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</div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sitio"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Conteníu" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Conteníu</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover a la barra llateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">despintar</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Entamu</div> </a> </li> <li id="toc-L'enfoque_termodinámicu:_la_ecuación_fundamental" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#L'enfoque_termodinámicu:_la_ecuación_fundamental"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>L'enfoque termodinámicu: la ecuación fundamental</span> </div> </a> <ul id="toc-L'enfoque_termodinámicu:_la_ecuación_fundamental-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Delles_variaciones_de_la_enerxía_interno" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Delles_variaciones_de_la_enerxía_interno"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Delles variaciones de la enerxía interno</span> </div> </a> <button aria-controls="toc-Delles_variaciones_de_la_enerxía_interno-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>Alternar subsección Delles variaciones de la enerxía interno</span> </button> <ul id="toc-Delles_variaciones_de_la_enerxía_interno-sublist" class="vector-toc-list"> <li id="toc-Variación_ensin_cambéu_d'estáu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variación_ensin_cambéu_d'estáu"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Variación ensin cambéu d'estáu</span> </div> </a> <ul id="toc-Variación_ensin_cambéu_d'estáu-sublist" class="vector-toc-list"> <li id="toc-Exemplu" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Exemplu"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Exemplu</span> </div> </a> <ul id="toc-Exemplu-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Enerxía_cinética_media_d'un_gas_ideal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Enerxía_cinética_media_d'un_gas_ideal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Enerxía cinética media d'un gas ideal</span> </div> </a> <ul id="toc-Enerxía_cinética_media_d'un_gas_ideal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variación_con_cambéu_de_la_composición_química" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variación_con_cambéu_de_la_composición_química"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Variación con cambéu de la composición química</span> </div> </a> <ul id="toc-Variación_con_cambéu_de_la_composición_química-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variación_nuclear" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variación_nuclear"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Variación nuclear</span> </div> </a> <ul id="toc-Variación_nuclear-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ver_tamién" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_tamién"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Ver tamién</span> </div> </a> <ul id="toc-Ver_tamién-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencies"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referencies</span> </div> </a> <ul id="toc-Referencies-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="Conteníu" 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">Enerxía interno</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 66 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-66" 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">66 llingües</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%AF%D8%A7%D8%AE%D9%84%D9%8A%D8%A9" title="طاقة داخلية – árabe" lang="ar" hreflang="ar" data-title="طاقة داخلية" 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%A3%D0%BD%D1%83%D1%82%D1%80%D0%B0%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F" title="Унутраная энергія – bielorrusu" lang="be" hreflang="be" data-title="Унутраная энергія" data-language-autonym="Беларуская" data-language-local-name="bielorrusu" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9D%D1%83%D1%82%D1%80%D0%B0%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D1%8D%D1%80%D0%B3%D1%96%D1%8F" title="Нутраная энэргія – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Нутраная энэргія" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D1%8A%D1%82%D1%80%D0%B5%D1%88%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Вътрешна енергия – búlgaru" lang="bg" hreflang="bg" data-title="Вътрешна енергия" data-language-autonym="Български" data-language-local-name="búlgaru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AD%E0%A7%8D%E0%A6%AF%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0%E0%A7%80%E0%A6%A3_%E0%A6%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF" title="অভ্যন্তরীণ শক্তি – bengalín" lang="bn" hreflang="bn" data-title="অভ্যন্তরীণ শক্তি" data-language-autonym="বাংলা" data-language-local-name="bengalín" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Unutra%C5%A1nja_energija" title="Unutrašnja energija – bosniu" lang="bs" hreflang="bs" data-title="Unutrašnja energija" data-language-autonym="Bosanski" data-language-local-name="bosniu" 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_interna" title="Energia interna – catalán" lang="ca" hreflang="ca" data-title="Energia interna" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%88%D8%B2%DB%95%DB%8C_%D9%86%D8%A7%D9%88%DB%95%DA%A9%DB%8C" title="وزەی ناوەکی – kurdu central" lang="ckb" hreflang="ckb" data-title="وزەی ناوەکی" data-language-autonym="کوردی" data-language-local-name="kurdu central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vnit%C5%99n%C3%AD_energie" title="Vnitřní energie – checu" lang="cs" hreflang="cs" data-title="Vnitřní energie" data-language-autonym="Čeština" data-language-local-name="checu" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D0%B0%D0%BB%D1%82%D0%B8_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Шалти энерги – chuvash" lang="cv" hreflang="cv" data-title="Шалти энерги" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Indre_energi" title="Indre energi – danés" lang="da" hreflang="da" data-title="Indre 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/Innere_Energie" title="Innere Energie – alemán" lang="de" hreflang="de" data-title="Innere Energie" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%83%CF%89%CF%84%CE%B5%CF%81%CE%B9%CE%BA%CE%AE_%CE%B5%CE%BD%CE%AD%CF%81%CE%B3%CE%B5%CE%B9%CE%B1" title="Εσωτερική ενέργεια – griegu" lang="el" hreflang="el" data-title="Εσωτερική ενέργεια" data-language-autonym="Ελληνικά" data-language-local-name="griegu" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Internal_energy" title="Internal energy – inglés" lang="en" hreflang="en" data-title="Internal 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/Interna_energio" title="Interna energio – esperanto" lang="eo" hreflang="eo" data-title="Interna energio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Energ%C3%ADa_interna" title="Energía interna – español" lang="es" hreflang="es" data-title="Energía interna" data-language-autonym="Español" data-language-local-name="español" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Siseenergia" title="Siseenergia – estoniu" lang="et" hreflang="et" data-title="Siseenergia" data-language-autonym="Eesti" data-language-local-name="estoniu" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Barne_energia" title="Barne energia – vascu" lang="eu" hreflang="eu" data-title="Barne energia" data-language-autonym="Euskara" data-language-local-name="vascu" 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%AF%D8%B1%D9%88%D9%86%DB%8C" title="انرژی درونی – persa" lang="fa" hreflang="fa" data-title="انرژی درونی" 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/Sis%C3%A4energia" title="Sisäenergia – finlandés" lang="fi" hreflang="fi" data-title="Sisäenergia" data-language-autonym="Suomi" data-language-local-name="finlandés" 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_interne" title="Énergie interne – francés" lang="fr" hreflang="fr" data-title="Énergie interne" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Fuinneamh_inmhe%C3%A1nach" title="Fuinneamh inmheánach – irlandés" lang="ga" hreflang="ga" data-title="Fuinneamh inmheánach" data-language-autonym="Gaeilge" data-language-local-name="irlandés" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Enerx%C3%ADa_interna" title="Enerxía interna – gallegu" lang="gl" hreflang="gl" data-title="Enerxía interna" data-language-autonym="Galego" data-language-local-name="gallegu" class="interlanguage-link-target"><span>Galego</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%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="אנרגיה פנימית – hebréu" lang="he" hreflang="he" data-title="אנרגיה פנימית" data-language-autonym="עברית" data-language-local-name="hebréu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%86%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A4%B0%E0%A4%BF%E0%A4%95_%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE" title="आन्तरिक ऊर्जा – hindi" lang="hi" hreflang="hi" data-title="आन्तरिक 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/Unutarnja_energija" title="Unutarnja energija – croata" lang="hr" hreflang="hr" data-title="Unutarnja energija" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/En%C3%A8ji_t%C3%A8mik" title="Enèji tèmik – haitianu" lang="ht" hreflang="ht" data-title="Enèji tèmik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitianu" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Bels%C5%91_energia" title="Belső energia – húngaru" lang="hu" hreflang="hu" data-title="Belső energia" data-language-autonym="Magyar" data-language-local-name="húngaru" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%86%D5%A5%D6%80%D6%84%D5%AB%D5%B6_%D5%A7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1" title="Ներքին էներգիա – armeniu" lang="hy" hreflang="hy" data-title="Ներքին էներգիա" data-language-autonym="Հայերեն" data-language-local-name="armeniu" 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_dalam" title="Energi dalam – indonesiu" lang="id" hreflang="id" data-title="Energi dalam" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiu" 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_interna" title="Energia interna – italianu" lang="it" hreflang="it" data-title="Energia interna" data-language-autonym="Italiano" data-language-local-name="italianu" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%85%E9%83%A8%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="内部エネルギー – xaponés" lang="ja" hreflang="ja" data-title="内部エネルギー" data-language-autonym="日本語" data-language-local-name="xaponés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%86%D1%88%D0%BA%D1%96_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Ішкі энергия – kazaquistanín" lang="kk" hreflang="kk" data-title="Ішкі энергия" data-language-autonym="Қазақша" data-language-local-name="kazaquistanín" 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/%EB%82%B4%EB%B6%80_%EC%97%90%EB%84%88%EC%A7%80" title="내부 에너지 – coreanu" lang="ko" hreflang="ko" data-title="내부 에너지" data-language-autonym="한국어" data-language-local-name="coreanu" 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%98%D1%87%D0%BA%D0%B8_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Ички энергия – kirguistanín" lang="ky" hreflang="ky" data-title="Ички энергия" data-language-autonym="Кыргызча" data-language-local-name="kirguistanín" 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/Vidin%C4%97_energija" title="Vidinė energija – lituanu" lang="lt" hreflang="lt" data-title="Vidinė energija" data-language-autonym="Lietuvių" data-language-local-name="lituanu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Iek%C5%A1%C4%93j%C4%81_ener%C4%A3ija" title="Iekšējā enerģija – letón" lang="lv" hreflang="lv" data-title="Iekšējā enerģija" data-language-autonym="Latviešu" data-language-local-name="letón" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D0%BD%D0%B0%D1%82%D1%80%D0%B5%D1%88%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%98%D0%B0" title="Внатрешна енергија – macedoniu" lang="mk" hreflang="mk" data-title="Внатрешна енергија" data-language-autonym="Македонски" data-language-local-name="macedoniu" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%B0%E0%B4%BF%E0%B4%95_%E0%B4%8A%E0%B5%BC%E0%B4%9C%E0%B5%8D%E0%B4%9C%E0%B4%82" title="ആന്തരിക ഊർജ്ജം – malayalam" lang="ml" hreflang="ml" data-title="ആന്തരിക ഊർജ്ജം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%94%D0%BE%D1%82%D0%BE%D0%BE%D0%B4_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Дотоод энерги – mongol" lang="mn" hreflang="mn" data-title="Дотоод энерги" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tenaga_dalaman" title="Tenaga dalaman – malayu" lang="ms" hreflang="ms" data-title="Tenaga dalaman" data-language-autonym="Bahasa Melayu" data-language-local-name="malayu" 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/Inwendige_energie" title="Inwendige energie – neerlandés" lang="nl" hreflang="nl" data-title="Inwendige energie" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Indre_energi" title="Indre energi – noruegu Nynorsk" lang="nn" hreflang="nn" data-title="Indre energi" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegu Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Indre_energi" title="Indre energi – noruegu Bokmål" lang="nb" hreflang="nb" data-title="Indre energi" data-language-autonym="Norsk bokmål" data-language-local-name="noruegu Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Energia_int%C3%A8rna" title="Energia intèrna – occitanu" lang="oc" hreflang="oc" data-title="Energia intèrna" data-language-autonym="Occitan" data-language-local-name="occitanu" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Energia_wewn%C4%99trzna" title="Energia wewnętrzna – polacu" lang="pl" hreflang="pl" data-title="Energia wewnętrzna" data-language-autonym="Polski" data-language-local-name="polacu" 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_interna" title="Energia interna – portugués" lang="pt" hreflang="pt" data-title="Energia interna" data-language-autonym="Português" data-language-local-name="portugués" 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/Energie_intern%C4%83" title="Energie internă – rumanu" lang="ro" hreflang="ro" data-title="Energie internă" data-language-autonym="Română" data-language-local-name="rumanu" 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%92%D0%BD%D1%83%D1%82%D1%80%D0%B5%D0%BD%D0%BD%D1%8F%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Внутренняя энергия – rusu" lang="ru" hreflang="ru" data-title="Внутренняя энергия" data-language-autonym="Русский" data-language-local-name="rusu" 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/Unutarnja_energija" title="Unutarnja energija – serbo-croata" lang="sh" hreflang="sh" data-title="Unutarnja energija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Internal_energy" title="Internal energy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Internal 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/Vn%C3%BAtorn%C3%A1_energia" title="Vnútorná energia – eslovacu" lang="sk" hreflang="sk" data-title="Vnútorná energia" data-language-autonym="Slovenčina" data-language-local-name="eslovacu" 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/Notranja_energija" title="Notranja energija – eslovenu" lang="sl" hreflang="sl" data-title="Notranja energija" data-language-autonym="Slovenščina" data-language-local-name="eslovenu" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Energjia_e_brendshme" title="Energjia e brendshme – albanu" lang="sq" hreflang="sq" data-title="Energjia e brendshme" data-language-autonym="Shqip" data-language-local-name="albanu" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Unutra%C5%A1nja_energija" title="Unutrašnja energija – serbiu" lang="sr" hreflang="sr" data-title="Unutrašnja energija" data-language-autonym="Српски / srpski" data-language-local-name="serbiu" 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/Inre_energi" title="Inre energi – suecu" lang="sv" hreflang="sv" data-title="Inre energi" data-language-autonym="Svenska" data-language-local-name="suecu" 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%85%E0%AE%95_%E0%AE%86%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D" title="அக ஆற்றல் – tamil" lang="ta" hreflang="ta" data-title="அக ஆற்றல்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0%C3%A7_enerji" title="İç enerji – turcu" lang="tr" hreflang="tr" data-title="İç enerji" data-language-autonym="Türkçe" data-language-local-name="turcu" 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%D0%BD%D1%83%D1%82%D1%80%D1%96%D1%88%D0%BD%D1%8F_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F" title="Внутрішня енергія – ucraín" lang="uk" hreflang="uk" data-title="Внутрішня енергія" data-language-autonym="Українська" data-language-local-name="ucraín" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ichki_energiya" title="Ichki energiya – uzbequistanín" lang="uz" hreflang="uz" data-title="Ichki energiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbequistanín" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/N%E1%BB%99i_n%C4%83ng" title="Nội năng – vietnamín" lang="vi" hreflang="vi" data-title="Nội năng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamín" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%86%85%E8%83%BD" title="内能 – chinu wu" lang="wuu" hreflang="wuu" data-title="内能" data-language-autonym="吴语" data-language-local-name="chinu wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%86%85%E8%83%BD" title="内能 – chinu" lang="zh" hreflang="zh" data-title="内能" data-language-autonym="中文" data-language-local-name="chinu" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%85%A7%E8%83%BD" title="內能 – chinu lliterariu" lang="lzh" hreflang="lzh" data-title="內能" data-language-autonym="文言" data-language-local-name="chinu lliterariu" 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width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Robot_icon.svg/24px-Robot_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Robot_icon.svg/32px-Robot_icon.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div></div> </div> <div id="siteSub" class="noprint">De Wikipedia</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="ast" dir="ltr"><p>En <a href="/wiki/F%C3%ADsica" title="Física">física</a>, la <b>enerxía interno</b> <i>(U)</i> d'un sistema intenta ser un reflexu de la enerxía a escala macroscópica. Más concretamente, ye la suma de: </p> <ul><li>la <i>enerxía cinético interno</i>, esto ye, de les sumes de les enerxíes cinétiques de les individualidaes que formen un cuerpu respeuto al centru de mases del sistema,</li> <li>la <i>enerxía potencial interno</i>, que ye la enerxía potencial acomuñada a les interacciones ente estes individualidaes.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li></ul><p> La enerxía interno nun inclúi la enerxía cinética traslacional o rotacional del sistema como un tou. Tampoco inclúi la enerxía potencial que'l cuerpu pueda tener pol so llocalización nun campu gravitacional o electrostático esternu. </p><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Exercise_ball.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Exercise_ball.jpg/150px-Exercise_ball.jpg" decoding="async" width="150" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Exercise_ball.jpg/225px-Exercise_ball.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Exercise_ball.jpg/300px-Exercise_ball.jpg 2x" data-file-width="456" data-file-height="458" /></a><figcaption>Tou cuerpu tien una enerxía acumulada nel so interior equivalente a la enerxía cinético interno más la enerxía potencial interno.</figcaption></figure> <p>Si pensamos en constituyentes atómicos o moleculares, va ser la resultancia de la suma de la <a href="/wiki/Enerx%C3%ADa_cin%C3%A9tica" class="mw-redirect" title="Enerxía cinética">enerxía cinética</a> de les <a href="/wiki/Mol%C3%A9cula" title="Molécula">molécules</a> o <a href="/wiki/%C3%81tomu" title="Átomu">átomos</a> que constitúin el sistema (de les sos enerxíes de traslación, rotación y vibración) y de la <a href="/wiki/Enerx%C3%ADa_potencial" title="Enerxía potencial">enerxía potencial</a> intermolecular (debida a les <a href="/w/index.php?title=Fuercies_intermoleculares&action=edit&redlink=1" class="new" title="Fuercies intermoleculares (la páxina nun esiste)">fuercies intermoleculares</a>) ya intramolecular de la <a href="/w/index.php?title=Enerx%C3%ADa_d%27enllaz&action=edit&redlink=1" class="new" title="Enerxía d'enllaz (la páxina nun esiste)">enerxía d'enllaz</a>. </p> <ul><li>Nun <a href="/wiki/Gas_ideal" title="Gas ideal">gas ideal</a> <a href="/w/index.php?title=Monoat%C3%B3mico&action=edit&redlink=1" class="new" title="Monoatómico (la páxina nun esiste)">monoatómico</a> va bastar con considerar la enerxía cinética de traslación de los sos átomos.</li> <li>Nun gas ideal poliatómico, tendremos de considerar amás la enerxía vibracional y rotacional de les mesmes.</li> <li>Nun líquidu o sólidu tendremos d'añader la enerxía potencial que representa les interacciones moleculares.</li></ul> <p>Dende'l puntu de vista de la <a href="/wiki/Termodin%C3%A1mica" title="Termodinámica">termodinámica</a>, nun <a href="/wiki/Sistema_zarr%C3%A1u" title="Sistema zarráu">sistema zarráu</a> (esto ye, de parés impermeables), la variación total d'enerxía interno ye igual a la suma de les cantidaes d'enerxía comunicaes al sistema en forma de calor y de trabayu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=Q+W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q+W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f4ec9e7a548ba5f79fc841c5352e571392540e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.931ex; height:2.509ex;" alt="{\displaystyle \Delta U=Q+W}"></span> (en termodinámica considérase'l trabayu negativu cuando esti entra nel sistema termodinámicu, positivu cuando sale). Anque'l calor tresmitíu depende del procesu en cuestión, la variación d'enerxía interno ye independiente del procesu, namái depende del estáu inicial y final, polo que se diz que ye una <a href="/wiki/Funci%C3%B3n_d%27est%C3%A1u" title="Función d'estáu">función d'estáu</a>. De la mesma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dU}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fad9083e6f626fcc9e4217e8fd3d751e1126da9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.998ex; height:2.176ex;" alt="{\displaystyle dU}"></span> ye una diferencial exacta, a diferencia de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eth Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ð</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eth Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8171b5a3631acaa619dcf4c2f7cf8253767aa583" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.131ex; height:2.676ex;" alt="{\displaystyle \eth Q}"></span>, que depende del procesu. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="L'enfoque_termodinámicu:_la_ecuación_fundamental"><span id="L.27enfoque_termodin.C3.A1micu:_la_ecuaci.C3.B3n_fundamental"></span>L'enfoque termodinámicu: la ecuación fundamental</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=1" title="Editar seición: L'enfoque termodinámicu: la ecuación fundamental" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=1" title="Editar el código fuente de la sección: L'enfoque termodinámicu: la ecuación fundamental"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/Termodin%C3%A1mica" title="Termodinámica">termodinámica</a> deduzse la esistencia<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> d'una ecuación de la forma :<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O=O(S,V,N)\qquad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo>=</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O=O(S,V,N)\qquad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fbb613e6215ffc4a6365d006abfbe01c31721bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.517ex; height:2.843ex;" alt="{\displaystyle O=O(S,V,N)\qquad }"></span> conocida como <i>ecuación fundamental en representación enerxética</i>, siendo <i>S</i>, <i>V</i> y <i>N</i> la <a href="/wiki/Entrop%C3%ADa" title="Entropía">entropía</a>, el <a href="/wiki/Volume" title="Volume">volume</a> y la <a href="/wiki/Cantid%C3%A1_de_sustancia" title="Cantidá de sustancia">cantidá de sustancia</a> en <a href="/wiki/Mol" title="Mol">moles</a>, respeutivamente. </p><p>La importancia de la mesma anicia en que concentra nuna sola ecuación tola información termodinámica d'un sistema. El llogru de resultaos concretes a partir de la mesma conviértese entós nun procesu sistemáticu. </p><p>Si calculamos el so diferencial: </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=\left({\frac {\partial O}{\partial S}}\right)dS+\left({\frac {\partial O}{\partial V}}\right)dV+\left({\frac {\partial O}{\partial N}}\right)dN}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>S</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>V</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>N</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=\left({\frac {\partial O}{\partial S}}\right)dS+\left({\frac {\partial O}{\partial V}}\right)dV+\left({\frac {\partial O}{\partial N}}\right)dN}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42d1777a0b08a29e1b433c98aa9c6e67e927189d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:44.287ex; height:6.176ex;" alt="{\displaystyle dU=\left({\frac {\partial O}{\partial S}}\right)dS+\left({\frac {\partial O}{\partial V}}\right)dV+\left({\frac {\partial O}{\partial N}}\right)dN}"></span></dd></dl> <p>defínense les sos derivaes parciales: </p> <ul><li>la temperatura <span class="mwe-math-element"><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={\frac {\partial O}{\partial S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {\partial O}{\partial S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5fc60b1a791a9a0f9eb4a2d322153ebbbdb79a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.662ex; height:5.509ex;" alt="{\displaystyle T={\frac {\partial O}{\partial S}}}"></span></li> <li>la presión <span class="mwe-math-element"><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=-{\frac {\partial O}{\partial V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=-{\frac {\partial O}{\partial V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/838e344dc5162cebe7de62ccec141b45467ed4b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.593ex; height:5.509ex;" alt="{\displaystyle P=-{\frac {\partial O}{\partial V}}}"></span></li> <li>el <a href="/w/index.php?title=Potencial_qu%C3%ADmicu&action=edit&redlink=1" class="new" title="Potencial químicu (la páxina nun esiste)">potencial químicu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu ={\frac {\partial O}{\partial N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>O</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>N</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu ={\frac {\partial O}{\partial N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13c4818764511fdf05bfb7dc330e215046f50a41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.718ex; height:5.509ex;" alt="{\displaystyle \mu ={\frac {\partial O}{\partial N}}}"></span>.</li></ul> <p><br /> Como T, P y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> son derivaes parciales d'U, van ser funciones de les mesmes variables qu'O: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=T(S,V,N)\qquad P=P(S,V,N)\qquad \mu =\mu (S,V,N)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mi>T</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mi>P</mi> <mo>=</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mi>μ</mi> <mo>=</mo> <mi>μ</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=T(S,V,N)\qquad P=P(S,V,N)\qquad \mu =\mu (S,V,N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/111e3431bfbce8fa179d90ddf4b5dfcd4d81d97c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:55.834ex; height:2.843ex;" alt="{\displaystyle T=T(S,V,N)\qquad P=P(S,V,N)\qquad \mu =\mu (S,V,N)}"></span></dd></dl> <p>Estes rellaciones reciben el nome de <a href="/w/index.php?title=Ecuaci%C3%B3n_d%27est%C3%A1u&action=edit&redlink=1" class="new" title="Ecuación d'estáu (la páxina nun esiste)"><i>ecuaciones d'estáu</i></a>. Polo xeneral nun se dispón de la ecuación fundamental d'un sistema. Nesi casu les sos sustitución pol conxuntu de toles ecuaciones d'estáu apurriría una información equivalente, anque de cutiu tengamos de conformanos con un subconxuntu de les mesmes. </p> <div class="mw-heading mw-heading2"><h2 id="Delles_variaciones_de_la_enerxía_interno"><span id="Delles_variaciones_de_la_enerx.C3.ADa_interno"></span>Delles variaciones de la enerxía interno</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=2" title="Editar seición: Delles variaciones de la enerxía interno" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=2" title="Editar el código fuente de la sección: Delles variaciones de la enerxía interno"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Al aumentar la <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> d'un sistema, aumenta la so enerxía interno, reflexada nel aumentu de la <a href="/w/index.php?title=Enerx%C3%ADa_t%C3%A9rmico&action=edit&redlink=1" class="new" title="Enerxía térmico (la páxina nun esiste)">enerxía térmico</a> del sistema completu, o de la materia estudiao. </p><p>Convencionalmente, cuando se produz una variación de la enerxía interno manifestao na variación del calor que puede ser vencíu, calteníu o absorbíu puede midise esti cambéu na enerxía interno indireutamente pola variación de la temperatura de la materia. </p> <div class="mw-heading mw-heading3"><h3 id="Variación_ensin_cambéu_d'estáu"><span id="Variaci.C3.B3n_ensin_camb.C3.A9u_d.27est.C3.A1u"></span>Variación ensin cambéu d'estáu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=3" title="Editar seición: Variación ensin cambéu d'estáu" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=3" title="Editar el código fuente de la sección: Variación ensin cambéu d'estáu"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ensin que se modificar l'<a href="/wiki/Est%C3%A1u_de_la_materia" class="mw-redirect" title="Estáu de la materia">estáu de la materia</a> que compón el sistema, fálase de variación de la enerxía interno sensible o <b><a href="/w/index.php?title=Calor_sensible&action=edit&redlink=1" class="new" title="Calor sensible (la páxina nun esiste)">calor sensible</a></b> y puede calculase d'alcuerdu a los siguientes parámetros: </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 Q=C_{y}m\Delta T\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>m</mi> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=C_{y}m\Delta T\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e5c1f87412996bb9cbf388d27d329757b5c4ae8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:13.26ex; height:2.843ex;" alt="{\displaystyle Q=C_{y}m\Delta T\!}"></span></dd></dl> <p>Onde cada términu coles sos unidaes nel <a href="/wiki/Sistema_Internacional" class="mw-redirect" title="Sistema Internacional">Sistema Internacional</a> son: </p><p><b>Q =</b> ye la variación d'enerxía o de calor del sistema nun tiempu definíu (J). </p><p><b>Ce =</b> <a href="/wiki/Calor_espec%C3%ADfico" title="Calor específico">calor específico</a> de la materia (J/kg·K). </p><p><b>m =</b> masa. </p><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 T\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62db053c1e0eceea7ddb19d2e2ed6f5ea87e5924" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle \Delta T\!}"></span><b>=</b> temperatura final del sistema - temperatura inicial (K). </p> <div class="mw-heading mw-heading4"><h4 id="Exemplu">Exemplu</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=4" title="Editar seición: Exemplu" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=4" title="Editar el código fuente de la sección: Exemplu"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Calcular la enerxía total d'un sistema compuestu de 1 g d'agua en condiciones normales, ye dicir al altor del mar, una atmósfera de presión y a 14 °C pa llevalo a 15 °C, sabiendo que la Ce de l'agua ye = 1 [cal/g·°C]. </p><p>Aplicando la fórmula <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=C_{y}m\Delta T\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>m</mi> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=C_{y}m\Delta T\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e5c1f87412996bb9cbf388d27d329757b5c4ae8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:13.26ex; height:2.843ex;" alt="{\displaystyle Q=C_{y}m\Delta T\!}"></span> y reemplazando los valores, tenemos; </p> <dl><dd>Q = 1 [cal/g·°C] · 1 [g] · (15 - 14) [°C] = 1 [cal]</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Enerxía_cinética_media_d'un_gas_ideal"><span id="Enerx.C3.ADa_cin.C3.A9tica_media_d.27un_gas_ideal"></span>Enerxía cinética media d'un gas ideal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=5" title="Editar seición: Enerxía cinética media d'un gas ideal" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=5" title="Editar el código fuente de la sección: Enerxía cinética media d'un gas ideal"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 Y_{cm}={\frac {3}{2}}(KT)={\frac {1}{2}}mv_{m}^{2}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{cm}={\frac {3}{2}}(KT)={\frac {1}{2}}mv_{m}^{2}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/189d4e19ad2cab0869d1068a2464ce6a5d3d8eb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:24.286ex; height:5.176ex;" alt="{\displaystyle Y_{cm}={\frac {3}{2}}(KT)={\frac {1}{2}}mv_{m}^{2}\!}"></span> </p><p>K = Constante de Boltzmann = 1,38·10<sup>-23</sup> J/K </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{m}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{m}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17c531e1c385dccaa3844dea8f17621be41edd28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.803ex; height:2.009ex;" alt="{\displaystyle v_{m}\!}"></span>=Velocidá media de la molécula </p><p>Les propiedaes termodinámiques d'un gas ideal pueden ser descrites por dos ecuaciones: </p><p>La <a href="/w/index.php?title=Ecuaci%C3%B3n_d%27est%C3%A1u&action=edit&redlink=1" class="new" title="Ecuación d'estáu (la páxina nun esiste)">ecuación d'estáu</a> d'un gas ideal clásicu que ye la <a href="/wiki/Llei_de_los_gases_ideales" title="Llei de los gases ideales">llei de los gases ideales</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 PV=nRT\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV=nRT\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3f5aa46a645e0fa301a9906df345f2d9707715d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.813ex; height:2.176ex;" alt="{\displaystyle PV=nRT\,}"></span></dd></dl> <p>y la <b>enerxía interno</b> a volume constante d'un gas ideal que queda determinada pola espresión: </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={\hat {c}}_{V}nRT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U={\hat {c}}_{V}nRT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8694bd77c197dcf14e9b4a3ece8decde872b9797" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.464ex; height:2.509ex;" alt="{\displaystyle U={\hat {c}}_{V}nRT}"></span></dd></dl> <p>onde :* <i>P</i> ye la <a href="/wiki/Presi%C3%B3n" title="Presión">presión</a> </p> <dl><dd><ul><li><i>V</i> ye'l <a href="/wiki/Volume" title="Volume">volume</a></li> <li><i>n</i> ye la <a href="/wiki/Cantid%C3%A1_de_sustancia" title="Cantidá de sustancia">cantidá de sustancia</a> d'un gas (en <a href="/wiki/Mol" title="Mol">moles</a>)</li> <li><i>R</i> ye la <a href="/w/index.php?title=Constante_de_los_gases&action=edit&redlink=1" class="new" title="Constante de los gases (la páxina nun esiste)">constante de los gases</a> (8.314 <a href="/wiki/Xuliu_(unid%C3%A1)" title="Xuliu (unidá)">J</a>·<a href="/wiki/Kelvin" title="Kelvin">K</a><sup>−1</sup><a href="/w/index.php?title=Mol_(unid%C3%A1)&action=edit&redlink=1" class="new" title="Mol (unidá) (la páxina nun esiste)">mol</a><sup>-1</sup>)</li> <li><i>T</i> ye la <a href="/w/index.php?title=Temperatura_absoluto&action=edit&redlink=1" class="new" title="Temperatura absoluto (la páxina nun esiste)">temperatura absoluto</a></li> <li><i>U</i> ye la <b>enerxía interno</b> del sistema</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 {\hat {c}}_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {c}}_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba0b6e14702dda394800c8f9fd64302d83ee8425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.788ex; height:2.509ex;" alt="{\displaystyle {\hat {c}}_{V}}"></span> ye'l <a href="/wiki/Calor_espec%C3%ADfico" title="Calor específico">calor específico</a> <a href="/w/index.php?title=Adimensional&action=edit&redlink=1" class="new" title="Adimensional (la páxina nun esiste)">adimensional</a> a volume constante, ≈ 3/2 pa un <a href="/w/index.php?title=Monoat%C3%B3mico&action=edit&redlink=1" class="new" title="Monoatómico (la páxina nun esiste)">gas monoatómico</a>, 5/2 pa un gas <a href="/w/index.php?title=Diat%C3%B3mico&action=edit&redlink=1" class="new" title="Diatómico (la páxina nun esiste)">diatómico</a> y 3 pa molécules más complexes.</li></ul></dd></dl> <p>La cantidá de gas en <a href="/w/index.php?title=Joule_(unid%C3%A1)&action=edit&redlink=1" class="new" title="Joule (unidá) (la páxina nun esiste)">J</a>·<a href="/wiki/Kelvin" title="Kelvin">K</a><sup>−1</sup> ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle nR=Nk_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>R</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle nR=Nk_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bf70ec8d9b983511f4f5f72fb76bab8812421ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.012ex; height:2.509ex;" alt="{\displaystyle nR=Nk_{B}}"></span> onde :* <i>N</i> ye'l númberu de partícules de gas </p> <dl><dd><ul><li><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 k_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70f38f7b73e53fd7b5d9ca64bec3a1438cc0eade" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.691ex; height:2.509ex;" alt="{\displaystyle k_{B}}"></span></i> ye la <a href="/wiki/Constante_de_Boltzmann" title="Constante de Boltzmann">constante de Boltzmann</a> (1.381×10<sup>−23</sup>J·K<sup>−1</sup>).</li></ul></dd></dl> <p>La distribución de probabilidá de les partícules por velocidá o enerxía queda determinada pola <a href="/w/index.php?title=Distribuci%C3%B3n_de_Boltzmann&action=edit&redlink=1" class="new" title="Distribución de Boltzmann (la páxina nun esiste)">distribución de Boltzmann</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Variación_con_cambéu_de_la_composición_química"><span id="Variaci.C3.B3n_con_camb.C3.A9u_de_la_composici.C3.B3n_qu.C3.ADmica"></span>Variación con cambéu de la composición química</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=6" title="Editar seición: Variación con cambéu de la composición química" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=6" title="Editar el código fuente de la sección: Variación con cambéu de la composición química"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si se produz alteración de la estructura atómica-molecular, como ye'l casu de les <a href="/wiki/Reacci%C3%B3n_qu%C3%ADmica" class="mw-redirect" title="Reacción química">reacciones químiques</a> o cambéu d'estáu, fálase de variación de la enerxía interno <b>químico</b> o variación de la enerxía interno <i><b>latente</b></i>. </p><p>Esta condición de cambéu d'estáu pue calculase d'alcuerdu 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 Q=C_{ce}m\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>e</mi> </mrow> </msub> <mi>m</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=C_{ce}m\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfcb2f7a2472bfb97fd0091f6353309e4d7a6a6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.338ex; width:10.301ex; height:2.509ex;" alt="{\displaystyle Q=C_{ce}m\!}"></span></dd></dl> <p>Onde <span class="mwe-math-element"><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_{ce}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>e</mi> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{ce}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d466daaa28c9678f9edf589c24614bda6399669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.372ex; height:2.509ex;" alt="{\displaystyle C_{ce}\!}"></span> <b>=</b> Coeficiente de cambéu d'estáu, midíu en [J/kg] </p> <style data-mw-deduplicate="TemplateStyles:r4219085">.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">Ver tamién: <a href="/wiki/Entalp%C3%ADa" title="Entalpía">Entalpía</a></div> <div class="mw-heading mw-heading3"><h3 id="Variación_nuclear"><span id="Variaci.C3.B3n_nuclear"></span>Variación nuclear</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=7" title="Editar seición: Variación nuclear" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=7" title="Editar el código fuente de la sección: Variación nuclear"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219085"><div role="note" class="hatnote navigation-not-searchable">Artículu principal: <a href="/wiki/Equivalencia_ente_masa_y_enerx%C3%ADa" title="Equivalencia ente masa y enerxía">Equivalencia ente masa y enerxía</a></div> <p>Finalmente, nes reacciones de <a href="/wiki/Fisi%C3%B3n_nuclear" title="Fisión nuclear">fisión</a> y <a href="/wiki/Fusi%C3%B3n_nuclear" title="Fusión nuclear">fusión</a> fálase d'enerxía interno <b>nuclear</b>. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_tamién"><span id="Ver_tami.C3.A9n"></span>Ver tamién</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=8" title="Editar seición: Ver tamién" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=8" title="Editar el código fuente de la sección: Ver tamién"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Calor" title="Calor">Calor</a></li> <li><a href="/wiki/Temperatura" title="Temperatura">Temperatura</a></li> <li><a href="/wiki/Termodin%C3%A1mica" title="Termodinámica">Termodinámica</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencies">Referencies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enerx%C3%ADa_interno&veaction=edit&section=9" title="Editar seición: Referencies" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Enerx%C3%ADa_interno&action=edit&section=9" title="Editar el código fuente de la sección: Referencies"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3503771">@media only screen and (max-width:600px){.mw-parser-output .llistaref{column-count:1!important}}</style><div class="llistaref" 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">Ibáñez, J.A. y Ortega M.R. <i>Termología 1</i>. <a href="/wiki/Especial:FuentesDeLibros/8440442912" class="internal mw-magiclink-isbn">ISBN 84-404-4291-2</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Biel, J. <i>Formalismu y métodos de la termodinámica (Vol 1)</i>.Granada, 1987. ISBN 641-1986 .(Capítulu 9).</span> </li> </ol></div> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r2260362">.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 #c8ccd1;background-color:#eaecf0;color:#222222}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}</style><div class="mw-authority-control navigation-not-searchable"><div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r4075543">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" 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tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title 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