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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">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</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">(Til toppen)</div> </a> </li> <li id="toc-Klassisk_innhold" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Klassisk_innhold"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Klassisk innhold</span> </div> </a> <button aria-controls="toc-Klassisk_innhold-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 Klassisk innhold</span> </button> <ul id="toc-Klassisk_innhold-sublist" class="vector-toc-list"> <li id="toc-Clausius'_formulering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Clausius'_formulering"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Clausius' formulering</span> </div> </a> <ul id="toc-Clausius'_formulering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kelvins_formulering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kelvins_formulering"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Kelvins formulering</span> </div> </a> <ul id="toc-Kelvins_formulering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Maksimalt_arbeide" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Maksimalt_arbeide"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Maksimalt arbeide</span> </div> </a> <ul id="toc-Maksimalt_arbeide-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistisk_fysikk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Statistisk_fysikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Statistisk fysikk</span> </div> </a> <button aria-controls="toc-Statistisk_fysikk-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 Statistisk fysikk</span> </button> <ul id="toc-Statistisk_fysikk-sublist" class="vector-toc-list"> <li id="toc-Entropiens_vekst" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Entropiens_vekst"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Entropiens vekst</span> </div> </a> <ul id="toc-Entropiens_vekst-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Entropi_i_Universet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Entropi_i_Universet"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Entropi i Universet</span> </div> </a> <button aria-controls="toc-Entropi_i_Universet-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 Entropi i Universet</span> </button> <ul id="toc-Entropi_i_Universet-sublist" class="vector-toc-list"> <li id="toc-Sorte_hull" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sorte_hull"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Sorte hull</span> </div> </a> <ul id="toc-Sorte_hull-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-«Skaperkommentaren»" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#«Skaperkommentaren»"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>«Skaperkommentaren»</span> </div> </a> <ul id="toc-«Skaperkommentaren»-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_også" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_også"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Se også</span> </div> </a> <ul id="toc-Se_også-sublist" class="vector-toc-list"> </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">7</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Litteratur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Litteratur"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Litteratur</span> </div> </a> <ul id="toc-Litteratur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksterne_lenker" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksterne_lenker"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Eksterne lenker</span> </div> </a> <ul id="toc-Eksterne_lenker-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="Innhold" 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="Vis/skjul innholdsfortegnelsen" > <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">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">Termodynamikkens andre hovedsetning</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 64 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-64" 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">64 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Termodynamikkens_2._lov" title="Termodynamikkens 2. lov – dansk" lang="da" hreflang="da" data-title="Termodynamikkens 2. lov" 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/Termodynamikens_andra_huvudsats" title="Termodynamikens andra huvudsats – svensk" lang="sv" hreflang="sv" data-title="Termodynamikens andra huvudsats" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Tweede_wet_van_termodinamika" title="Tweede wet van termodinamika – afrikaans" lang="af" hreflang="af" data-title="Tweede wet van termodinamika" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%A7%D9%84%D8%AB%D8%A7%D9%86%D9%8A_%D9%84%D9%84%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D8%A7%D9%84%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A%D8%A9" title="القانون الثاني للديناميكا الحرارية – arabisk" lang="ar" hreflang="ar" data-title="القانون الثاني للديناميكا الحرارية" 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/Segundu_principiu_de_la_termodin%C3%A1mica" title="Segundu principiu de la termodinámica – asturisk" lang="ast" hreflang="ast" data-title="Segundu principiu de la termodinámica" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Termodinamikan%C4%B1n_ikinci_qanunu" title="Termodinamikanın ikinci qanunu – aserbajdsjansk" lang="az" hreflang="az" data-title="Termodinamikanın ikinci qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0_%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%A4%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="তাপগতিবিদ্যার দ্বিতীয় সূত্র – bengali" lang="bn" hreflang="bn" data-title="তাপগতিবিদ্যার দ্বিতীয় সূত্র" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%80%D1%83%D0%B3%D1%96_%D0%BF%D0%B0%D1%87%D0%B0%D1%82%D0%B0%D0%BA_%D1%82%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D1%96" title="Другі пачатак тэрмадынамікі – belarusisk" lang="be" hreflang="be" data-title="Другі пачатак тэрмадынамікі" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D1%82%D0%BE%D1%80%D0%B8_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BD%D0%B0_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0%D1%82%D0%B0" title="Втори закон на термодинамиката – bulgarsk" lang="bg" hreflang="bg" data-title="Втори закон на термодинамиката" 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/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – bosnisk" lang="bs" hreflang="bs" data-title="Drugi zakon termodinamike" 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/Segon_principi_de_la_termodin%C3%A0mica" title="Segon principi de la termodinàmica – katalansk" lang="ca" hreflang="ca" data-title="Segon principi de la termodinàmica" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%C4%83%D0%BD_%D0%B8%D0%BA%D0%BA%C4%95%D0%BC%C4%95%D1%88_%D0%BF%D1%83%C3%A7%D0%BB%D0%B0%D0%BC%C4%83%D1%88%C4%95" title="Термодинамикăн иккĕмĕш пуçламăшĕ – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Термодинамикăн иккĕмĕш пуçламăшĕ" 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/Druh%C3%BD_termodynamick%C3%BD_z%C3%A1kon" title="Druhý termodynamický zákon – tsjekkisk" lang="cs" hreflang="cs" data-title="Druhý termodynamický zákon" 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/Zweiter_Hauptsatz_der_Thermodynamik" title="Zweiter Hauptsatz der Thermodynamik – tysk" lang="de" hreflang="de" data-title="Zweiter Hauptsatz der Thermodynamik" 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/Termod%C3%BCnaamika_teine_seadus" title="Termodünaamika teine seadus – estisk" lang="et" hreflang="et" data-title="Termodünaamika teine seadus" 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%94%CE%B5%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CF%82_%CE%B8%CE%B5%CF%81%CE%BC%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CF%8C%CF%82_%CE%BD%CF%8C%CE%BC%CE%BF%CF%82" title="Δεύτερος θερμοδυναμικός νόμος – gresk" lang="el" hreflang="el" data-title="Δεύτερος θερμοδυναμικός νόμος" 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/Second_law_of_thermodynamics" title="Second law of thermodynamics – engelsk" lang="en" hreflang="en" data-title="Second law of thermodynamics" 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/Segundo_principio_de_la_termodin%C3%A1mica" title="Segundo principio de la termodinámica – spansk" lang="es" hreflang="es" data-title="Segundo principio de la termodinámica" 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/Dua_le%C4%9Do_de_termodinamiko" title="Dua leĝo de termodinamiko – esperanto" lang="eo" hreflang="eo" data-title="Dua leĝo de termodinamiko" 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/Termodinamikaren_bigarren_legea" title="Termodinamikaren bigarren legea – baskisk" lang="eu" hreflang="eu" data-title="Termodinamikaren bigarren legea" 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/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%AF%D9%88%D9%85_%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="قانون دوم ترمودینامیک – persisk" lang="fa" hreflang="fa" data-title="قانون دوم ترمودینامیک" 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/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique – fransk" lang="fr" hreflang="fr" data-title="Deuxième principe de la thermodynamique" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Segunda_lei_da_termodin%C3%A1mica" title="Segunda lei da termodinámica – galisisk" lang="gl" hreflang="gl" data-title="Segunda lei da termodinámica" 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/%EC%97%B4%EC%97%AD%ED%95%99_%EC%A0%9C2%EB%B2%95%EC%B9%99" title="열역학 제2법칙 – koreansk" lang="ko" hreflang="ko" data-title="열역학 제2법칙" 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%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1%D5%B5%D5%AB_%D5%A5%D6%80%D5%AF%D6%80%D5%B8%D6%80%D5%A4_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Ջերմադինամիկայի երկրորդ օրենք – armensk" lang="hy" hreflang="hy" data-title="Ջերմադինամիկայի երկրորդ օրենք" 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%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80_%E0%A4%95%E0%A4%BE_%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊष्मागतिकी का द्वितीय नियम – hindi" lang="hi" hreflang="hi" data-title="ऊष्मागतिकी का द्वितीय नियम" 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/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – kroatisk" lang="hr" hreflang="hr" data-title="Drugi zakon termodinamike" 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/Hukum_termodinamika_kedua" title="Hukum termodinamika kedua – indonesisk" lang="id" hreflang="id" data-title="Hukum termodinamika kedua" 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/Secondo_principio_della_termodinamica" title="Secondo principio della termodinamica – italiensk" lang="it" hreflang="it" data-title="Secondo principio della termodinamica" 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%94%D7%97%D7%95%D7%A7_%D7%94%D7%A9%D7%A0%D7%99_%D7%A9%D7%9C_%D7%94%D7%AA%D7%A8%D7%9E%D7%95%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94" title="החוק השני של התרמודינמיקה – hebraisk" lang="he" hreflang="he" data-title="החוק השני של התרמודינמיקה" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%94%E1%83%9D%E1%83%A0%E1%83%94_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="თერმოდინამიკის მეორე კანონი – georgisk" lang="ka" hreflang="ka" data-title="თერმოდინამიკის მეორე კანონი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0%D0%BD%D1%8B%D2%A3_%D0%B5%D0%BA%D1%96%D0%BD%D1%88%D1%96_%D0%B7%D0%B0%D2%A3%D1%8B" title="Термодинамиканың екінші заңы – kasakhisk" lang="kk" hreflang="kk" data-title="Термодинамиканың екінші заңы" 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/Dezy%C3%A8m_lwa_t%C3%A8modinamik" title="Dezyèm lwa tèmodinamik – haitisk" lang="ht" hreflang="ht" data-title="Dezyèm lwa tèmodinamik" 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-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Altera_lex_thermodynamica" title="Altera lex thermodynamica – latin" lang="la" hreflang="la" data-title="Altera lex thermodynamica" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Otrais_termodinamikas_likums" title="Otrais termodinamikas likums – latvisk" lang="lv" hreflang="lv" data-title="Otrais termodinamikas likums" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/A_termodinamika_m%C3%A1sodik_f%C5%91t%C3%A9tele" title="A termodinamika második főtétele – ungarsk" lang="hu" hreflang="hu" data-title="A termodinamika második főtétele" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_termodinamik_kedua" title="Hukum termodinamik kedua – malayisk" lang="ms" hreflang="ms" data-title="Hukum termodinamik kedua" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Tweede_wet_van_de_thermodynamica" title="Tweede wet van de thermodynamica – nederlandsk" lang="nl" hreflang="nl" data-title="Tweede wet van de thermodynamica" 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/%E7%86%B1%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%BA%8C%E6%B3%95%E5%89%87" title="熱力学第二法則 – japansk" lang="ja" hreflang="ja" data-title="熱力学第二法則" 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/Segond_principi_de_la_termodinamica" title="Segond principi de la termodinamica – oksitansk" lang="oc" hreflang="oc" data-title="Segond principi de la termodinamica" 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/Termodinamikaning_ikkinchi_qonuni" title="Termodinamikaning ikkinchi qonuni – usbekisk" lang="uz" hreflang="uz" data-title="Termodinamikaning ikkinchi qonuni" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A5%E0%A8%B0%E0%A8%AE%E0%A9%8B%E0%A8%A1%E0%A8%BE%E0%A8%87%E0%A8%A8%E0%A8%BE%E0%A8%AE%E0%A8%BF%E0%A8%95%E0%A8%B8_%E0%A8%A6%E0%A8%BE_%E0%A8%A6%E0%A9%82%E0%A8%9C%E0%A8%BE_%E0%A8%A8%E0%A8%BF%E0%A8%AF%E0%A8%AE" title="ਥਰਮੋਡਾਇਨਾਮਿਕਸ ਦਾ ਦੂਜਾ ਨਿਯਮ – panjabi" lang="pa" hreflang="pa" data-title="ਥਰਮੋਡਾਇਨਾਮਿਕਸ ਦਾ ਦੂਜਾ ਨਿਯਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%DA%BE%D8%B1%D9%85%D9%88%DA%88%D8%A7%D8%A6%D9%86%D8%A7%D9%85%DA%A9%D8%B3_%D8%AF%D8%A7_%D8%AF%D9%88%D8%AC%D8%A7_%D9%82%D9%86%D9%88%D9%86" title="تھرموڈائنامکس دا دوجا قنون – vestpunjabi" lang="pnb" hreflang="pnb" data-title="تھرموڈائنامکس دا دوجا قنون" data-language-autonym="پنجابی" data-language-local-name="vestpunjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Druga_zasada_termodynamiki" title="Druga zasada termodynamiki – polsk" lang="pl" hreflang="pl" data-title="Druga zasada termodynamiki" 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/Segunda_lei_da_termodin%C3%A2mica" title="Segunda lei da termodinâmica – portugisisk" lang="pt" hreflang="pt" data-title="Segunda lei da termodinâmica" 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/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii – rumensk" lang="ro" hreflang="ro" data-title="Principiul al doilea al termodinamicii" 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%D1%82%D0%BE%D1%80%D0%BE%D0%B5_%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%BE_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B8" title="Второе начало термодинамики – russisk" lang="ru" hreflang="ru" data-title="Второе начало термодинамики" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8F%E0%B6%B4%E0%B6%9C%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80%E0%B7%9A_%E0%B6%AF%E0%B7%99%E0%B7%80%E0%B6%B1_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="තාපගති විද්‍යාවේ දෙවන නියමය – singalesisk" lang="si" hreflang="si" data-title="තාපගති විද්‍යාවේ දෙවන නියමය" data-language-autonym="සිංහල" data-language-local-name="singalesisk" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Second law of thermodynamics" 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/Druh%C3%A1_termodynamick%C3%A1_veta" title="Druhá termodynamická veta – slovakisk" lang="sk" hreflang="sk" data-title="Druhá termodynamická veta" 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/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – slovensk" lang="sl" hreflang="sl" data-title="Drugi zakon termodinamike" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D1%80%D1%83%D0%B3%D0%B8_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B5" title="Други принцип термодинамике – serbisk" lang="sr" hreflang="sr" data-title="Други принцип термодинамике" 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/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – serbokroatisk" lang="sh" hreflang="sh" data-title="Drugi zakon termodinamike" 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/Termodynamiikan_toinen_p%C3%A4%C3%A4s%C3%A4%C3%A4nt%C3%B6" title="Termodynamiikan toinen pääsääntö – finsk" lang="fi" hreflang="fi" data-title="Termodynamiikan toinen pääsääntö" 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%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA_%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%87%E0%AE%B0%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%BE%E0%AE%AE%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="வெப்ப இயக்கவியலின் இரண்டாம் விதி – tamil" lang="ta" hreflang="ta" data-title="வெப்ப இயக்கவியலின் இரண்டாம் விதி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%8E%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%AA%E0%B8%AD%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AD%E0%B8%B8%E0%B8%93%E0%B8%AB%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="กฎข้อที่สองของอุณหพลศาสตร์ – thai" lang="th" hreflang="th" data-title="กฎข้อที่สองของอุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Termodinami%C4%9Fin_ikinci_yasas%C4%B1" title="Termodinamiğin ikinci yasası – tyrkisk" lang="tr" hreflang="tr" data-title="Termodinamiğin ikinci yasası" 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%94%D1%80%D1%83%D0%B3%D0%B8%D0%B9_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B8" title="Другий закон термодинаміки – ukrainsk" lang="uk" hreflang="uk" data-title="Другий закон термодинаміки" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%B1%D8%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA_%DA%A9%D8%A7_%D8%AF%D9%88%D8%B3%D8%B1%D8%A7_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="حرحرکیات کا دوسرا قانون – urdu" lang="ur" hreflang="ur" data-title="حرحرکیات کا دوسرا قانون" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_lu%E1%BA%ADt_th%E1%BB%A9_hai_c%E1%BB%A7a_nhi%E1%BB%87t_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Định luật thứ hai của nhiệt động lực học – vietnamesisk" lang="vi" hreflang="vi" data-title="Định luật thứ hai của nhiệt động lực học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" 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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"><span class="mw-redirectedfrom">(Omdirigert fra «<a href="/w/index.php?title=Termodynamikkens_andre_lov&redirect=no" class="mw-redirect" title="Termodynamikkens andre lov">Termodynamikkens andre lov</a>»)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nb" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Increasing_disorder.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Increasing_disorder.svg/320px-Increasing_disorder.svg.png" decoding="async" width="320" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Increasing_disorder.svg/480px-Increasing_disorder.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Increasing_disorder.svg/640px-Increasing_disorder.svg.png 2x" data-file-width="464" data-file-height="131" /></a><figcaption>Partiklene i to forskjellige gasser vil spontant blandes når skilleveggen mellom dem fjernes og entropien øker.</figcaption></figure> <p><b>Termodynamikkens andre hovedsetning</b> sier at <a href="/wiki/Entropi" title="Entropi">entropien</a> til et isolert system aldri kan avta ved noen forandring. Mens den <a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Termodynamikkens første hovedsetning">første hovedsetningen</a> sier at <a href="/wiki/Energi" title="Energi">energien</a> i slike prosesser må være bevart, vil den andre hovedsetningen kunne forby noen forandringer. Selv om <a href="/wiki/Varme" title="Varme">varme</a> er en form for energi, sier denne loven for eksempel at den ikke kan flytte seg spontant fra et kaldere til et varmere sted. </p><p>Andre hovedsetning ble etablert i forbindelse med utviklingen av <a href="/wiki/Varmekraftmaskin" title="Varmekraftmaskin">varmekraftmaskiner</a>. Den ble gitt et mer fundamentalt innhold da termodynamiske prosesser kunne beskrives ved <a href="/wiki/Statistisk_mekanikk" class="mw-redirect" title="Statistisk mekanikk">statistisk mekanikk</a> basert på innsikten at de involverer veldig store antall med <a href="/wiki/Atom" title="Atom">atomer</a> og <a href="/wiki/Molekyl" title="Molekyl">molekyler</a>. Entropiens vekst skyldes da at slike system vil automatisk søke mot de mest sannsynlige tilstander i overensstemmelse med energiens bevarelse. I en spontan prosess vil et system bevege seg fra en tilstand med liten sannsynlighet til en annen med større sannsynlighet og dermed også større entropi. </p><p>Spontane prosesser er <b>irreversible</b> da de ikke kan gå motsatt vei. Bitene fra et glass som knuses, vil ikke automatisk kunne samle seg igjen til et nytt glass. Når entropien øker, skapes det samtidig mer uorden. Slike hendelser gjør også tydelig at det er en forskjell på fortid og fremtid, det vil si den gir en klar formening om tidens retning. Av denne grunn kan termodynamikkens andre hovedsetning knyttes til fundamentale egenskaper ved vårt <a href="/wiki/Univers" class="mw-redirect" title="Univers">Univers</a> som dets <a href="/wiki/Hubbles_lov" title="Hubbles lov">ekspansjon</a> og <a href="/wiki/Big_Bang" title="Big Bang">opprinnelse</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Klassisk_innhold">Klassisk innhold</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=1" title="Rediger avsnitt: Klassisk innhold" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=1" title="Rediger kildekoden til seksjonen Klassisk innhold"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oppdagelsen av denne fundamentale naturloven har sitt utgangspunkt i teoretiske betraktninger som den franske ingeniør <a href="/wiki/Sadi_Carnot" title="Sadi Carnot">Sadi Carnoti</a> gjorde i første halvdel av 1800-tallet om det <a href="/wiki/Arbeid_(fysikk)" title="Arbeid (fysikk)">arbeid</a> som kan utføres av <a href="/wiki/Varmekraftmaskin" title="Varmekraftmaskin">varmekraftmaskiner</a>. Selv om at de fleste på den tiden tenkte seg varme som en vektløs substans <a href="/wiki/Kalorikk" title="Kalorikk">kalorikk</a>, viste likevel <a href="/wiki/Carnot-prosess" title="Carnot-prosess">resultatene</a> til Carnot seg å være korrekte. Eksperimentelle undersøkelser av varmens egenskaper omtrent på samme tid av <a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Benjamin Thompson</a> (grev Rumford) og <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Joule</a> gjorde det klart at den er en form for energi som skyldes bevegelse av materiens minste bestanddeler. Denne samlede innsikten kunne så <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> og <a href="/wiki/William_Thomson" class="mw-redirect" title="William Thomson">William Thomson</a> (Lord Kelvin) formulere i form av <a href="/wiki/Termodynamikk" title="Termodynamikk">termodynamikkens</a> to hovedsetninger.<sup id="cite_ref-Longair_1-0" class="reference"><a href="#cite_note-Longair-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Clausius'_formulering"><span id="Clausius.27_formulering"></span>Clausius' formulering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=2" title="Rediger avsnitt: Clausius' formulering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=2" title="Rediger kildekoden til seksjonen Clausius' formulering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Clausius formulerte den andre hovedsetningen ved å si at <b>ingen prosess kan foregå med det eneste resultat at varme går fra et kaldere til et varmere system</b>. Denne loven var basert på Carnots betraktninger rundt virkningsgraden til <a href="/wiki/Dampmaskin" title="Dampmaskin">dampmaskiner</a>. De fikk Clausius til å definere <a href="/wiki/Entropi" title="Entropi">entropi</a> <i>S </i> som en ny egenskap ved termodynamiske system. Hvis det blir tilført en liten varmemengde Δ<i>Q </i> ved <a href="/wiki/Absolutt_temperatur" class="mw-redirect" title="Absolutt temperatur">temperaturen</a> <i>T</i>, så vil forandringen i systemets <a href="/wiki/Entropi" title="Entropi">entropi</a> alltid tilfredsstille <a href="/wiki/Ulikhet_(matematikk)" title="Ulikhet (matematikk)">ulikheten</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 \Delta S\geq {\Delta Q \over T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>≥</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S\geq {\Delta Q \over T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73628399603e275ae2691d7f64c35d6b290ea4e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.144ex; height:5.343ex;" alt="{\displaystyle \Delta S\geq {\Delta Q \over T}}"></span></dd></dl> <p>som bærer navnet til Clausius. Likhetstegnet gjelder kun når forandringen skjer så langsomt at systemet forblir i likevekt og derfor er «reversibel».<sup id="cite_ref-Atkins_2-0" class="reference"><a href="#cite_note-Atkins-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>For et isolert system er <span class="nowrap">Δ<i>Q </i> = 0</span> og derfor Δ<i>S</i> ≥ 0. Entropien til et slikt system kan derfor ikke avta. Dette gjelder også for systemer med forskjellige temperaturer <i>T</i><sub>1</sub> og <i>T</i><sub>2</sub> som er i termisk kontakt med hverandre, men ellers isolert fra omgivelsene. For at det da skal av seg selv flyte en liten varmemengde Δ<i>Q </i> fra <i>T</i><sub>1</sub> til <i>T</i><sub>2</sub>, må entropiforandringen </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S=\Delta Q\left({1 \over T_{2}}-{1 \over T_{1}}\right)\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S=\Delta Q\left({1 \over T_{2}}-{1 \over T_{1}}\right)\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c8d3758fa83826f6fdc1e0dbe4d6f2e2efdf9bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.713ex; height:6.176ex;" alt="{\displaystyle \Delta S=\Delta Q\left({1 \over T_{2}}-{1 \over T_{1}}\right)\geq 0}"></span></dd></dl> <p>Det innebærer at <i>T</i><sub>1</sub> ≥ <i>T</i><sub>2</sub> som er i overensstemmelse med Clausius' formulering av første hovedsetning. Når <span class="nowrap">Δ<i>S</i> = 0</span>, er den totale entropien i systemene maksimal, og de befinner seg i <a href="/wiki/Termisk_likevekt" class="mw-redirect" title="Termisk likevekt">termisk likevekt</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Kelvins_formulering">Kelvins formulering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=3" title="Rediger avsnitt: Kelvins formulering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=3" title="Rediger kildekoden til seksjonen Kelvins formulering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den unge <a href="/wiki/William_Thomson" class="mw-redirect" title="William Thomson">William Thomson</a> var også klar over betydningen til Carnots betraktninger rundt dampmaskinens virkemåte. De sammenfattet han i sin versjon av andre hovedsetning.Vanligvis formuleres den som at <b>ingen prosess er mulig når den har som eneste resultat at varme omsettes i arbeid</b>. Skulle denne loven ikke gjelde, ville det for eksempel være mulig å drive alle skip med varmeenergien som er lagret i verdenshavene. </p><p>Selv om loven på denne formen er litt forskjellig fra Clausius' formulering, er de to likevel ekvivalente. Hvis det ikke er tilfellet, kunne man ta arbeidet fra et varmeresovoar til å drive en <a href="/wiki/Varmepumpe" title="Varmepumpe">varmepumpe</a> som transporterer varme fra et kaldere sted til reservoaret. Det eneste resultatet av denne sammensatte prosessen vil da være at varme gikk fra et kaldere til et varmere sted, noe som skal være umulig ifølge Clausius.<sup id="cite_ref-Longair_1-1" class="reference"><a href="#cite_note-Longair-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Maksimalt_arbeide">Maksimalt arbeide</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=4" title="Rediger avsnitt: Maksimalt arbeide" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=4" title="Rediger kildekoden til seksjonen Maksimalt arbeide"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Når Clausius' ulikhet kombineres med <a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Termodynamikkens første hovedsetning">den første hovedsetningen</a>, forandres den til </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\Delta S\geq \Delta U+\Delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>≥</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\Delta S\geq \Delta U+\Delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac5e90c61e0804e87a3d00daa1ade68ae1f526b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.1ex; height:2.343ex;" alt="{\displaystyle T\Delta S\geq \Delta U+\Delta W}"></span></dd></dl> <p>På denne måten forbindes forandringen Δ<i>U </i> i et systems <a href="/wiki/Indre_energi" title="Indre energi">indre energi</a> og arbeidet Δ<i>W </i> som det samtidig utfører, med entropiforandring Δ<i>S</i> det gjennomgår. Hvis denne er null, må man derfor 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 \Delta W\leq -(\Delta U)_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>W</mi> <mo>≤</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta W\leq -(\Delta U)_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81d088eb2b785b4b59cbf453a703e46c1bbfb445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.098ex; height:2.843ex;" alt="{\displaystyle \Delta W\leq -(\Delta U)_{S}}"></span></dd></dl> <p>Det maksimale arbeid som et system kan utføre uten noen forandring i dets entropi, er derfor direkte lik med reduksjonen av systemets indre energi. Når det utførte arbeidet er mekanisk i form av en liten volumutvidelse Δ<i>V </i> mot et eksternt <a href="/wiki/Trykk" title="Trykk">trykk</a> <i>P</i>, vil Δ<i>W</i> = <i>P</i>Δ<i>V</i>. Det gir betingelsen </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\Delta U)_{S,V}\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mo>,</mo> <mi>V</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\Delta U)_{S,V}\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab8c58d734f34edf8d7eaeb23a03ae4f6ad69bb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.802ex; height:3.009ex;" alt="{\displaystyle (\Delta U)_{S,V}\leq 0}"></span></dd></dl> <p>for at en spontan forandring skal skje i systemet ved konstant volum og uten forandring i dets entropi.<sup id="cite_ref-Jaffe_3-0" class="reference"><a href="#cite_note-Jaffe-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Av større betydning er spontane forandringer som skjer ved konstant temperatur. Da kan ulikheten skrives som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta W\leq -(\Delta F)_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>W</mi> <mo>≤</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>F</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta W\leq -(\Delta F)_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fe7349ee4cf9df39b20b594501c922938648cea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.153ex; height:2.843ex;" alt="{\displaystyle \Delta W\leq -(\Delta F)_{T}}"></span></dd></dl> <p>hvor <i>F</i> = <i>U</i> - <i>TS </i> er <a href="/wiki/Helmholtz_fri_energi" title="Helmholtz fri energi">Helmholtz fri energi</a>. Forandringen av denne gir nå det maksimale arbeidet som kan utføres, Når entropiforandringen Δ<i>S</i> < 0, er dette derfor mindre enn den negative forandringen av den indre energien. Derimot hvis Δ<i>S</i> > 0, vil det være større enn -Δ<i>U</i>. Det skyldes at i dette tilfellet kan energi i form av varme strømme inn i systemet uten at den totale entropi i både system og omgivelser avtar. Hvis arbeidet er mekanisk av formen Δ<i>W</i> = <i>P</i>Δ<i>V</i>, vil da </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\Delta F)_{T,V}\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>F</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>V</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\Delta F)_{T,V}\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/346a95b5a20d87863f01761fa7cedf8f5a42029f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.857ex; height:3.009ex;" alt="{\displaystyle (\Delta F)_{T,V}\leq 0}"></span></dd></dl> <p>være betingelsen for at en spontan forandring skal foregå i systemet når både volum og temperatur holdes konstante. På tilsvarende vis finner man at det maksimale arbeid som kan resultere fra en prosess som skjer ved konstant temperatur og trykk, er gitt ved forandringen i <a href="/wiki/Gibbs_fri_energi" title="Gibbs fri energi">Gibbs fri energi</a>. Dette har stor betydning for forståelsen av <a href="/wiki/Kjemisk_reaksjon" title="Kjemisk reaksjon">kjemiske reaksjoner</a>.<sup id="cite_ref-Atkins_2-1" class="reference"><a href="#cite_note-Atkins-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Statistisk_fysikk">Statistisk fysikk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=5" title="Rediger avsnitt: Statistisk fysikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=5" title="Rediger kildekoden til seksjonen Statistisk fysikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En dypere forståelse av termodynamikkens andre hovedsetning kan føres tilbake til <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> og hans arbeider fra midten av 1800-tallet. Han var inspirert av betraktningene til <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Maxwell</a> som hadde beregnet sannsynligheten for å finne partikler med bestemte hastigheter i en <a href="/wiki/Gass" title="Gass">gass</a> som er i <a href="/wiki/Termisk_likevekt" class="mw-redirect" title="Termisk likevekt">termisk likevekt</a>. Selv om dens volum og temperatur er gitt, kan partiklene bevege seg med vidt forskjellige hastigheter som også hele tiden forandrer seg på grunn av gjensidige kollisjoner.<sup id="cite_ref-Longair_1-2" class="reference"><a href="#cite_note-Longair-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Boltzmann forsto at for hver makroskopisk tilstand av gassen ville det være et stort antall <i>W </i> mikroskopiske tilstander som de enkelte partiklene kunne innta. Desto flere slike tilgjengelige tilstander for partiklene, desto større ville sannsynligheten for den tilsvarende makroskopiske tilstanden være. Dette antallet kunne han forbinde med <a href="/wiki/Entropi" title="Entropi">entropien</a> til makrotilstanden. Siden den er additiv for to systemer som settes sammen, mens sannsynlighetene er multiplikative ved en slik kombinasjon, kom Boltzmann frem til at entropien må være gitt ved <a href="/wiki/Logaritme" title="Logaritme">logaritmen</a> til antall tilgjengelige mikrotilstander <i>W</i>. I dag skrives denne sammenhengen som </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 S=k_{B}\ln W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=k_{B}\ln W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b54263a8601115f499c4aa7ac82e89c0f757c115" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.437ex; height:2.509ex;" alt="{\displaystyle S=k_{B}\ln W}"></span></dd></dl> <p>hvor <i>k<sub>B</sub></i> er <a href="/wiki/Boltzmanns_konstant" title="Boltzmanns konstant">Boltzmanns konstant</a> som på denne måten ble definert av <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>. Når et system med <i>W</i><sub>1</sub> mikrotilstanderr settes sammen med et annet med <i>W</i><sub>2</sub> slike tilstander, får det kombinerte systemet i alt <i>W</i> = <i>W</i><sub>1</sub><i>W</i><sub>2</sub> mulige tilstander. Det vil derfor ha en total entropi </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 S=k_{B}\ln(W_{1}W_{2})=k_{B}(\ln W_{1}+\ln W_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=k_{B}\ln(W_{1}W_{2})=k_{B}(\ln W_{1}+\ln W_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/989b1feef7a6eb786e73692ab96f49ae50fd41d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.508ex; height:2.843ex;" alt="{\displaystyle S=k_{B}\ln(W_{1}W_{2})=k_{B}(\ln W_{1}+\ln W_{2})}"></span></dd></dl> <p>eller <i>S</i> = <i>S</i><sub>1</sub> + <i>S</i><sub>2</sub> som forventet. Storparten av all terrmodynamikk kan utledes fra denne enkle formelen for entropien til et system.<sup id="cite_ref-KK_4-0" class="reference"><a href="#cite_note-KK-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Entropiens_vekst">Entropiens vekst</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=6" title="Rediger avsnitt: Entropiens vekst" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=6" title="Rediger kildekoden til seksjonen Entropiens vekst"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Desto flere mikrotilstander som er tillgjengelig for en viss makrotilstand, desto mer sannsynlig er denne. For eksempel kan bestandelene i et egg settes sammen til et knust egg på mange flere måter enn i den spesielle utgaven av et helt egg. Det knuste egget vil derfor ikke selv kunne gå tilbake til en makrotilstand som et uknust egg er. </p><p>Denne generelle tendens til at entropien alltid øker, kan man illustrere med partiklene i en gass innesluttet i en beholder. Ved en gitt temperatur vil de da befinne seg noenlunde jevnt fordelt i hele dette volumet. Med et makroskopisk stort antall partikler er det da fullstendig usannsynlig at alle partiklene vil bevege seg inn i et hjørne til beholderen. Mer nøyaktig er sannsynligheten for at én partikkel skal befinne seg i den ene halvdelen av volumet lik med 1/2. Sannsynligheten for at to partikler skal samtidig være der, er da (1/2)<sup>2</sup> og (1/2)<sup><i>N</i></sup> for at alle <i>N </i> partikler i gassen skal gjøre det samme. Dette ville bety en reduksjon av entropien til gassen som er </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S=k_{B}\ln(1/2)^{N}=-Nk_{B}\ln 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mi>N</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S=k_{B}\ln(1/2)^{N}=-Nk_{B}\ln 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28dffb1623a29dcf01627d0104aa75126108534" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.076ex; height:3.176ex;" alt="{\displaystyle \Delta S=k_{B}\ln(1/2)^{N}=-Nk_{B}\ln 2}"></span></dd></dl> <p>og derfor strider mot andre hovedsetning.Tilsvarende ville entropien øke like mye hvis alle partiklene opprinnelig befant seg i den ene halvdelen. Dette er i overensstemmelse med det <a href="/wiki/Entropi#Ideell_gass" title="Entropi">termodynamiske resultatet</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 \Delta S=Nk_{B}\ln(V_{2}/V_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S=Nk_{B}\ln(V_{2}/V_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8201e94124437dbbbd10ec68d27baa5eb08f8f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.405ex; height:2.843ex;" alt="{\displaystyle \Delta S=Nk_{B}\ln(V_{2}/V_{1})}"></span></dd></dl> <p>hvor forholdet mellom volumene nå er <i>V</i><sub>2</sub>/<i>V</i><sub>1</sub> = 2. Under en slik fri ekspansjon øker derfor entropien i verden på samme måte som når et egg faller ned og knuses.<sup id="cite_ref-Feynman_5-0" class="reference"><a href="#cite_note-Feynman-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Gassens frie ekspansjon er en <i>irreversibel</i> prosess. Den kan gjøres reversibel ved å la ekspansjonen foregå langsomt mot et stempel som balanserer trykket i gassen slik at den forblir i likevekt ved samme temperatur <i>T</i>. På den måten utfører den et arbeid <span class="nowrap">Δ<i>W</i> = <i>T</i>Δ<i>S </i></span> Energien til dette blir tatt fra omgivelsene i form av varme som strømmer inn i gassen. Økningen av entropien til gassen blir derfor i dette tilfellet kompensert ved en tilsvarende reduksjon av entropien til omgivelsene. Den totale entropiforandringen ved en reversibel prosess er null. </p> <div class="mw-heading mw-heading2"><h2 id="Entropi_i_Universet">Entropi i Universet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=7" title="Rediger avsnitt: Entropi i Universet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=7" title="Rediger kildekoden til seksjonen Entropi i Universet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Irreversible prosesser går allltid kun én vei og bidrar til at entropien omkring oss øker. Den vil være større i morgen, og den var mindre i går. På den måten gir entropiens vekst et éntydig uttrykk for hvordan <a href="/wiki/Tid" title="Tid">tiden</a> hele tiden går fremover, den gir tiden «en retning». Først når verden omkring oss er kommet i <a href="/wiki/Termisk_likevekt" class="mw-redirect" title="Termisk likevekt">termisk likevekt</a>, vil entropien ha nådd et maksimum og forbli konstant. Det er vanskelig å tenke seg slike forhold hvor ikke noe lenger vil skje spontant. Man kan ikke lenger skille fortid og fremtid, noe som betyr at tiden ikke lenger har noen retning. <a href="/wiki/Univers" class="mw-redirect" title="Univers">Universet</a> vil da ha gått inn i en tilstand som noen ganger omtales som <a href="/wiki/Varmed%C3%B8den" title="Varmedøden">varmedøden</a>.<sup id="cite_ref-Davies_6-0" class="reference"><a href="#cite_note-Davies-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>På tilsvarende vis burde entropien i Universet bli mindre og mindre når man går tilbake i dets historie og nærmer seg dets begynnelse i <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a>. De fysiske forholdene like etterpå er godt forstått i moderne <a href="/wiki/Kosmologi" title="Kosmologi">kosmologi</a>. Materien som da fantes, var i termisk likevekt med strålingen slik at tilsammen utgjorde de et system med maksimal entropi. Men dette må ha vært en meget spesiell tilstand som likevel hadde liten total entropi. Det kan skyldes <a href="/wiki/Gravitasjon" title="Gravitasjon">gravitasjonskreftene</a> som etterhvert forårsaket at materien klumpet seg sammen i stjerner og galakser til å danne dagens Univers hvor entropien fortsetter å vokse.<sup id="cite_ref-Carroll_7-0" class="reference"><a href="#cite_note-Carroll-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Sorte_hull">Sorte hull</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=8" title="Rediger avsnitt: Sorte hull" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=8" title="Rediger kildekoden til seksjonen Sorte hull"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gravitasjonskraften i tilstrekkelig tunge stjerner medfører at de til slutt faller sammen til <a href="/wiki/Sort_hull" title="Sort hull">sorte hull</a>. Disse kan så fortsette å sluke opp omliggende materie og også andre stjerner eller sorte hull. Rundt 1970 ble det klart at <a href="/wiki/Generell_relativitet" class="mw-redirect" title="Generell relativitet">Einsteins gravitasjonsteori</a> har som konsekvens at overflaten <span class="nowrap"><i>A</i> = 4<i>π R</i><sup> 2</sup></span> til et sort hull ikke kan avta. Her er <span class="nowrap"><i>R</i> = 2<i>GM</i>/<i>c</i><sup> 2</sup></span> <a href="/wiki/Schwarzschild-radius" title="Schwarzschild-radius">Schwarzschild-radiusen</a> til hullet. Hvis to hull med overflater <i>A</i><sub>1</sub> og <i>A</i><sub>2</sub> kombineres i et nytt, sort hull med overfalte <i>A</i>, vil man alltid ha at <span class="nowrap"><i>A</i> ≥ <i>A</i><sub>1</sub> + <i>A</i><sub>2</sub>.</span> Dette fikk <a href="/wiki/Jacob_Bekenstein" title="Jacob Bekenstein">Jacob Bekenstein</a> til å foreslå at et sort hull har en entropi som er proporsjonal med dets overflate. For at denne skal ha riktig dimensjon, antok han derfor at entropien må kunne skrives som </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 S=fk_{B}{A \over \ell ^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>f</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=fk_{B}{A \over \ell ^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/827bbbd1befe2174aff64d760663618f42b95486" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.427ex; height:5.676ex;" alt="{\displaystyle S=fk_{B}{A \over \ell ^{2}}}"></span></dd></dl> <p>hvor <i>f </i> er en dimensjonsløs konstant og ℓ  er en lengde. Han valgte å sette denne lik med <a href="/wiki/Naturlige_enheter#Planck-enheter" title="Naturlige enheter">Planck-lengden</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 \ell _{P}={\sqrt {\hbar G/c^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{P}={\sqrt {\hbar G/c^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca4722ca6c96a6038d5968a535d9fe2ead84a63d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:14.215ex; height:4.843ex;" alt="{\displaystyle \ell _{P}={\sqrt {\hbar G/c^{3}}}}"></span> til hullet.<sup id="cite_ref-Blundell_8-0" class="reference"><a href="#cite_note-Blundell-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>I tillegg antok Bekenstein at en liten forandring <i>dS </i> i denne entropien måtte forbindes med en tilvarende forandring <i>dU </i> i hullets <a href="/wiki/Indre_energi" title="Indre energi">indre energi</a> <span class="nowrap"><i>U</i> = <i>Mc</i><sup> 2</sup> </span> i overensstemmelse med <a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Termodynamikkens første hovedsetning">den første hovedsetningen</a>. Det betyr at et sort hull også må tilskrives en temperatur <i>T </i> slik at <span class="nowrap"><i>dU</i> = <i>TdS</i></span>. Selv om <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a> i utgangspunktet var negativ til dette forslaget, kunne han ved bruk av <a href="/wiki/Kvantefeltteori" title="Kvantefeltteori">kvantefeltteori</a> bekrefte at det stemte. Han fant da at konstanten <i>f</i> = 1/4 som betyr at temperaturen til hullet er gitt ved </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 k_{B}T={\hbar c^{3} \over 8\pi GM}}"> <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> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> <mi>M</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}T={\hbar c^{3} \over 8\pi GM}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1d9f96c560fdde5b9f1bddd44a3c9ec1442945" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.025ex; height:5.843ex;" alt="{\displaystyle k_{B}T={\hbar c^{3} \over 8\pi GM}}"></span></dd></dl> <p>Det sorte hullet vil emittere stråling som et <a href="/wiki/Sort_legeme" class="mw-redirect" title="Sort legeme">sort legeme</a> ved denne temperatur og gradvis tape masse. Denne <a href="/wiki/Hawking-str%C3%A5ling" title="Hawking-stråling">Hawking-strålingen</a> medfører derfor at dets entropi også avtar, men det blir kompensert ved en enda større økning av entropien til omgivelsene. Etter hvert som Universet utvider seg, vil entropien i sorte hull vokse og dominere den fra gjenværende partikler og stråling.<sup id="cite_ref-SCF_9-0" class="reference"><a href="#cite_note-SCF-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Men denne situasjonen kan videre utvikle seg ved at også de sorte hullene forsvinner ved at de sender ut Hawking-stråling. Nøyaktig hva som kan hende videre, er avhengig av Universets innhold av <a href="/wiki/M%C3%B8rk_energi" title="Mørk energi">mørk energi</a>.<sup id="cite_ref-Carroll_7-1" class="reference"><a href="#cite_note-Carroll-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="«Skaperkommentaren»"><span id=".C2.ABSkaperkommentaren.C2.BB"></span>«Skaperkommentaren»</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=9" title="Rediger avsnitt: «Skaperkommentaren»" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=9" title="Rediger kildekoden til seksjonen «Skaperkommentaren»"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den amerikanske termodynamikeren fysikeren <a href="/wiki/Gordon_Van_Wylen" title="Gordon Van Wylen">Gordon Van Wylen</a> (død av covid i 2020) gjorde seg bemerket for sin åpne dristighet i 1959 ved å nevne «a Creator» (en Skaper) i sin oppsummering av termodynamikkens andre hovedsetning. </p> <dl><dd><dl><dd><i>«A final point to be made is that the second law of thermodynamics and the principle of increase in <a href="/wiki/Entropi" title="Entropi">entropy</a> have great philosophical implications. The question that arises is how did the universe get into the state of reduced entropy in the first place, since all natural processes known to us tend to increase entropy? ... The author has found that the second law tends to increase his conviction that there is a Creator who has the answer for the future destiny of man and the universe.»<sup id="cite_ref-VW_10-0" class="reference"><a href="#cite_note-VW-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></i></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Se_også"><span id="Se_ogs.C3.A5"></span>Se også</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=10" title="Rediger avsnitt: Se også" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=10" title="Rediger kildekoden til seksjonen Se også"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Entropi" title="Entropi">Entropi</a></li> <li><a href="/wiki/Fri_energi" title="Fri energi">Fri energi</a></li> <li><a href="/wiki/Termodynamikk" title="Termodynamikk">Termodynamikk</a></li> <li><a href="/wiki/Varmepumpe" title="Varmepumpe">Varmepumpe</a></li> <li><a href="/wiki/Varmemaskin" class="mw-redirect" title="Varmemaskin">Varmemaskin</a></li> <li><a href="/wiki/Dampmaskin" title="Dampmaskin">Dampmaskin</a></li></ul> <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=Termodynamikkens_andre_hovedsetning&veaction=edit&section=11" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=11" 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-Longair-1"><b>^</b> <a href="#cite_ref-Longair_1-0"><sup>a</sup></a> <a href="#cite_ref-Longair_1-1"><sup>b</sup></a> <a href="#cite_ref-Longair_1-2"><sup>c</sup></a> <span class="reference-text"> M. Longair, <i>Theoretical Concepts in Physics</i>, Cambridge University Press, England (2003). <a href="/wiki/Spesial:Bokkilder/9780521528788" class="internal mw-magiclink-isbn">ISBN 978-0-521-52878-8</a>.</span> </li> <li id="cite_note-Atkins-2"><b>^</b> <a href="#cite_ref-Atkins_2-0"><sup>a</sup></a> <a href="#cite_ref-Atkins_2-1"><sup>b</sup></a> <span class="reference-text">P.W. Atkins, <i>Physical Chemistry</i>, Oxford University Press, England (1988). <a href="/wiki/Spesial:Bokkilder/019855186X" class="internal mw-magiclink-isbn">ISBN 0-19-855186-X</a>.</span> </li> <li id="cite_note-Jaffe-3"><b><a href="#cite_ref-Jaffe_3-0">^</a></b> <span class="reference-text"> R.L. Jaffe and W. Taylor, <a rel="nofollow" class="external text" href="https://books.google.no/books?id=x1lNAQAACAAJ&printsec=frontcover&hl=no&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false"><i>The Physics of Energy</i></a>, Cambridge University Press, England (2018). <a href="/wiki/Spesial:Bokkilder/9781107016651" class="internal mw-magiclink-isbn">ISBN 978-1-107-01665-1</a>. </span> </li> <li id="cite_note-KK-4"><b><a href="#cite_ref-KK_4-0">^</a></b> <span class="reference-text"> C. Kittel and H. Kroemer, <i>Thermal Physics</i>, W.H. Freeman and Company, San Fransisco (1980). <a href="/wiki/Spesial:Bokkilder/0716710889" class="internal mw-magiclink-isbn">ISBN 0-7167-1088-9</a>.</span> </li> <li id="cite_note-Feynman-5"><b><a href="#cite_ref-Feynman_5-0">^</a></b> <span class="reference-text"> R.P. Feynman, <a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/I_toc.html"><i>Lectures on Physics</i></a>, Volume 1 (1964). </span> </li> <li id="cite_note-Davies-6"><b><a href="#cite_ref-Davies_6-0">^</a></b> <span class="reference-text">Davies, P.C.W. <i>The Physics of Time Symmetry</i>, University of California Press, Los Angeles (1974).</span> </li> <li id="cite_note-Carroll-7"><b>^</b> <a href="#cite_ref-Carroll_7-0"><sup>a</sup></a> <a href="#cite_ref-Carroll_7-1"><sup>b</sup></a> <span class="reference-text"> S. Carroll, <i>From Eternity to Here: The Quest for the Ultimate Theory of Time</i>, Dutton (2010). <a rel="nofollow" class="external text" href="https://www.preposterousuniverse.com/eternitytohere/">Website</a>.</span> </li> <li id="cite_note-Blundell-8"><b><a href="#cite_ref-Blundell_8-0">^</a></b> <span class="reference-text">K. Blundell, <i>Black Holes: A Very Short Introduction</i>, Oxford University Press, Oxford (2015). <a href="/wiki/Spesial:Bokkilder/9780199602667" class="internal mw-magiclink-isbn">ISBN 978-0-19-960266-7</a>.</span> </li> <li id="cite_note-SCF-9"><b><a href="#cite_ref-SCF_9-0">^</a></b> <span class="reference-text"> S.C. Frautschi, <i>Entropy in an Expanding Universe</i>, Science <b>217</b> (1560), 593-599 (1982). <a rel="nofollow" class="external text" href="https://www.informationphilosopher.com/solutions/scientists/layzer/Frautschi_Science_1982.pdf">PDF</a> </span> </li> <li id="cite_note-VW-10"><b><a href="#cite_ref-VW_10-0">^</a></b> <span class="reference-text"> Gordon Van Wylen, <i>Thermodynamics</i>, p. 159, John Wiley & Co., New York (1959).</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=Termodynamikkens_andre_hovedsetning&veaction=edit&section=12" title="Rediger avsnitt: Litteratur" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=12" title="Rediger kildekoden til seksjonen Litteratur"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Karl Stephan, Franz Mayinger: <i>Thermodynamik. Grundlagen und technische Anwendungen.</i> 2 Bände, Springer Verlag <ul><li>Band 1: <i>Einstoffsysteme</i>. 15. Auflage, 1998, <a href="/wiki/Spesial:Bokkilder/3540642501" class="internal mw-magiclink-isbn">ISBN 3-540-64250-1</a>.</li> <li>Band 2: <i>Mehrstoffsysteme und chemische Reaktionen</i>. 14. Auflage, 1999, <a href="/wiki/Spesial:Bokkilder/3540644814" class="internal mw-magiclink-isbn">ISBN 3-540-64481-4</a>.</li></ul></li> <li>Hans D. Baehr, S. Kabelac: <i>Thermodynamik, Grundlagen und technische Anwendungen</i> 13., neu bearb. u. erw. Aufl., Springer Verlag, 2006, <a href="/wiki/Spesial:Bokkilder/3540325131" class="internal mw-magiclink-isbn">ISBN 3-540-32513-1</a>.</li> <li>Hans D. Baehr, Karl Stephan: <i>Wärme- und Stoffübertragung</i> 5., neu bearb. Aufl., 2006, Springer Verlag, <a href="/wiki/Spesial:Bokkilder/3540323341" class="internal mw-magiclink-isbn">ISBN 3-540-32334-1</a>.</li> <li>Klaus Langeheinecke, Peter Jany, Eugen Sapper: <i>Thermodynamik für Ingenieure</i>. 5. Auflage. Vieweg Verlag, Wiesbaden 2004, <a href="/wiki/Spesial:Bokkilder/3528447850" class="internal mw-magiclink-isbn">ISBN 3-528-44785-0</a>.</li> <li>Hannelore Bernhardt: <i>Zur Geschichte der statistischen Interpretation des 2. Hauptsatzes der Thermodynamik.</i> Rostocker physikalische Manuskripte 3/1 (1978), S. 95–104.</li> <li>R.E. Sonntag, C. Borgnakke and <a href="/wiki/Gordon_J._Van_Wylen" class="mw-redirect" title="Gordon J. Van Wylen">Gordon J. Van Wylen</a>, <i>Fundamentals of Thermodynamics</i>, John Wiley & Sons, New York (1999). <a href="/wiki/Spesial:Bokkilder/9171512653" class="internal mw-magiclink-isbn">ISBN 9171-51-265-3</a>. <a rel="nofollow" class="external text" href="https://archive.org/details/1999-res-fundamentals-of-thermodynamics-5th-ed-tand-a/page/n1/mode/2up?view=theater">Internet archive</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Eksterne_lenker">Eksterne lenker</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&veaction=edit&section=13" title="Rediger avsnitt: Eksterne lenker" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_andre_hovedsetning&action=edit&section=13" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>S. Wolfram, <a rel="nofollow" class="external text" href="https://writings.stephenwolfram.com/2023/02/a-50-year-quest-my-personal-journey-with-the-second-law-of-thermodynamics/"><i>A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics</i></a>, historisk interessant og personlig spennende fremstilling av andre hovedsetning.</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 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