BF_%D5%A7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1" title="Հելմհոլցի ազատ էներգիա (armenio)" lang="hy" hreflang="hy" data-title="Հելմհոլցի ազատ էներգիա" data-language-autonym="Հայերեն" data-language-local-name="armenio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Energi_bebas_Helmholtz" title="Energi bebas Helmholtz (indonesio)" lang="id" hreflang="id" data-title="Energi bebas Helmholtz" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" 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_Helmholtz" title="Energia libera di Helmholtz (italiano)" lang="it" hreflang="it" data-title="Energia libera di Helmholtz" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D1%81%D1%8B" title="Гельмгольц энергиясы (kazajo)" lang="kk" hreflang="kk" data-title="Гельмгольц энергиясы" data-language-autonym="Қазақша" data-language-local-name="kazajo" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%97%AC%EB%A6%84%ED%99%80%EC%B8%A0_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" title="헬름홀츠 자유 에너지 (coreano)" lang="ko" hreflang="ko" data-title="헬름홀츠 자유 에너지" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D1%81%D1%8B" title="Гельмгольц энергиясы (kirguís)" lang="ky" hreflang="ky" data-title="Гельмгольц энергиясы" data-language-autonym="Кыргызча" data-language-local-name="kirguís" 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/Helmholco_laisvoji_energija" title="Helmholco laisvoji energija (lituano)" lang="lt" hreflang="lt" data-title="Helmholco laisvoji energija" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86%D1%8B%D0%BD_%D1%87%D3%A9%D0%BB%D3%A9%D3%A9%D1%82_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Гельмгольцын чөлөөт энерги (mongol)" lang="mn" hreflang="mn" data-title="Гельмгольцын чөлөөт энерги" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Helmholtzenergie" title="Helmholtzenergie (neerlandés)" lang="nl" hreflang="nl" data-title="Helmholtzenergie" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Helmholtz_fri_energi" title="Helmholtz fri energi (noruego bokmal)" lang="nb" hreflang="nb" data-title="Helmholtz fri energi" data-language-autonym="Norsk bokmål" data-language-local-name="noruego bokmal" 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/Energia_swobodna_Helmholtza" title="Energia swobodna Helmholtza (polaco)" lang="pl" hreflang="pl" data-title="Energia swobodna Helmholtza" data-language-autonym="Polski" data-language-local-name="polaco" 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_Helmholtz" title="Energia livre de Helmholtz (portugués)" lang="pt" hreflang="pt" data-title="Energia livre de Helmholtz" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86%D0%B0" title="Свободная энергия Гельмгольца (ruso)" lang="ru" hreflang="ru" data-title="Свободная энергия Гельмгольца" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Helmholcova_slobodna_energija" title="Helmholcova slobodna energija (serbocroata)" lang="sh" hreflang="sh" data-title="Helmholcova slobodna energija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Helmholcova_slobodna_energija" title="Helmholcova slobodna energija (serbio)" lang="sr" hreflang="sr" data-title="Helmholcova slobodna energija" data-language-autonym="Српски / srpski" data-language-local-name="serbio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Helmholtz_fria_energi" title="Helmholtz fria energi (sueco)" lang="sv" hreflang="sv" data-title="Helmholtz fria energi" data-language-autonym="Svenska" data-language-local-name="sueco" 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%AF%86%E0%AE%B2%E0%AF%8D%E0%AE%AE%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%9A%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%95%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BF%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AE%BE_%E0%AE%86%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D" title="கெல்ம்கோட்சின் கட்டில்லா ஆற்றல் (tamil)" lang="ta" hreflang="ta" data-title="கெல்ம்கோட்சின் கட்டில்லா ஆற்றல்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</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%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86%D0%B0" title="Вільна енергія Гельмгольца (ucraniano)" lang="uk" hreflang="uk" data-title="Вільна енергія Гельмгольца" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%A5%E5%A7%86%E9%9C%8D%E5%85%B9%E8%87%AA%E7%94%B1%E8%83%BD" title="亥姆霍兹自由能 (chino)" lang="zh" hreflang="zh" data-title="亥姆霍兹自由能" data-language-autonym="中文" data-language-local-name="chino" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%A5%E5%A7%86%E9%9C%8D%E8%8C%B2%E8%87%AA%E7%94%B1%E8%83%BD" title="亥姆霍茲自由能 (cantonés)" lang="yue" hreflang="yue" data-title="亥姆霍茲自由能" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q865821#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espacios de nombres"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Apariencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De Wikipedia, la enciclopedia libre</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="es" dir="ltr"><p>La <b>energía de Helmholtz</b> (también denominada <b>función de Helmholtz</b>, <b>energía libre de Helmholtz</b> o <b>función trabajo</b>) es una <a href="/wiki/Magnitud_extensiva" class="mw-redirect" title="Magnitud extensiva">magnitud extensiva</a>, <a href="/wiki/Funci%C3%B3n_de_estado" title="Función de estado">función de estado</a> y <a href="/wiki/Potencial_termodin%C3%A1mico" title="Potencial termodinámico">potencial termodinámico</a>, de un <a href="/wiki/Sistema_termodin%C3%A1mico" title="Sistema termodinámico">sistema termodinámico</a> que mide el trabajo obtenible en un sistema cerrado, en condiciones de temperatura constante. No depende del proceso sufrido, sino del estado final e inicial del sistema. Se usa para ver qué procesos son espontáneos en condiciones de temperatura y volumen constantes. Si el volumen no se mantiene constante, parte del trabajo se efectua en el entorno. Previamente era denominada energía <b>libre</b>, término que actualmente se retiró de acuerdo a la proposición de la <a href="/wiki/IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a>.<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> </p><p>La energía de Helmholtz fue desarrollada por <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a>, un físico alemán, y suele denominarse con la letra F. Sin embargo la IUPAC recomienda el uso de la letra A (del alemán <i>Arbeit</i>, «trabajo») y el uso del nombre «energía de Helmholtz». </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Propiedades_de_la_energía_de_Helmholtz"><span id="Propiedades_de_la_energ.C3.ADa_de_Helmholtz"></span>Propiedades de la energía de Helmholtz</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energ%C3%ADa_de_Helmholtz&action=edit&section=1" title="Editar sección: Propiedades de la energía de Helmholtz"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se mide en <a href="/wiki/Julio_(unidad)" title="Julio (unidad)">julios</a> [J], <a href="/wiki/Calor%C3%ADa" title="Caloría">calorías</a> [cal] o cualquier otra unidad de <a href="/wiki/Energ%C3%ADa" title="Energía">energía</a>. Sus variables canónicas son la <a href="/wiki/Temperatura" title="Temperatura">temperatura</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> y el <a href="/wiki/Volumen" title="Volumen">volumen</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> del <a href="/wiki/Sistema_termodin%C3%A1mico" title="Sistema termodinámico">sistema</a>. Además, se suele simbolizar con la letra <i>A</i>, de «trabajo» (<i>arbeit</i>, en <a href="/wiki/Idioma_alem%C3%A1n" title="Idioma alemán">alemán</a>) o la letra <i>F</i>, de libre (<i>free</i>, en <a href="/wiki/Idioma_ingl%C3%A9s" title="Idioma inglés">inglés</a>). La definición es: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(T,V)=U(T,V)-TS(T,V)\,\quad {\mbox{o}}\quad F=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>o</mtext> </mstyle> </mrow> <mspace width="1em" /> <mi>F</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(T,V)=U(T,V)-TS(T,V)\,\quad {\mbox{o}}\quad F=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1675d6533b38f5c316441509f120b4865120db74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:50.19ex; height:2.843ex;" alt="{\displaystyle F(T,V)=U(T,V)-TS(T,V)\,\quad {\mbox{o}}\quad F=U-TS}"></span> </p> </blockquote> <p>donde <i>U</i> es la <a href="/wiki/Energ%C3%ADa_interna" title="Energía interna">energía interna</a> y <i>S</i> la <a href="/wiki/Entrop%C3%ADa" title="Entropía">entropía</a>. La definición anterior implica la <a href="/wiki/1-forma" title="1-forma">1-forma</a> diferencial viene dada por: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dF=-SdT-PdV\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mi>d</mi> <mi>T</mi> <mo>−</mo> <mi>P</mi> <mi>d</mi> <mi>V</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dF=-SdT-PdV\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5c886de7977d8f437f04e4d4b899184fac3b5cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.191ex; height:2.343ex;" alt="{\displaystyle dF=-SdT-PdV\,}"></span> </p> </blockquote> <p>donde <i>P</i> es la <a href="/wiki/Presi%C3%B3n" title="Presión">presión</a> del sistema. En consecuencia: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(V,T)=-\left({\frac {\partial F}{\partial V}}\right)_{T},\qquad S(V,T)=-\left({\frac {\partial F}{\partial T}}\right)_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>V</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>,</mo> <mspace width="2em" /> <mi>S</mi> <mo stretchy="false">(</mo> <mi>V</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(V,T)=-\left({\frac {\partial F}{\partial V}}\right)_{T},\qquad S(V,T)=-\left({\frac {\partial F}{\partial T}}\right)_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84e2fd653f7e23e6aeed80efa6c8e82d60bbaf63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.834ex; height:6.176ex;" alt="{\displaystyle P(V,T)=-\left({\frac {\partial F}{\partial V}}\right)_{T},\qquad S(V,T)=-\left({\frac {\partial F}{\partial T}}\right)_{V}}"></span> </p> </blockquote> <div class="mw-heading mw-heading2"><h2 id="Otros_datos_importantes">Otros datos importantes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energ%C3%ADa_de_Helmholtz&action=edit&section=2" title="Editar sección: Otros datos importantes"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se relaciona con la <a href="/wiki/Energ%C3%ADa_de_Gibbs" title="Energía de Gibbs">energía de Gibbs</a> mediante la expresión </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span style="float: right; width: 10%; text-align: right;">(<cite id="Equation_3" style="font-style: normal;"><a href="#Eqnref_3">3</a></cite>)</span> </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=dF+d(PV)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>G</mi> <mo>=</mo> <mi>d</mi> <mi>F</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mi>V</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dG=dF+d(PV)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9d9233aa8da997d16d423cb99aebf13c1f048a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.883ex; height:2.843ex;" alt="{\displaystyle dG=dF+d(PV)\,}"></span></dd></dl> </blockquote> <p>Notar de la ecuación (1), que del <a href="/wiki/Primer_principio_de_termodin%C3%A1mica" class="mw-redirect" title="Primer principio de termodinámica">primer principio de termodinámica</a> </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=Q-W=\Delta (TS)+\Delta F\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mo>−</mo> <mi>W</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mi>S</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>F</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q-W=\Delta (TS)+\Delta F\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d00e52d80c0c79780e25c84b52b6c53f70ddf650" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.814ex; height:2.843ex;" alt="{\displaystyle \Delta U=Q-W=\Delta (TS)+\Delta F\,}"></span> </p> </blockquote> <p>Donde </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4716a2c49bbbe155e8b399117ca78342e802cbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.718ex; height:2.176ex;" alt="{\displaystyle \Delta U}"></span> = variación de <a href="/wiki/Energ%C3%ADa_interna" title="Energía interna">energía interna</a> del sistema</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> = <a href="/wiki/Calor" title="Calor">calor</a> recibido por el sistema</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> = <a href="/wiki/Trabajo_(f%C3%ADsica)" title="Trabajo (física)">trabajo</a> realizado por el sistema</dd></dl> <p>Siendo: </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 TdS=dQ_{r}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>=</mo> <mi>d</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TdS=dQ_{r}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46cc878f7464e6949ae6161a86f0f475e55b1d27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.865ex; height:2.509ex;" alt="{\displaystyle TdS=dQ_{r}\,}"></span> el <a href="/wiki/Calor" title="Calor">calor</a> <a href="/wiki/Proceso_reversible" title="Proceso reversible">reversible</a> (es decir, que se puede evacuar o recuperar del <a href="/wiki/Sistema" title="Sistema">sistema</a> cuantas veces se quiera, sin requerir un gasto extra de energía en este proceso).</dd></dl> <p>Integrando 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> constante: </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 (TS)=Q_{r}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta (TS)=Q_{r}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8066a455bb6692e3b6a5c93f0fcc9f745a7df63b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.178ex; height:2.843ex;" alt="{\displaystyle \Delta (TS)=Q_{r}\,}"></span></dd></dl> <p>Por lo tanto, en un proceso reversible, el <a href="/wiki/Trabajo_(f%C3%ADsica)" title="Trabajo (física)">trabajo</a> realizado por el sistema es el negativo de la variación de su energía de Helmholtz: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{r}=-\Delta F\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>F</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{r}=-\Delta F\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/330713b3acfc2c8be15aeb8d5101ec91d6d7ec20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.138ex; height:2.509ex;" alt="{\displaystyle W_{r}=-\Delta F\,}"></span> </p> </blockquote> <p>De ahí que también reciba el nombre de «función trabajo». </p><p>La energía de Helmholtz es muy importante en <a href="/wiki/Mec%C3%A1nica_estad%C3%ADstica" title="Mecánica estadística">mecánica estadística</a>, ya que su relación con el <a href="/wiki/Colectivo_can%C3%B3nico" class="mw-redirect" title="Colectivo canónico">colectivo canónico</a> permite determinar las propiedades termodinámicas del sistema. Dicha relación viene dada por: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(T,V,N)=-kT\ln {\mathcal {Q}}(T,V,N)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">Q</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(T,V,N)=-kT\ln {\mathcal {Q}}(T,V,N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cebaa78c3e319eb8e7347bf6bc8f7a80438219c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.836ex; height:2.843ex;" alt="{\displaystyle F(T,V,N)=-kT\ln {\mathcal {Q}}(T,V,N)}"></span> </p> </blockquote> <p>donde <span class="mwe-math-element"><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 {Q}}(T,V,N)}"> <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">Q</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {Q}}(T,V,N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f04656d9cc694b745ae83e77dd8f42d010f0f80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.263ex; height:2.843ex;" alt="{\displaystyle {\mathcal {Q}}(T,V,N)}"></span> representa la función de partición canónica, que en el caso de que las N partículas del sistema sean no interactuantes, se puede escribir a partir de la función de partición de partículas individuales: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {Q}}(T,V,N)={\mathcal {Z}}^{N}=(\sum _{i}e^{-\epsilon _{i}/KT})^{N}}"> <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">Q</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">Z</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>K</mi> <mi>T</mi> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {Q}}(T,V,N)={\mathcal {Z}}^{N}=(\sum _{i}e^{-\epsilon _{i}/KT})^{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aba39b1bcc8e2f72e73be558bb2fcaaaca87ec30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.533ex; height:5.509ex;" alt="{\displaystyle {\mathcal {Q}}(T,V,N)={\mathcal {Z}}^{N}=(\sum _{i}e^{-\epsilon _{i}/KT})^{N}}"></span> </p> </blockquote> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energ%C3%ADa_de_Helmholtz&action=edit&section=3" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Termodin%C3%A1mica" title="Termodinámica">Termodinámica</a></li> <li><a href="/wiki/Entalp%C3%ADa" title="Entalpía">Entalpía</a></li> <li><a href="/wiki/Reacci%C3%B3n_qu%C3%ADmica" title="Reacción química">Reacción química</a></li> <li><a href="/wiki/Termoqu%C3%ADmica" title="Termoquímica">Termoquímica</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energ%C3%ADa_de_Helmholtz&action=edit&section=4" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Green Book, 2nd ed.: IUPAC Quantities, Units and Symbols in Physical Chemistry. Second Edition, Blackwell Scientific Publications, Oxford, 1993.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Enlaces_externos">Enlaces externos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energ%C3%ADa_de_Helmholtz&action=edit&section=5" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070908102836/http://www.netcom.es/pilar_mu/equilibrio.htm">Más información</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; 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