CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="nb" dir="ltr"> <head> <meta charset="UTF-8"> <title>Termodynamikkens første hovedsetning – Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )nowikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t."," \t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","januar","februar","mars","april","mai","juni","juli","august","september","oktober","november","desember"],"wgRequestId":"aa450b01-1e4f-415b-a9d8-3b4ddd972938","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Termodynamikkens_første_hovedsetning","wgTitle":"Termodynamikkens første hovedsetning","wgCurRevisionId":24685348,"wgRevisionId":24685348,"wgArticleId":157262,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Sider som bruker magiske ISBN-lenker","Artikler med autoritetsdatalenker fra Wikidata","Termodynamikk","Fysiske lover"],"wgPageViewLanguage":"nb","wgPageContentLanguage":"nb","wgPageContentModel":"wikitext","wgRelevantPageName":"Termodynamikkens_første_hovedsetning","wgRelevantArticleId":157262,"wgTempUserName":null,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[], "wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"nb","pageLanguageDir":"ltr","pageVariantFallbacks":"nb"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q179380","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={ "ext.gadget.InterProjectLinks":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.UkensKonkurranse","ext.gadget.link-missing-label","ext.gadget.new-section","ext.gadget.superinterwiki","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init", "ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=nb&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=ext.gadget.InterProjectLinks&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="noindex,nofollow,max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/3/3d/Bockdampfmaschine.JPG"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1600"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bockdampfmaschine.JPG/800px-Bockdampfmaschine.JPG"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="1067"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bockdampfmaschine.JPG/640px-Bockdampfmaschine.JPG"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="853"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Termodynamikkens første hovedsetning – Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//no.m.wikipedia.org/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning"> <link rel="alternate" type="application/x-wiki" title="Rediger" href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (nb)"> <link rel="EditURI" type="application/rsd+xml" href="//no.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://no.wikipedia.org/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom-mating" href="/w/index.php?title=Spesial:Siste_endringer&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Termodynamikkens_første_hovedsetning rootpage-Termodynamikkens_første_hovedsetning skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Hopp til innhold</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Nettsted"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Hovedmeny" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Hovedmeny</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Hovedmeny</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">skjul</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigasjon </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Forside" title="Gå til hovedsiden [z]" accesskey="z"><span>Forside</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig" title="Vis en tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Portal" title="Stedet for å få hjelp"><span>Hjelp</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Siste_endringer" title="Liste over siste endringer på wikien. [r]" accesskey="r"><span>Siste endringer</span></a></li> </ul> </div> </div> <div id="p-prosjekt" class="vector-menu mw-portlet mw-portlet-prosjekt" > <div class="vector-menu-heading"> Prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Prosjektportal" class="mw-list-item"><a href="/wiki/Wikipedia:Portal"><span>Prosjektportal</span></a></li><li id="n-bidra" class="mw-list-item"><a href="/wiki/Wikipedia:Bidra_til_Wikipedia"><span>Hvordan bidra?</span></a></li><li id="n-tinget" class="mw-list-item"><a href="/wiki/Wikipedia:Tinget"><span>Tinget</span></a></li><li id="n-torget" class="mw-list-item"><a href="/wiki/Wikipedia:Torget"><span>Torget</span></a></li><li id="n-konkurranser" class="mw-list-item"><a href="/wiki/Wikipedia:Konkurranser"><span>Konkurranser</span></a></li> </ul> </div> </div> <div id="p-Wikipedia" class="vector-menu mw-portlet mw-portlet-Wikipedia" > <div class="vector-menu-heading"> Wikipedia </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-kontakt" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakt Wikipedia</span></a></li><li id="n-wmno" class="mw-list-item"><a href="https://www.wikimedia.no" rel="nofollow" title="Medlemsorganisasjon for wikipedianere"><span>Wikimedia Norge</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Forside" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-no.svg" width="121" height="14" style="width: 7.5625em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Spesial:S%C3%B8k" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Søk i Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Søk</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Søk i Wikipedia" aria-label="Søk i Wikipedia" autocapitalize="sentences" title="Søk i Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesial:Søk"> </div> <button class="cdx-button cdx-search-input__end-button">Søk</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personlig"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Endre skriftstørrelse, bredde og farge på siden." > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Utseende" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Utseende</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb" class=""><span>Doner</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Opprett_konto&returnto=Termodynamikkens+f%C3%B8rste+hovedsetning&returntoquery=veaction%3Dedit" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Logg_inn&returnto=Termodynamikkens+f%C3%B8rste+hovedsetning&returntoquery=veaction%3Dedit" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o" class=""><span>Logg inn</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out user-links-collapsible-item" title="Flere alternativer" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personlig" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personlig</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukermeny" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb"><span>Doner</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Termodynamikkens+f%C3%B8rste+hovedsetning&returntoquery=veaction%3Dedit" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Termodynamikkens+f%C3%B8rste+hovedsetning&returntoquery=veaction%3Dedit" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Nettsted"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Innhold" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">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-Eksempel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksempel"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Eksempel</span> </div> </a> <ul id="toc-Eksempel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Termodynamisk_arbeid" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Termodynamisk_arbeid"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Termodynamisk arbeid</span> </div> </a> <ul id="toc-Termodynamisk_arbeid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differensiell_formulering" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Differensiell_formulering"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Differensiell formulering</span> </div> </a> <button aria-controls="toc-Differensiell_formulering-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 Differensiell formulering</span> </button> <ul id="toc-Differensiell_formulering-sublist" class="vector-toc-list"> <li id="toc-Termodynamisk_deriverte" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Termodynamisk_deriverte"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Termodynamisk deriverte</span> </div> </a> <ul id="toc-Termodynamisk_deriverte-sublist" class="vector-toc-list"> </ul> </li> </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">4</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">5</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-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">6</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 første 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Den_f%C3%B8rste_termodynamikklova" title="Den første termodynamikklova – norsk nynorsk" lang="nn" hreflang="nn" data-title="Den første termodynamikklova" 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/Termodynamikkens_1._lov" title="Termodynamikkens 1. lov – dansk" lang="da" hreflang="da" data-title="Termodynamikkens 1. lov" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-af badge-Q70894304 mw-list-item" title=""><a href="https://af.wikipedia.org/wiki/Eerste_wet_van_termodinamika" title="Eerste wet van termodinamika – afrikaans" lang="af" hreflang="af" data-title="Eerste 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%A3%D9%88%D9%84_%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 الأول للديناميكا الحرارية – arabisk" lang="ar" hreflang="ar" data-title="القانون الأول 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/Primer_principiu_de_la_termodin%C3%A1mica" title="Primer principiu de la termodinámica – asturisk" lang="ast" hreflang="ast" data-title="Primer 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_birinci_qanunu" title="Termodinamikanın birinci qanunu – aserbajdsjansk" lang="az" hreflang="az" data-title="Termodinamikanın birinci 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%AA%E0%A7%8D%E0%A6%B0%E0%A6%A5%E0%A6%AE_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="তাপগতিবিদ্যার প্রথম সূত্র – bengali" lang="bn" hreflang="bn" data-title="তাপগতিবিদ্যার প্রথম 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%9F%D0%B5%D1%80%D1%88%D1%8B_%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="Першы пачатак тэрмадынамікі – belarusisk" lang="be" hreflang="be" data-title="Першы 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%9F%D1%8A%D1%80%D0%B2%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="Първи закон на термодинамиката – bulgarsk" lang="bg" hreflang="bg" data-title="Първи 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – bosnisk" lang="bs" hreflang="bs" data-title="Prvi 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/Primer_principi_de_la_termodin%C3%A0mica" title="Primer principi de la termodinàmica – katalansk" lang="ca" hreflang="ca" data-title="Primer 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%BF%C4%95%D1%80%D1%80%D0%B5%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 пĕрремĕш пуçламăшĕ – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Термодинамикăн пĕрремĕш 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/Prvn%C3%AD_termodynamick%C3%BD_z%C3%A1kon" title="První termodynamický zákon – tsjekkisk" lang="cs" hreflang="cs" data-title="První 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/Erster_Hauptsatz_der_Thermodynamik" title="Erster Hauptsatz der Thermodynamik – tysk" lang="de" hreflang="de" data-title="Erster 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_esimene_seadus" title="Termodünaamika esimene seadus – estisk" lang="et" hreflang="et" data-title="Termodünaamika esimene 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%A0%CF%81%CF%8E%CF%84%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="Πρώτος θερμοδυναμικός νόμος – gresk" lang="el" hreflang="el" data-title="Πρώτος 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/First_law_of_thermodynamics" title="First law of thermodynamics – engelsk" lang="en" hreflang="en" data-title="First 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/Primer_principio_de_la_termodin%C3%A1mica" title="Primer principio de la termodinámica – spansk" lang="es" hreflang="es" data-title="Primer 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/Unua_le%C4%9Do_de_termodinamiko" title="Unua leĝo de termodinamiko – esperanto" lang="eo" hreflang="eo" data-title="Unua 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_lehenengo_legea" title="Termodinamikaren lehenengo legea – baskisk" lang="eu" hreflang="eu" data-title="Termodinamikaren lehenengo 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%A7%D9%88%D9%84_%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="قانون اول ترمودینامیک – persisk" lang="fa" hreflang="fa" data-title="قانون اول 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/Premier_principe_de_la_thermodynamique" title="Premier principe de la thermodynamique – fransk" lang="fr" hreflang="fr" data-title="Premier 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/Primeira_lei_da_termodin%C3%A1mica" title="Primeira lei da termodinámica – galisisk" lang="gl" hreflang="gl" data-title="Primeira 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%9C1%EB%B2%95%EC%B9%99" title="열역학 제1법칙 – koreansk" lang="ko" hreflang="ko" data-title="열역학 제1법칙" 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/%D4%B9%D5%A5%D6%80%D5%B4%D5%B8%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1%D5%B5%D5%AB_%D5%A1%D5%BC%D5%A1%D5%BB%D5%AB%D5%B6_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Թերմոդինամիկայի առաջին օրենք – armensk" lang="hy" hreflang="hy" data-title="Թերմոդինամիկայի առաջին 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%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊष्मागतिकी का प्रथम नियम – hindi" lang="hi" hreflang="hi" data-title="ऊष्मागतिकी का प्रथम 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – kroatisk" lang="hr" hreflang="hr" data-title="Prvi 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_pertama_termodinamika" title="Hukum pertama termodinamika – indonesisk" lang="id" hreflang="id" data-title="Hukum pertama termodinamika" 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/Primo_principio_della_termodinamica" title="Primo principio della termodinamica – italiensk" lang="it" hreflang="it" data-title="Primo 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%A8%D7%90%D7%A9%D7%95%D7%9F_%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 הראשון של התרמודינמיקה – hebraisk" lang="he" hreflang="he" data-title="החוק הראשון 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%9E%E1%83%98%E1%83%A0%E1%83%95%E1%83%94%E1%83%9A%E1%83%98_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="თერმოდინამიკის პირველი კანონი – georgisk" lang="ka" hreflang="ka" data-title="თერმოდინამიკის პირველი 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%B1%D1%96%D1%80%D1%96%D0%BD%D1%88%D1%96_%D0%B1%D0%B0%D1%81%D1%82%D0%B0%D0%BC%D0%B0%D1%81%D1%8B" title="Термодинамиканың бірінші бастамасы – kasakhisk" lang="kk" hreflang="kk" data-title="Термодинамиканың бірінші бастамасы" 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/Premye_lwa_t%C3%A8modinamik" title="Premye lwa tèmodinamik – haitisk" lang="ht" hreflang="ht" data-title="Premye 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-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Pirmais_termodinamikas_likums" title="Pirmais termodinamikas likums – latvisk" lang="lv" hreflang="lv" data-title="Pirmais 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_els%C5%91_f%C5%91t%C3%A9tele" title="A termodinamika első főtétele – ungarsk" lang="hu" hreflang="hu" data-title="A termodinamika első főtétele" 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%9F%D1%80%D0%B2_%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="Прв закон на термодинамиката – makedonsk" lang="mk" hreflang="mk" data-title="Прв закон на термодинамиката" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A5%87%E0%A4%9A%E0%A5%8D%E0%A4%AF%E0%A4%BE_%E0%A4%85%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%AF%E0%A5%8D%E0%A4%AF%E0%A4%A4%E0%A5%87%E0%A4%9A%E0%A4%BE_%E0%A4%AA%E0%A4%B9%E0%A4%BF%E0%A4%B2%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊर्जेच्या अक्षय्यतेचा पहिला नियम – marathi" lang="mr" hreflang="mr" data-title="ऊर्जेच्या अक्षय्यतेचा पहिला नियम" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_termodinamik_pertama" title="Hukum termodinamik pertama – malayisk" lang="ms" hreflang="ms" data-title="Hukum termodinamik pertama" 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/Eerste_wet_van_de_thermodynamica" title="Eerste wet van de thermodynamica – nederlandsk" lang="nl" hreflang="nl" data-title="Eerste 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%B8%80%E6%B3%95%E5%89%87" title="熱力学第一法則 – japansk" lang="ja" hreflang="ja" data-title="熱力学第一法則" 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/Premier_principi_de_la_termodinamica" title="Premier principi de la termodinamica – oksitansk" lang="oc" hreflang="oc" data-title="Premier 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_birinchi_qonuni" title="Termodinamikaning birinchi qonuni – usbekisk" lang="uz" hreflang="uz" data-title="Termodinamikaning birinchi 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pierwsza_zasada_termodynamiki" title="Pierwsza zasada termodynamiki – polsk" lang="pl" hreflang="pl" data-title="Pierwsza 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/Primeira_lei_da_termodin%C3%A2mica" title="Primeira lei da termodinâmica – portugisisk" lang="pt" hreflang="pt" data-title="Primeira 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_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii – rumensk" lang="ro" hreflang="ro" data-title="Principiul întâi 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%9F%D0%B5%D1%80%D0%B2%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="Первое начало термодинамики – russisk" lang="ru" hreflang="ru" data-title="Первое 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-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/First_law_o_thermodynamics" title="First law o thermodynamics – skotsk" lang="sco" hreflang="sco" data-title="First law o thermodynamics" data-language-autonym="Scots" data-language-local-name="skotsk" class="interlanguage-link-target"><span>Scots</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%B4%E0%B7%85%E0%B6%B8%E0%B7%94_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="තාප ගති විද්‍යාවේ පළමු නියමය – singalesisk" lang="si" hreflang="si" data-title="තාප ගති විද්‍යාවේ පළමු 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/First_law_of_thermodynamics" title="First law of thermodynamics – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="First 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/Prv%C3%A1_termodynamick%C3%A1_veta" title="Prvá termodynamická veta – slovakisk" lang="sk" hreflang="sk" data-title="Prvá 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – slovensk" lang="sl" hreflang="sl" data-title="Prvi 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-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DB%8C%D8%A7%D8%B3%D8%A7%DB%8C_%DB%8C%DB%95%DA%A9%DB%95%D9%85%DB%8C_%D8%AA%DB%8E%D8%B1%D9%85%DB%86%D8%AF%D8%A7%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="یاسای یەکەمی تێرمۆداینامیک – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="یاسای یەکەمی تێرمۆداینامیک" 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/%D0%9F%D1%80%D0%B2%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="Први принцип термодинамике – serbisk" lang="sr" hreflang="sr" data-title="Први 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – serbokroatisk" lang="sh" hreflang="sh" data-title="Prvi 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 badge-Q70893996 mw-list-item" title=""><a href="https://fi.wikipedia.org/wiki/Termodynamiikan_ensimm%C3%A4inen_p%C3%A4%C3%A4s%C3%A4%C3%A4nt%C3%B6" title="Termodynamiikan ensimmäinen pääsääntö – finsk" lang="fi" hreflang="fi" data-title="Termodynamiikan ensimmäinen 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%AE%E0%AF%81%E0%AE%A4%E0%AE%B2%E0%AE%BE%E0%AE%B5%E0%AE%A4%E0%AF%81_%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%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="முதலாவது வெப்ப இயக்கவியல் விதி – tamil" lang="ta" hreflang="ta" data-title="முதலாவது வெப்ப இயக்கவியல் 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%AB%E0%B8%99%E0%B8%B6%E0%B9%88%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="กฎข้อที่หนึ่งของอุณหพลศาสตร์ – thai" lang="th" hreflang="th" data-title="กฎข้อที่หนึ่งของอุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D1%88%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="Перший закон термодинаміки – ukrainsk" lang="uk" hreflang="uk" data-title="Перший 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_%D9%BE%DB%81%D9%84%D8%A7_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="حرحرکیات کا پہلا قانون – urdu" lang="ur" hreflang="ur" data-title="حرحرکیات کا پہلا قانون" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Primo_prinsipio_de_%C5%82a_termodin%C3%A0mica" title="Primo prinsipio de ła termodinàmica – venetiansk" lang="vec" hreflang="vec" data-title="Primo prinsipio de ła termodinàmica" data-language-autonym="Vèneto" data-language-local-name="venetiansk" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nguy%C3%AAn_l%C3%BD_th%E1%BB%A9_nh%E1%BA%A5t_c%E1%BB%A7a_nhi%E1%BB%87t_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Nguyên lý thứ nhất của nhiệt động lực học – vietnamesisk" lang="vi" hreflang="vi" data-title="Nguyên lý thứ nhất của nhiệt động lực học" 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%B8%80%E5%AE%9A%E5%BE%8B" title="热力学第一定律 – wu" lang="wuu" hreflang="wuu" data-title="热力学第一定律" 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/%E7%86%B1%E5%8A%9B%E5%AD%B8%E7%AC%AC%E4%B8%80%E5%AE%9A%E5%BE%8B" title="熱力學第一定律 – kantonesisk" lang="yue" hreflang="yue" data-title="熱力學第一定律" 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/%E7%83%AD%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%B8%80%E5%AE%9A%E5%BE%8B" title="热力学第一定律 – kinesisk" lang="zh" hreflang="zh" data-title="热力学第一定律" 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/Q179380#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskusjon:Termodynamikkens_f%C3%B8rste_hovedsetning" rel="discussion" title="Diskusjon om innholdssiden [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Bytt språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">norsk bokmål</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visninger"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning"><span>Les</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Verktøy" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Verktøy</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Termodynamikkens_f%C3%B8rste_hovedsetning" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=no" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Spesialsider" title="Liste over alle spesialsider [q]" accesskey="q"><span>Spesialsider</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&oldid=24685348" title="Permanent lenke til denne versjonen av siden"><span>Permanent lenke</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=info" title="Mer informasjon om denne siden"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siteringshjelp&page=Termodynamikkens_f%C3%B8rste_hovedsetning&id=24685348&wpFormIdentifier=titleform" title="Informasjon om hvordan denne siden kan siteres"><span>Siter denne siden</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fno.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DTermodynamikkens_f%25C3%25B8rste_hovedsetning%26veaction%3Dedit"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fno.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DTermodynamikkens_f%25C3%25B8rste_hovedsetning%26veaction%3Dedit"><span>Last ned QR-kode</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Skriv ut / eksporter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesial:DownloadAsPdf&page=Termodynamikkens_f%C3%B8rste_hovedsetning&action=show-download-screen"><span>Last ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&printable=yes" title="Utskriftsvennlig versjon av denne siden [p]" accesskey="p"><span>Utskriftsvennlig versjon</span></a></li> </ul> </div> </div> <div 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/Q179380" 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"><figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Bockdampfmaschine.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bockdampfmaschine.JPG/240px-Bockdampfmaschine.JPG" decoding="async" width="240" height="320" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bockdampfmaschine.JPG/360px-Bockdampfmaschine.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bockdampfmaschine.JPG/480px-Bockdampfmaschine.JPG 2x" data-file-width="960" data-file-height="1280" /></a><figcaption>Første hovedsetning kommer fra forklaringen av <a href="/wiki/Dampmaskin" title="Dampmaskin">dampmaskinens</a> virkemåte.</figcaption></figure> <p><b>Termodynamikkens første hovedsetning</b> eller lov sier at <a href="/wiki/Energi" title="Energi">energi</a> kan aldri oppstå eller tilintetgjøres, men kun kan gå over i andre former. Den betyr at energimengden i et <a href="/wiki/Isolert_system" title="Isolert system">isolert system</a> er konstant. Likedan har den som konsekvens at det er umulig å lage en <a href="/wiki/Perpetuum_mobile" title="Perpetuum mobile">perpetuum mobile</a> eller <i>evighetsmaskin</i>. </p><p>Sammen med <a href="/wiki/Termodynamikkens_andre_hovedsetning" title="Termodynamikkens andre hovedsetning">termodynamikkens andre hovedsetning</a> danner den grunnlaget for all <a href="/wiki/Termodynamikk" title="Termodynamikk">termodynamikk</a>. Den ble etablert på midten av 1800-tallet da det ble klart at <a href="/wiki/Varme" title="Varme">varme</a> kan skapes av mekanisk <a href="/wiki/Arbeid_(fysikk)" title="Arbeid (fysikk)">arbeid</a> og at begge er forskjellige manifestasjoner av energi. Dette hadde praktisk betydning for utvikling av <a href="/wiki/Dampmaskin" title="Dampmaskin">dampmaskinen</a> som ble forklart av <a href="/wiki/Sadi_Carnot" title="Sadi Carnot">Sadi Carnot</a>. Selve loven ble først formulert av <a href="/wiki/Julius_Robert_von_Mayer" class="mw-redirect" title="Julius Robert von Mayer">Robert Mayer</a> og gitt et mer solid fundament ved arbeidene til <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> og <a href="/wiki/William_Thomson" class="mw-redirect" title="William Thomson">William Thomson</a> rundt 1850. </p><p>Første hovedsetning fikk en matematisk utforming av <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>. Den beskriver et termodynamisk system som kan utveksle energi med omgivelsene både i form av varme og arbeid. Mottar det en varmemengde <i>Q </i> samtidig som det utfører et arbeid <i>W </i> på omgivelsene, vil det medføre en forandring Δ<i>U </i> i dets <a href="/wiki/Indre_energi" title="Indre energi">indre energi</a> 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 U=Q-W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mo>−</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q-W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e02cf059e743ecc2291c2fe20291b44cc977ccde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.931ex; height:2.509ex;" alt="{\displaystyle \Delta U=Q-W}"></span></dd></dl> <p>Den tilførte energien i form av varme forsvinner ikke, men går bare over i de to andre formene. I denne formuleringen er <i>Q </i> positiv når varme tilføres systemet fra omgivelsene, mens <i>W </i> er positiv når systemet utfører et arbeid på omgivelsene. Noen ganger defineres dette bidraget med motsatt fortegn, for eksempel innen <a href="/wiki/Kjemi" title="Kjemi">kjemi</a>. </p><p>Mer generelt omtales denne fundamentale <a href="/wiki/Naturlov" title="Naturlov">naturloven</a> som <a href="/wiki/Energiprinsippet" title="Energiprinsippet">energiprinsippet</a> eller <b>loven om energiens bevarelse</b>. Det ble formulert av <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> omtrent på samme tid og gjelder for alle fysiske prosesser. Også etter at <a href="/wiki/Kvantemekanikk" title="Kvantemekanikk">kvantemekanikken</a> og <a href="/wiki/Relativitetsteori" title="Relativitetsteori">relativitetsteorien</a> ble etablert, gjelder dette prinsippet. I dag er det forstått som en konsekvens av at en fysisk prosess skal gi samme resultat uavhengig av når den foregår.<sup id="cite_ref-Holton_1-0" class="reference"><a href="#cite_note-Holton-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Eksempel">Eksempel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit&section=1" title="Rediger avsnitt: Eksempel" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit&section=1" title="Rediger kildekoden til seksjonen Eksempel"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Denne termodynamiske loven kan brukes på mange forskjellig måter, avhengig av hva man betrakter som system og hva som skal beskrives. Er det termisk isolert, kan det ikke motta eller avgi varme slik at det kun kan foreta <a href="/wiki/Adiabatisk_prosess" title="Adiabatisk prosess">adiabatiske</a> forandringer med <i>Q</i> = 0. Da er forandringen i indre energi <span class="nowrap">Δ<i>U</i> = - <i>W</i>.</span> For at denne skal være positiv, må det det derfor utføres et arbeid på systemet. Dette behøver ikke å være mekanisk, men kunne i stedet være elektrisk eller kjemisk.<sup id="cite_ref-Rock_2-0" class="reference"><a href="#cite_note-Rock-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fil:Pil_som_suser_mot_blink.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Pil_som_suser_mot_blink.jpg/240px-Pil_som_suser_mot_blink.jpg" decoding="async" width="240" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Pil_som_suser_mot_blink.jpg/360px-Pil_som_suser_mot_blink.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b0/Pil_som_suser_mot_blink.jpg 2x" data-file-width="420" data-file-height="300" /></a><figcaption>Ved <a href="/wiki/Bueskyting" title="Bueskyting">bueskyting</a> opptrer forskjellige energiformer.</figcaption></figure> <p>En <a href="/wiki/Varmekraftmaskin" title="Varmekraftmaskin">varmekraftmaskin</a> er <i>syklisk</i> i den forstand at den går fra en tilstand tilbake til samme tilstand gjennom flere trinn der den utveksler arbeid <i>W </i> og varme <i>Q </i> med omgivelsene. Men siden den indre energien <i>U </i> til maskinen er en <a href="/wiki/Termodynamisk_potensial" title="Termodynamisk potensial">tilstandsfunksjon</a>, vil den totale forandringen <span class="nowrap">Δ<i>U</i> = 0</span> etter å ha kommet tilbake til samme tilstand. Arbeidet <i>W </i> som maskinen i den prosessen da har utført, må være likt med den tilførte mengde varme, <span class="nowrap"><i>Q</i> = <i>W</i>.</span> Det er denne sammenhengen som ligger til grunn for <a href="/wiki/Carnot-prosess" title="Carnot-prosess">Carnot-prosessen</a> som er den ideelle varmekraftmaskinen.<sup id="cite_ref-LHL_3-0" class="reference"><a href="#cite_note-LHL-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Loven omhandler <a href="/wiki/Energiprinsippet" title="Energiprinsippet">bevarelse</a> av energi som kan gå fra en form til en helt annen. Ved <a href="/wiki/Bueskyting" title="Bueskyting">bueskyting</a> går den <a href="/wiki/Potensiell_energi" title="Potensiell energi">potensielle energien</a> i buen når den spennes, over til å bli <a href="/wiki/Kinetisk_energi" title="Kinetisk energi">kinetisk energi</a> for pilen. Når denne treffer blinken, stopper den opp og dens energi bidrar til å øke den indre energien til blinken. Dette skjer ved <a href="/wiki/Friksjon" title="Friksjon">friksjon</a> som er et mekanisk arbeid som den blir tilført, det vil si <i>W</i> < 0. Da blinken ikke mottar noen varme, vil <span class="nowrap">Δ<i>U</i> = - <i>W</i> > 0.</span> Denne økningen i indre energi arter seg ved at molekylene i blinken vibrerer noe raskere og dens temperatur øker llit. </p><p>Omvendt kunne man tenke seg at denne lille oppvarmingen av blinken kunne samle seg og omdannes til mekanisk energi som ville slynge pilen tilbake mot bueskytteren. Dette er fullt mulig ifølge første hovedsetning. At det ikke skjer i virkeligheten, skyldes <a href="/wiki/Termodynamikkens_andre_hovedsetning" title="Termodynamikkens andre hovedsetning">termodynamikkens andre hovedsetning</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Termodynamisk_arbeid">Termodynamisk arbeid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit&section=2" title="Rediger avsnitt: Termodynamisk arbeid" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit&section=2" title="Rediger kildekoden til seksjonen Termodynamisk arbeid"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Energi i form av varme <i>Q </i> kan tilføres systemet når det kommer i kontakt med det annet system som har en annen temperatur. Derimot er energien som det mottar eller avgir i form av arbeid <i>W</i>, uavhengig av en slik temperaturforskjell med omgivelsene. Det klassiske bildet på et utført arbeid er den energien som går med til å heve en <a href="/wiki/Masse" title="Masse">masse</a> en viss høyde mot <a href="/wiki/Tyngdekraft" title="Tyngdekraft">tyngdekraften</a>.<sup id="cite_ref-Holton_1-1" class="reference"><a href="#cite_note-Holton-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>I en <a href="/wiki/Dampmaskin" title="Dampmaskin">dampmaskin</a> skapes et slikt arbeid ved at oppvarmet <a href="/wiki/Vanndamp" title="Vanndamp">vanndamp</a> presser på et stempel som holder den på plass i et volum <i>V</i>. Hvis tverrsnittet til stempelet har et areal <i>A</i>, vil det bli utsatt for en kraft <span class="nowrap"><i>F</i> = <i>PA </i></span> fra <a href="/wiki/Trykk" title="Trykk">trykket</a> <i>P </i> i dampen. Stempelet vil dermed bevege seg et lite stykke Δ<i>x</i> langs <i>x</i>-aksen, noe som tilsvarer at det har utført arbeidet <span class="nowrap">Δ<i>W</i> = <i>F</i>Δ<i>x</i>.</span> Dette kan nå 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=P\Delta V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>W</mi> <mo>=</mo> <mi>P</mi> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta W=P\Delta V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05b4284f4c902affc714cd310e4d1f06c4eb9bd3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.938ex; height:2.176ex;" alt="{\displaystyle \Delta W=P\Delta V}"></span></dd></dl> <p>hvor <span class="nowrap">Δ<i>V</i> = <i>A</i>Δ<i>x </i></span> er forandringen av volumet til gassen. </p><p>På lignende måte kan noen systemer bli holdt sammen ved en <a href="/wiki/Overflatespenning" title="Overflatespenning">overflatespenning</a> <i>σ</i>. Utvides arealet <i>A </i> til overflaten med Δ<i>A</i>, vil systemet da måtte utføre et arbeid Δ<i>W</i> = - <i>σ</i>Δ<i>A</i>. Spenningen er definert slik at arbeidet er positivt når overflaten blir litt mindre, det vil si når systemet trekker seg sammen.<sup id="cite_ref-Castellan_4-0" class="reference"><a href="#cite_note-Castellan-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <table class="navbox" style="width: 18em; margin-left: 1em; float: right;"> <tbody><tr> <th colspan="2">Konjugerte variabler<br />i termodynamikk </th></tr> <tr> <td><a href="/wiki/Trykk" title="Trykk">Trykk</a></td> <td><a href="/wiki/Volum" title="Volum">Volum</a> </td></tr> <tr> <td>(<a href="/wiki/Spenning_(mekanikk)" title="Spenning (mekanikk)">Spenning </a>)</td> <td>(<a href="/wiki/Deformasjon#Tøyning" title="Deformasjon">Tøyning</a>) </td></tr> <tr> <td><a href="/wiki/Temperatur" title="Temperatur">Temperatur</a></td> <td><a href="/wiki/Entropi" title="Entropi">Entropi</a> </td></tr> <tr> <td><a href="/wiki/Kjemisk_potensial" title="Kjemisk potensial">Kjemisk potensial</a></td> <td><a href="/wiki/Partikkelnummer" title="Partikkelnummer">Partikkelnummer</a> </td></tr></tbody></table> <p>Systemet kan også ufføre et <a href="/wiki/Kjemi" title="Kjemi">kjemisk</a> arbeid hvis det kan utveksle materie eller partikler med omgivelsene. Dette er beskrevet ved det <a href="/wiki/Kjemisk_potensial" title="Kjemisk potensial">kjemiske potensialet</a> <i>μ</i>. Ved <a href="/wiki/Termodynamisk_likevekt" title="Termodynamisk likevekt">termodynamisk likevekt</a> har det samme verdi både i systemet og omgivelsene. Hvis det blir overført et lite antall partikler Δ<i>N </i> fra systemet til omgivelsene, vil da arbeidet </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=-\mu \Delta N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>W</mi> <mo>=</mo> <mo>−</mo> <mi>μ</mi> <mi mathvariant="normal">Δ</mi> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta W=-\mu \Delta N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07a261e9796c20e078d43e4d52e74ed84197671" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.679ex; height:2.676ex;" alt="{\displaystyle \Delta W=-\mu \Delta N}"></span></dd></dl> <p>bli utført. På samme måte som for andre termodynamiske arbeid, består dette kjemiske arbeidet av et produkt mellom en <a href="/wiki/Intensive_og_ekstensive_egenskaper" title="Intensive og ekstensive egenskaper">intensiv</a> variabel <i>μ </i> og en <a href="/wiki/Intensive_og_ekstensive_egenskaper" title="Intensive og ekstensive egenskaper">ekstensiv</a> variabel Δ<i>N</i>. De sies å være <b>konjugerte variable</b>. </p><p>Når systemet inneholder elektriske <a href="/wiki/Elektrisk_ladning" title="Elektrisk ladning">ladninger</a> og <a href="/wiki/Elektrisk_str%C3%B8m" title="Elektrisk strøm">strømmer</a>, kan det også koble til omgivelsene gjennom <a href="/wiki/Elektrisk_felt" title="Elektrisk felt">elektriske</a> eller <a href="/wiki/Magnetfelt" title="Magnetfelt">magnetiske</a> felt. Hvis Φ  er den elektriske <a href="/wiki/Elektrisk_potensial" title="Elektrisk potensial">potensialforskjellen</a> mellom systemet og omgivelsene, vil en overføring av Δ<i>Q<sub>el</sub> </i> ladning bety et utført arbeid <span class="nowrap">Δ<i>W</i> = ΦΔ<i>Q<sub>el</sub></i>.</span> Når dette skjer ved utveksling av elektrisk ladete partikler, kan det beskrives som et kjemisk arbeid hvor det kjemiske potensialet <i>μ </i> får et tillegg proporsjonalt med det elektriske potensialet.<sup id="cite_ref-Castellan_4-1" class="reference"><a href="#cite_note-Castellan-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Tilsvarende må et <a href="/wiki/Magnetfelt" title="Magnetfelt">magnetfelt</a> <i>B </i> utføre et arbeid <i>B</i>Δ<i>M </i> på et system med <a href="/wiki/Magnetisering" title="Magnetisering">magnetisering</a> <i>M </i> for å forandre denne med Δ<i>M</i>. Det følger fra den magnetiske <a href="/wiki/Magnetfelt#Magnetisk_energi" title="Magnetfelt">vekselvirkningsenergien</a> mellom systemet og omgivelsene. Arbeidet som systemet utfører ved en slik forandring, er derfor </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=-B\Delta M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>W</mi> <mo>=</mo> <mo>−</mo> <mi>B</mi> <mi mathvariant="normal">Δ</mi> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta W=-B\Delta M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/065a23ebe6fbafe92fee91045c5157b21efa140e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.42ex; height:2.343ex;" alt="{\displaystyle \Delta W=-B\Delta M}"></span></dd></dl> <p>Dette magnetiske arbeidet kan i termodynamisk sammenheng forklare hvorfor magnetisering av et materiale vil forsvinne ved tilstrekkelig høye temperaturer.<sup id="cite_ref-KK_5-0" class="reference"><a href="#cite_note-KK-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Samtidig som systemet utfører slike små arbeid, kan det også motta en varmemengde Δ<i>Q</i>. Det resulterer i en tilsvarende forandring Δ<i>U </i> i systemets indre energi. Den er gitt ved første hovedsetning som nå kan 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 U=\Delta Q-\Delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=\Delta Q-\Delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb42dc99e2fb6fd5c896a5ccd8e3e5af6f548683" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.803ex; height:2.509ex;" alt="{\displaystyle \Delta U=\Delta Q-\Delta W}"></span></dd></dl> <p>Alle disse små forandringene er forbundet gjennom systemets <a href="/wiki/Tilstandsligning" title="Tilstandsligning">tilstandsligning</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Differensiell_formulering">Differensiell formulering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit&section=3" title="Rediger avsnitt: Differensiell formulering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit&section=3" title="Rediger kildekoden til seksjonen Differensiell formulering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Første og andre hovedsetning ble først klart formulert av <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>. Han viste også hvordan man kan beskrive termodynamiske prosesser med <a href="/wiki/Matematisk_analyse" title="Matematisk analyse">matematisk analyse</a> som omfatter differensial- og integralregning. Det er mulig i grensen hvor man antar at forandringer som Δ<i>U </i> og Δ<i>V </i> er så små at de kan betraktes som <a href="/wiki/Differensial_(matematikk)" title="Differensial (matematikk)">differrensial</a> <i>dU</i> og <i>dV</i>. De har den egenskapen at for eksempel volumintegralet </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 \int _{1}^{2}\!dV=V_{2}-V_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="negativethinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{1}^{2}\!dV=V_{2}-V_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d488bc07266ad004d61d3166446c647dbc101b5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.279ex; height:6.176ex;" alt="{\displaystyle \int _{1}^{2}\!dV=V_{2}-V_{1}}"></span></dd></dl> <p>er gitt ved differensen mellom volumet i sluttilstanden og begynnelsestilstanden. Det gjelder også for integralet av energidifferensialet <i>dU </i> da den indre energien er en <a href="/wiki/Termodynamisk_potensial" title="Termodynamisk potensial">tilstandsfunksjon</a>. Men det er ikke hverken det utførte arbeidet <i>W </i> eller den tilførte varmen <i>Q</i>. De avhenger ikke bare av begynnelse- og sluttilstand, men også av selve prosessen som medfører forandringen. Infinitesemale forandringer av disse størrelsene skrives derfor som δ<i>W </i> og δ<i>Q </i> hvor nå <span class="nowrap">δ<i>W</i> = <i>PdV </i></span> hvis arbeidet er mekanisk. Denne forskjellen mellom differensialene tilsvarer forskjellen mellom ekte og uekte <a href="/wiki/Differensialform" title="Differensialform">differensialformer</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Med denne forståelsen kan første hovedsetning derfor skrives på differensiell form 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 dU=\delta Q-\delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dU=\delta Q-\delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cde6dc0d4ae04f62ec8f1f1aac711c889b2717ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.308ex; height:2.676ex;" alt="{\displaystyle dU=\delta Q-\delta W}"></span></dd></dl> <p>Når varmetilførselen δ<i>Q </i> foregår på en reversibel måte slik at systemet forblir i <a href="/wiki/Termisk_likevekt" class="mw-redirect" title="Termisk likevekt">termisk likevekt</a>, vil den medføre en forandring <i>dS </i> av systemets <a href="/wiki/Entropi" title="Entropi">entropi</a> <i>S</i>. Den er et eksakt differensial da entropi også er en tilstandsfunksjon. Fra <a href="/wiki/Entropi#Clausius_og_termodynamikk" title="Entropi">Clausius' likhet</a> følger da at <span class="nowrap">δ<i>Q</i> = <i>TdS </i></span> når <i>T </i> er temperaturen til systemet og omgivelsene. Ved å ta med både mekanisk og kjemisk arbeid, kan nå loven skrives på formen </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</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>som inneholder bare eksakte differensial. Denne fundamentale sammenhengen blir vanligvis omtalt som «den termodynamiske identitet».<sup id="cite_ref-Rock_2-1" class="reference"><a href="#cite_note-Rock-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Termodynamisk_deriverte">Termodynamisk deriverte</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit&section=4" title="Rediger avsnitt: Termodynamisk deriverte" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&action=edit&section=4" title="Rediger kildekoden til seksjonen Termodynamisk deriverte"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hvis partikkeltallet <i>N </i> i systemet er konstant, blir første hovedsetning på differensiell form </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>Den viser at entropi <i>S </i> og volum <i>V </i> er <i>naturlige</i> variable for den indre energien <i>U</i>. <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Willard Gibbs</a> omtalte den som «termodynamikkens fundamente ligning» og gjorde mye ut av den. Da denne energien er en <a href="/wiki/Termodynamisk_potensial" title="Termodynamisk potensial">tilstandsfunksjon</a>, vil det finnes en matematisk sammenheng <i>U</i> = <i>U</i>(<i>S,V</i>). Ved <a href="/wiki/Derivasjon" title="Derivasjon">partiell derivasjon</a> er 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 dU=\left({\frac {\partial U}{\partial S}}\right)_{V}dS+\left({\frac {\partial U}{\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({\frac {\partial U}{\partial S}}\right)_{V}dS+\left({\frac {\partial U}{\partial V}}\right)_{S}dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3a0003e947a6ca9fcc57c596b897cc13508a865" 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({\frac {\partial U}{\partial S}}\right)_{V}dS+\left({\frac {\partial U}{\partial V}}\right)_{S}dV}"></span></dd></dl> <p>Når disse to differensialene sammenlignes, finner man for de 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({\frac {\partial U}{\partial S}}\right)_{V}=T,\;\;\;\left({\frac {\partial U}{\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> <mo>,</mo> <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({\frac {\partial U}{\partial S}}\right)_{V}=T,\;\;\;\left({\frac {\partial U}{\partial V}}\right)_{S}=-P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f4aeba9191924d11ea264260ed677ae9040e372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.865ex; height:6.176ex;" alt="{\displaystyle \left({\frac {\partial U}{\partial S}}\right)_{V}=T,\;\;\;\left({\frac {\partial U}{\partial V}}\right)_{S}=-P}"></span></dd></dl> <p>Da to partielle derivasjoner etter hverandre kan byttes om slik at <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial ^{2}U/\partial S\partial V=\partial ^{2}U/\partial V\partial S,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> <mi mathvariant="normal">∂</mi> <mi>V</mi> <mo>=</mo> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> <mi mathvariant="normal">∂</mi> <mi>S</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial ^{2}U/\partial S\partial V=\partial ^{2}U/\partial V\partial S,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d2daf130aef7f653dacc5c6bde49f076fe3c37f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.276ex; height:3.176ex;" alt="{\displaystyle \partial ^{2}U/\partial S\partial V=\partial ^{2}U/\partial V\partial S,}"></span> resulterer det i den termodynamiske 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 \left({\frac {\partial T}{\partial V}}\right)_{S}=-\left({\frac {\partial P}{\partial S}}\right)_{V}}"> <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>T</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> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>P</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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial T}{\partial V}}\right)_{S}=-\left({\frac {\partial P}{\partial S}}\right)_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91fd3b8b085521fc48c608a752b53ba53d63eb6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.378ex; height:6.176ex;" alt="{\displaystyle \left({\frac {\partial T}{\partial V}}\right)_{S}=-\left({\frac {\partial P}{\partial S}}\right)_{V}}"></span></dd></dl> <p>Dette er et eksempel på en <a href="/wiki/Maxwell-relasjon" title="Maxwell-relasjon">Maxwell-relasjon</a>. Den og mange lignende har stor betydning for praktisk utnyttelse av de termodynamiske lovene.<sup id="cite_ref-Castellan_4-2" class="reference"><a href="#cite_note-Castellan-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <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_f%C3%B8rste_hovedsetning&veaction=edit&section=5" 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_f%C3%B8rste_hovedsetning&action=edit&section=5" 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/Termodynamikk" title="Termodynamikk">Termodynamikk</a></li> <li><a href="/wiki/Termodynamikkens_andre_hovedsetning" title="Termodynamikkens andre hovedsetning">Termodynamikkens andre hovedsetning</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_f%C3%B8rste_hovedsetning&veaction=edit&section=6" 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_f%C3%B8rste_hovedsetning&action=edit&section=6" 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-Holton-1"><b>^</b> <a href="#cite_ref-Holton_1-0"><sup>a</sup></a> <a href="#cite_ref-Holton_1-1"><sup>b</sup></a> <span class="reference-text"> G. Holton and S.G. Brush, <i>Physics, the Human Adventure</i>, Rutgers University Press, New Jersey (2006). <a href="/wiki/Spesial:Bokkilder/0813529085" class="internal mw-magiclink-isbn">ISBN 0-8135-2908-5</a>.</span> </li> <li id="cite_note-Rock-2"><b>^</b> <a href="#cite_ref-Rock_2-0"><sup>a</sup></a> <a href="#cite_ref-Rock_2-1"><sup>b</sup></a> <span class="reference-text">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>.</span> </li> <li id="cite_note-LHL-3"><b><a href="#cite_ref-LHL_3-0">^</a></b> <span class="reference-text"> 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>.</span> </li> <li id="cite_note-Castellan-4"><b>^</b> <a href="#cite_ref-Castellan_4-0"><sup>a</sup></a> <a href="#cite_ref-Castellan_4-1"><sup>b</sup></a> <a href="#cite_ref-Castellan_4-2"><sup>c</sup></a> <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-KK-5"><b><a href="#cite_ref-KK_5-0">^</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-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"> T. Lindstrøm, <i>Kalkulus</i>, Universitetsforlaget, Oslo (2016). <a href="/wiki/Spesial:Bokkilder/9788215027104" class="internal mw-magiclink-isbn">ISBN 978-82-15-02710-4</a>.</span> </li> </ol></div> <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_f%C3%B8rste_hovedsetning&veaction=edit&section=7" 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_f%C3%B8rste_hovedsetning&action=edit&section=7" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>PhysLibreTexts, <a rel="nofollow" class="external text" href="https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/14%3A_Thermodynamics/14.2%3A_The_First_Law_of_Thermodynamics"><i>The First Law of Thermodynamics</i></a>, med instruktiv video.</li> <li>YouTube, <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=NyOYW07-L5g"><i>First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry</i></a>, god introduksjon</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 dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r24561737">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}</style></div><div role="navigation" class="navbox" aria-labelledby="Oppslagsverk/autoritetsdata" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Oppslagsverk/autoritetsdata" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hjelp:Autoritetsdata" title="Hjelp:Autoritetsdata">Oppslagsverk/autoritetsdata</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0em 0.25em"><a rel="nofollow" class="external text" href="https://denstoredanske.lex.dk/første_hovedsætning">Store Danske Encyklopædi</a></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Hentet fra «<a dir="ltr" href="https://no.wikipedia.org/w/index.php?title=Termodynamikkens_første_hovedsetning&oldid=24685348">https://no.wikipedia.org/w/index.php?title=Termodynamikkens_første_hovedsetning&oldid=24685348</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Kategori:Kategorier" title="Kategori:Kategorier">Kategorier</a>: <ul><li><a href="/wiki/Kategori:Termodynamikk" title="Kategori:Termodynamikk">Termodynamikk</a></li><li><a href="/wiki/Kategori:Fysiske_lover" title="Kategori:Fysiske lover">Fysiske lover</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skjulte kategorier: <ul><li><a href="/wiki/Kategori:Sider_som_bruker_magiske_ISBN-lenker" title="Kategori:Sider som bruker magiske ISBN-lenker">Sider som bruker magiske ISBN-lenker</a></li><li><a href="/wiki/Kategori:Artikler_med_autoritetsdatalenker_fra_Wikidata" title="Kategori:Artikler med autoritetsdatalenker fra Wikidata">Artikler med autoritetsdatalenker fra Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Denne siden ble sist redigert 18. sep. 2024 kl. 11:15.</li> <li id="footer-info-copyright">Innholdet er tilgjengelig under <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no">Creative Commons-lisensen Navngivelse-DelPåSammeVilkår</a>, men ytterligere betingelser kan gjelde. Se <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">bruksvilkårene</a> for detaljer.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Personvern</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Om">Om Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Generelle_forbehold">Forbehold</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Atferdsnorm</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Utviklere</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/no.wikipedia.org">Statistikk</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Erklæring om informasjonskapsler</a></li> <li id="footer-places-mobileview"><a href="//no.m.wikipedia.org/w/index.php?title=Termodynamikkens_f%C3%B8rste_hovedsetning&veaction=edit&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobilvisning</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5c59558b9d-zt8rb","wgBackendResponseTime":167,"wgPageParseReport":{"limitreport":{"cputime":"0.181","walltime":"0.270","ppvisitednodes":{"value":1068,"limit":1000000},"postexpandincludesize":{"value":4941,"limit":2097152},"templateargumentsize":{"value":491,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":8784,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 164.905 1 -total"," 88.99% 146.741 1 Mal:Autoritetsdata"," 51.97% 85.707 1 Mal:Navboks"," 49.79% 82.111 1 Mal:Navbox"," 2.05% 3.387 1 Mal:Konjugerte_variabler_(termodynamikk)"," 1.96% 3.237 10 Mal:Nowrap"]},"scribunto":{"limitreport-timeusage":{"value":"0.100","limit":"10.000"},"limitreport-memusage":{"value":1737790,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-559c9fd9f4-mfc2x","timestamp":"20241126142200","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Termodynamikkens f\u00f8rste hovedsetning","url":"https:\/\/no.wikipedia.org\/wiki\/Termodynamikkens_f%C3%B8rste_hovedsetning","sameAs":"http:\/\/www.wikidata.org\/entity\/Q179380","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q179380","author":{"@type":"Organization","name":"Bidragsytere til Wikimedia-prosjektene"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2006-06-02T09:03:31Z","dateModified":"2024-09-18T10:15:46Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/3\/3d\/Bockdampfmaschine.JPG"}</script> </body> </html>