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Indre energi – Wikipedia
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</a> <button aria-controls="toc-Matematiske_relasjoner-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>Vis/skjul underseksjonen Matematiske relasjoner</span> </button> <ul id="toc-Matematiske_relasjoner-sublist" class="vector-toc-list"> <li id="toc-Åpne_system" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Åpne_system"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Åpne system</span> </div> </a> <ul id="toc-Åpne_system-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li 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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">Vis/skjul innholdsfortegnelsen</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">Indre energi</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="Gå til en artikkel på et annet språk. Tilgjengelig på 66 språk" > <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 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Indre_energi" title="Indre energi – norsk nynorsk" lang="nn" hreflang="nn" data-title="Indre energi" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Indre_energi" title="Indre energi – dansk" lang="da" hreflang="da" data-title="Indre energi" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Inre_energi" title="Inre energi – svensk" lang="sv" hreflang="sv" data-title="Inre energi" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><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 – arabisk" lang="ar" hreflang="ar" data-title="طاقة داخلية" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Enerx%C3%ADa_interno" title="Enerxía interno – asturisk" lang="ast" hreflang="ast" data-title="Enerxía interno" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</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 – bengali" lang="bn" hreflang="bn" data-title="অভ্যন্তরীণ শক্তি" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/L%C5%8De-l%C3%AAng" title="Lōe-lêng – minnan" lang="nan" hreflang="nan" data-title="Lōe-lêng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-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 – belarusisk" lang="be" hreflang="be" data-title="Унутраная энергія" data-language-autonym="Беларуская" data-language-local-name="belarusisk" 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 – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Нутраная энэргія" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" 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 – bulgarsk" lang="bg" hreflang="bg" data-title="Вътрешна енергия" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Unutra%C5%A1nja_energija" title="Unutrašnja energija – bosnisk" lang="bs" hreflang="bs" data-title="Unutrašnja energija" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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 – katalansk" lang="ca" hreflang="ca" data-title="Energia interna" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D0%B0%D0%BB%D1%82%D0%B8_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Шалти энерги – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Шалти энерги" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vnit%C5%99n%C3%AD_energie" title="Vnitřní energie – tsjekkisk" lang="cs" hreflang="cs" data-title="Vnitřní energie" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Innere_Energie" title="Innere Energie – tysk" lang="de" hreflang="de" data-title="Innere Energie" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Siseenergia" title="Siseenergia – estisk" lang="et" hreflang="et" data-title="Siseenergia" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%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 – gresk" lang="el" hreflang="el" data-title="Εσωτερική ενέργεια" data-language-autonym="Ελληνικά" data-language-local-name="gresk" 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 – engelsk" lang="en" hreflang="en" data-title="Internal energy" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Energ%C3%ADa_interna" title="Energía interna – spansk" lang="es" hreflang="es" data-title="Energía interna" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/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-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Barne_energia" title="Barne energia – baskisk" lang="eu" hreflang="eu" data-title="Barne energia" data-language-autonym="Euskara" data-language-local-name="baskisk" 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 – persisk" lang="fa" hreflang="fa" data-title="انرژی درونی" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89nergie_interne" title="Énergie interne – fransk" lang="fr" hreflang="fr" data-title="Énergie interne" data-language-autonym="Français" data-language-local-name="fransk" 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 – irsk" lang="ga" hreflang="ga" data-title="Fuinneamh inmheánach" data-language-autonym="Gaeilge" data-language-local-name="irsk" 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 – galisisk" lang="gl" hreflang="gl" data-title="Enerxía interna" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%82%B4%EB%B6%80_%EC%97%90%EB%84%88%EC%A7%80" title="내부 에너지 – koreansk" lang="ko" hreflang="ko" data-title="내부 에너지" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%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 – armensk" lang="hy" hreflang="hy" data-title="Ներքին էներգիա" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%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 – kroatisk" lang="hr" hreflang="hr" data-title="Unutarnja energija" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Energi_dalam" title="Energi dalam – indonesisk" lang="id" hreflang="id" data-title="Energi dalam" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" 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 – italiensk" lang="it" hreflang="it" data-title="Energia interna" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A0%D7%A8%D7%92%D7%99%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="אנרגיה פנימית – hebraisk" lang="he" hreflang="he" data-title="אנרגיה פנימית" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%86%D1%88%D0%BA%D1%96_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Ішкі энергия – kasakhisk" lang="kk" hreflang="kk" data-title="Ішкі энергия" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/En%C3%A8ji_t%C3%A8mik" title="Enèji tèmik – haitisk" lang="ht" hreflang="ht" data-title="Enèji tèmik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitisk" class="interlanguage-link-target"><span>Kreyòl ayisyen</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 – kirgisisk" lang="ky" hreflang="ky" data-title="Ички энергия" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</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 – latvisk" lang="lv" hreflang="lv" data-title="Iekšējā enerģija" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vidin%C4%97_energija" title="Vidinė energija – litauisk" lang="lt" hreflang="lt" data-title="Vidinė energija" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Bels%C5%91_energia" title="Belső energia – ungarsk" lang="hu" hreflang="hu" data-title="Belső energia" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%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 – makedonsk" lang="mk" hreflang="mk" data-title="Внатрешна енергија" data-language-autonym="Македонски" data-language-local-name="makedonsk" 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-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tenaga_dalaman" title="Tenaga dalaman – malayisk" lang="ms" hreflang="ms" data-title="Tenaga dalaman" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%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 – mongolsk" lang="mn" hreflang="mn" data-title="Дотоод энерги" data-language-autonym="Монгол" data-language-local-name="mongolsk" 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/Inwendige_energie" title="Inwendige energie – nederlandsk" lang="nl" hreflang="nl" data-title="Inwendige energie" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%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 – japansk" lang="ja" hreflang="ja" data-title="内部エネルギー" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</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 – oksitansk" lang="oc" hreflang="oc" data-title="Energia intèrna" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ichki_energiya" title="Ichki energiya – usbekisk" lang="uz" hreflang="uz" data-title="Ichki energiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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 – polsk" lang="pl" hreflang="pl" data-title="Energia wewnętrzna" data-language-autonym="Polski" data-language-local-name="polsk" 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 – portugisisk" lang="pt" hreflang="pt" data-title="Energia interna" data-language-autonym="Português" data-language-local-name="portugisisk" 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 – rumensk" lang="ro" hreflang="ro" data-title="Energie internă" data-language-autonym="Română" data-language-local-name="rumensk" 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 – russisk" lang="ru" hreflang="ru" data-title="Внутренняя энергия" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</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 – albansk" lang="sq" hreflang="sq" data-title="Energjia e brendshme" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Internal_energy" title="Internal energy – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Internal energy" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" 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 – slovakisk" lang="sk" hreflang="sk" data-title="Vnútorná energia" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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 – slovensk" lang="sl" hreflang="sl" data-title="Notranja energija" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%88%D8%B2%DB%95%DB%8C_%D9%86%D8%A7%D9%88%DB%95%DA%A9%DB%8C" title="وزەی ناوەکی – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="وزەی ناوەکی" data-language-autonym="کوردی" data-language-local-name="sentralkurdisk" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Unutra%C5%A1nja_energija" title="Unutrašnja energija – serbisk" lang="sr" hreflang="sr" data-title="Unutrašnja energija" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Unutarnja_energija" title="Unutarnja energija – serbokroatisk" lang="sh" hreflang="sh" data-title="Unutarnja energija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Sis%C3%A4energia" title="Sisäenergia – finsk" lang="fi" hreflang="fi" data-title="Sisäenergia" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</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 – tyrkisk" lang="tr" hreflang="tr" data-title="İç enerji" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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 – ukrainsk" lang="uk" hreflang="uk" data-title="Внутрішня енергія" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/N%E1%BB%99i_n%C4%83ng" title="Nội năng – vietnamesisk" lang="vi" hreflang="vi" data-title="Nội năng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%85%A7%E8%83%BD" title="內能 – klassisk kinesisk" lang="lzh" hreflang="lzh" data-title="內能" data-language-autonym="文言" data-language-local-name="klassisk kinesisk" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%86%85%E8%83%BD" title="内能 – wu" lang="wuu" hreflang="wuu" data-title="内能" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%85%A7%E8%83%BD" title="內能 – kantonesisk" lang="yue" hreflang="yue" data-title="內能" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%86%85%E8%83%BD" title="内能 – kinesisk" lang="zh" hreflang="zh" data-title="内能" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q180241#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</a></span></div> </div> </div> </div> </header> 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id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andre prosjekter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q180241" title="Lenke til koblet dataregisterelement [g]" accesskey="g"><span>Wikidata-element</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</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">Fra Wikipedia, den frie encyklopedi</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="nb" dir="ltr"><p><b>Indre energi</b> er en viktig størrelse i <a href="/wiki/Termodynamikk" title="Termodynamikk">termodynamikk</a> og betegner <a href="/wiki/Energi" title="Energi">energien</a> som finnes i en lukket mengde med stoff. Dette er i hovedsak <a href="/wiki/Termisk_energi" title="Termisk energi">termisk energi</a> og <a href="/wiki/Kjemisk_energi" title="Kjemisk energi">kjemisk energi</a>. Termisk energi er den <a href="/wiki/Kinetisk_energi" title="Kinetisk energi">kinetiske energien</a> som materialet har på grunn av uordnede bevegelser til atomer og molekyler. Kjemisk energi er ordnet <a href="/wiki/Bindingsenergi" title="Bindingsenergi">bindingsenergi</a> til de samme partiklene og skyldes i stor grad deres <a href="/wiki/Potensiell_energi" title="Potensiell energi">potensielle</a> <a href="/wiki/Energi" title="Energi">energi</a>. Konvensjonelt regnes ikke <a href="/wiki/Masseenergiloven" title="Masseenergiloven">masseenergi</a> som indre energi, siden denne stort sett er uendret i termodynamiske og kjemiske reaksjoner.<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> Den indre energien kan beregnes med metoder fra <a href="/wiki/Kinetisk_teori" title="Kinetisk teori">kinetisk teori</a> eller <a href="/wiki/Statistisk_fysikk" title="Statistisk fysikk">statistisk fysikk</a>. Den er vanligvis betegnet ved symbolene <i>U</i> eller <i>E </i> og måles i <a href="/wiki/SI-enheten" class="mw-redirect" title="SI-enheten">SI-enheten</a> <a href="/wiki/Joule" title="Joule">Joule</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Matematiske_relasjoner">Matematiske relasjoner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indre_energi&veaction=edit&section=1" title="Rediger avsnitt: Matematiske relasjoner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indre_energi&action=edit&section=1" title="Rediger kildekoden til seksjonen Matematiske relasjoner"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For et termodynamisk system beskrevet ved de termodynamiske variablene volum <i>V</i>, trykk <i>P</i> og temperatur <i>T</i>, vil enhver infinitesemal forandring medføre en forandring i systemets indre energi <i>U</i> og <a href="/wiki/Entropi" title="Entropi">entropi</a> <i>S</i> som må oppfylle <a href="/wiki/Termodynamikkens_andre_hovedsetning" title="Termodynamikkens andre hovedsetning">termodynamikkens andre hovedsetning</a>. Matematisk betyr det at de tilsvarende differensialene er forbundet ved ligningen </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=TdS-PdV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>−<!-- − --></mo> <mi>P</mi> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=TdS-PdV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4e6257520ed1135ddd89440bbb193bb086d49fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.037ex; height:2.343ex;" alt="{\displaystyle dU=TdS-PdV}"></span></dd></dl> <p>Dette gjør det naturlig å betrakte den indre energien som en funksjon av entropien <i>S</i> og volumet <i>V</i>.<sup id="cite_ref-Müller_2-0" class="reference"><a href="#cite_note-Müller-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>Da vil differensialet av den indre energien være </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({\partial U \over \partial S}\right)_{V}dS+\left({\partial U \over \partial V}\right)_{S}dV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>d</mi> <mi>S</mi> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=\left({\partial U \over \partial S}\right)_{V}dS+\left({\partial U \over \partial V}\right)_{S}dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0c245cd9c86c07395560f93ec23075b72f75340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.165ex; height:6.176ex;" alt="{\displaystyle dU=\left({\partial U \over \partial S}\right)_{V}dS+\left({\partial U \over \partial V}\right)_{S}dV}"></span></dd></dl> <p>slik at man må ha </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\partial U \over \partial S}\right)_{V}=T\,,\;\;\;\;\;\;\;\left({\partial U \over \partial V}\right)_{S}=-P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−<!-- − --></mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\partial U \over \partial S}\right)_{V}=T\,,\;\;\;\;\;\;\;\left({\partial U \over \partial V}\right)_{S}=-P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71e24a36f04162a545eb17ea8c0e7b4052bf603b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.833ex; height:6.176ex;" alt="{\displaystyle \left({\partial U \over \partial S}\right)_{V}=T\,,\;\;\;\;\;\;\;\left({\partial U \over \partial V}\right)_{S}=-P}"></span></dd></dl> <p>Slike <b>termodynamiske deriverte</b> spiller en viktig rolle i alle anvendelser av de termodynamiske lovene. </p><p><a href="/wiki/Varmekapasitet" title="Varmekapasitet">Varmekapasiteten</a> for systemet er gitt ved forholdet mellom en liten, reversibelt tilført varmemengde <i>ΔQ = TΔS </i> og den resulterende økningen <i>ΔT </i> i temperaturen. Skjer dette ved konstant volum slik at <i>ΔV = 0</i>, vil derfor varmekapasiteten være gitt ved den deriverte </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 C_{V}=\left({\partial U \over \partial T}\right)_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</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 C_{V}=\left({\partial U \over \partial T}\right)_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/858c30116c24aee1e28c8a5861b5c38503114df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.11ex; height:6.176ex;" alt="{\displaystyle C_{V}=\left({\partial U \over \partial T}\right)_{V}}"></span></dd></dl> <p>som gjør det mulig å beregne den ved bruk av <a href="/wiki/Statistisk_fysikk" title="Statistisk fysikk">statistisk fysikk</a>. Varmekapasiteten ved konstant trykk <i>P</i> er gitt ved en tilsvarende derivert av <a href="/wiki/Entalpi" title="Entalpi">entalpien</a> til systemet. </p> <div class="mw-heading mw-heading3"><h3 id="Åpne_system"><span id=".C3.85pne_system"></span>Åpne system</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indre_energi&veaction=edit&section=2" title="Rediger avsnitt: Åpne system" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indre_energi&action=edit&section=2" title="Rediger kildekoden til seksjonen Åpne system"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/wiki/Kjemisk_reaksjon" title="Kjemisk reaksjon">kjemiske reaksjoner</a> og mange andre, praktiske sammenhenger vil antall partikler <i>N</i> i systemet forandres ved at de skapes eller forsvinner i vekselvirkning med andre partikler eller med omgivelsene. I slike sammenhenger kan det utføres et arbeid som er gitt ved <a href="/wiki/Kjemisk_potensial" title="Kjemisk potensial">det kjemiske potensialet</a> <i>μ</i>. Ved en liten forandring <i>ΔN </i> i partikkeltallet, vil det medføre arbeidet <span class="nowrap"><i>ΔW = - μΔN </i></span>. Matematisk vil man dermed ha den differensielle sammenhengen </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=TdS-PdV+\mu dN}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mi>d</mi> <mi>S</mi> <mo>−<!-- − --></mo> <mi>P</mi> <mi>d</mi> <mi>V</mi> <mo>+</mo> <mi>μ<!-- μ --></mi> <mi>d</mi> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=TdS-PdV+\mu dN}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c763f4383936a30f6823e1bbbf8bd3fb6d1ceac7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.559ex; height:2.676ex;" alt="{\displaystyle dU=TdS-PdV+\mu dN}"></span></dd></dl> <p>Denne gir nå de termodynamiske deriverte </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\partial U \over \partial S}\right)_{VN}=T\,,\;\;\;\;\ \left({\partial U \over \partial V}\right)_{SN}=-P\,,\;\;\;\;\ \left({\partial U \over \partial N}\right)_{SV}=\mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>S</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mtext> </mtext> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo>−<!-- − --></mo> <mi>P</mi> <mspace width="thinmathspace" /> <mo>,</mo> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <mtext> </mtext> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>N</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mi>μ<!-- μ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\partial U \over \partial S}\right)_{VN}=T\,,\;\;\;\;\ \left({\partial U \over \partial V}\right)_{SN}=-P\,,\;\;\;\;\ \left({\partial U \over \partial N}\right)_{SV}=\mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45b0a1543ab72e1d40f441526d962755428c3add" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:55.674ex; height:6.176ex;" alt="{\displaystyle \left({\partial U \over \partial S}\right)_{VN}=T\,,\;\;\;\;\ \left({\partial U \over \partial V}\right)_{SN}=-P\,,\;\;\;\;\ \left({\partial U \over \partial N}\right)_{SV}=\mu }"></span></dd></dl> <p>som likedan har mange anvendelser. </p><p>Temperaturen <i>T</i>, trykket <i>P</i> og kjemisk potensial <i>μ</i> er <a href="/wiki/Intensive_og_ekstensive_egenskaper" title="Intensive og ekstensive egenskaper">intensive variable</a> som er uavhengige av systemets størrelse. Derimot er de variable <i>N</i>, <i>U</i> og <i>S</i> proporsjonale med systemets størrelse og kalles for <i>ekstensive variable</i>. Tar man f.eks. to identiske system med samme trykk, temperatur og kjemisk potensial og legger dem sammen, så får man et dobbelt så stort system med samme trykk, temperatur og kjemisk potensial, men med dobbelt så stor indre energi, entropi og partikkeltall. Matematisk sett kan det bare bety at <i>U = TS - PV + μN</i>. De forskjellige, termodynamiske variable må derfor være sammenknyttet på denne enkle måten som kan noen ganger forenkle deres bestemmelse. </p> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indre_energi&veaction=edit&section=3" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indre_energi&action=edit&section=3" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text">G.W. Castellan, <i>Physical Chemistry</i>, Addison-Wesley Publishing Company, New York (1971). <a href="/wiki/Spesial:Bokkilder/0201103869" class="internal mw-magiclink-isbn">ISBN 0-20-110386-9</a>.</span> </li> <li id="cite_note-Müller-2"><b><a href="#cite_ref-Müller_2-0">^</a></b> <span class="reference-text">R. Müller, <i>Thermodynamik: Vom Tautropfen zum Solarkraftwerk</i>, Walter de Gruyther GmbH, Berlin (2014). <a href="/wiki/Spesial:Bokkilder/9783110301984" class="internal mw-magiclink-isbn">ISBN 978-3-11-030198-4</a>. </span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Litteratur">Litteratur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indre_energi&veaction=edit&section=4" title="Rediger avsnitt: Litteratur" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indre_energi&action=edit&section=4" title="Rediger kildekoden til seksjonen Litteratur"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>E. Lillestøl, O. Hunderi og J.R. Lien, <i>Generell Fysikk, Bind 2</i>, Universitetsforlaget, Oslo (2001). <a href="/wiki/Spesial:Bokkilder/8215000061" class="internal mw-magiclink-isbn">ISBN 82-15-00006-1</a>.</li> <li>P.A. Rock, <i>Chemical Thermodynamics</i>, University Science Books, Oxford (1983). <a href="/wiki/Spesial:Bokkilder/0198557125" class="internal mw-magiclink-isbn">ISBN 0-19-855712-5</a>.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23230704">.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 .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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