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="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Rudolf Clausius - 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(/(?:^|; )enwikimwclientpreferences=([^;]+)/);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":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"9501ddfe-67d5-4467-9693-cdd9655f53ce","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Rudolf_Clausius","wgTitle":"Rudolf Clausius","wgCurRevisionId":1259907066,"wgRevisionId":1259907066,"wgArticleId":175146,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 German-language sources (de)","Articles with short description","Short description is different from Wikidata","Biography with signature","Articles with hCards","Pages with German IPA","CS1 French-language sources (fr)","Commons category link is on Wikidata","Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference","Articles with Project Gutenberg links","Articles with Internet Archive links","1822 births","1888 deaths", "People from Koszalin","Academic staff of ETH Zurich","Thermodynamicists","German military personnel of the Franco-Prussian War","19th-century German physicists","German fluid dynamicists","People from the Province of Pomerania","Recipients of the Iron Cross (1870)","Recipients of the Copley Medal","Recipients of the Pour le Mérite (civil class)","Humboldt University of Berlin alumni","Academic staff of the University of Bonn","Academic staff of the University of Würzburg","Foreign members of the Royal Society","Foreign associates of the National Academy of Sciences","Members of the Royal Netherlands Academy of Arts and Sciences","Members of the Royal Swedish Academy of Sciences","German theoretical physicists","Prussian Army personnel"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Rudolf_Clausius","wgRelevantArticleId":175146,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[], "wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q30693","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false, "wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","mediawiki.page.gallery.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"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","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","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.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","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=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cmediawiki.page.gallery.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=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/1200px-Rudolf_Clausius_01.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1841"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/800px-Rudolf_Clausius_01.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="1227"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/640px-Rudolf_Clausius_01.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="982"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Rudolf Clausius - 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="//en.m.wikipedia.org/wiki/Rudolf_Clausius"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Rudolf_Clausius&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 (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Rudolf_Clausius"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&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-Rudolf_Clausius rootpage-Rudolf_Clausius skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</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="Site"> <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="Main menu" > <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">Main menu</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">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" 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="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </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/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</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="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search 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="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <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="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <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="Appearance" > <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">Appearance</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="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</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=Special:CreateAccount&returnto=Rudolf+Clausius" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</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=Special:UserLogin&returnto=Rudolf+Clausius" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</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" title="Log in and more options" > <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="Personal tools" > <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">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <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="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Rudolf+Clausius" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Rudolf+Clausius" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</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="Site"> <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="Contents" 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">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</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">(Top)</div> </a> </li> <li id="toc-Life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Life"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Life</span> </div> </a> <ul id="toc-Life-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Work" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Work</span> </div> </a> <button aria-controls="toc-Work-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>Toggle Work subsection</span> </button> <ul id="toc-Work-sublist" class="vector-toc-list"> <li id="toc-Entropy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Entropy"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Entropy</span> </div> </a> <ul id="toc-Entropy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Tributes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tributes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Tributes</span> </div> </a> <ul id="toc-Tributes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Publications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Publications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Publications</span> </div> </a> <ul id="toc-Publications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Rudolf Clausius</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="Go to an article in another language. Available in 68 languages" > <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-68" 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">68 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Afrikaans" lang="af" hreflang="af" data-title="Rudolf Clausius" 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%B1%D9%88%D8%AF%D9%88%D9%84%D9%81_%D9%83%D9%84%D8%A7%D9%88%D8%B2%D9%8A%D9%88%D8%B3" title="رودولف كلاوزيوس – Arabic" lang="ar" hreflang="ar" data-title="رودولف كلاوزيوس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Rudolf_Klauzius" title="Rudolf Klauzius – Azerbaijani" lang="az" hreflang="az" data-title="Rudolf Klauzius" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B1%D9%88%D8%AF%D9%84%D9%81_%DA%A9%D9%84%D8%A7%D9%88%D8%B2%DB%8C%D9%88%D8%B3" title="رودلف کلاوزیوس – South Azerbaijani" lang="azb" hreflang="azb" data-title="رودلف کلاوزیوس" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A7%81%E0%A6%A1%E0%A6%B2%E0%A6%AB_%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BE%E0%A6%89%E0%A6%9C%E0%A6%BF%E0%A6%89%E0%A6%B8" title="রুডলফ ক্লাউজিউস – Bangla" lang="bn" hreflang="bn" data-title="রুডলফ ক্লাউজিউস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Minnan" lang="nan" hreflang="nan" data-title="Rudolf Clausius" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D1%83%D0%B4%D0%BE%D0%BB%D1%8C%D1%84_%D0%AE%D0%BB%D1%96%D1%83%D1%81_%D0%AD%D0%BC%D0%B0%D0%BD%D1%83%D1%8D%D0%BB%D1%8C_%D0%9A%D0%BB%D0%B0%D1%9E%D0%B7%D1%96%D1%83%D1%81" title="Рудольф Юліус Эмануэль Клаўзіус – Belarusian" lang="be" hreflang="be" data-title="Рудольф Юліус Эмануэль Клаўзіус" data-language-autonym="Беларуская" data-language-local-name="Belarusian" 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%A0%D1%83%D0%B4%D0%BE%D0%BB%D1%84_%D0%9A%D0%BB%D0%B0%D1%83%D0%B7%D0%B8%D1%83%D1%81" title="Рудолф Клаузиус – Bulgarian" lang="bg" hreflang="bg" data-title="Рудолф Клаузиус" data-language-autonym="Български" data-language-local-name="Bulgarian" 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/Rudolf_Clausius" title="Rudolf Clausius – Bosnian" lang="bs" hreflang="bs" data-title="Rudolf Clausius" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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/Rudolf_Clausius" title="Rudolf Clausius – Catalan" lang="ca" hreflang="ca" data-title="Rudolf Clausius" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Czech" lang="cs" hreflang="cs" data-title="Rudolf Clausius" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Danish" lang="da" hreflang="da" data-title="Rudolf Clausius" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – German" lang="de" hreflang="de" data-title="Rudolf Clausius" data-language-autonym="Deutsch" data-language-local-name="German" 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/Rudolf_Clausius" title="Rudolf Clausius – Estonian" lang="et" hreflang="et" data-title="Rudolf Clausius" data-language-autonym="Eesti" data-language-local-name="Estonian" 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%A1%CE%BF%CF%8D%CE%BD%CF%84%CE%BF%CE%BB%CF%86_%CE%9A%CE%BB%CE%B1%CE%BF%CF%8D%CE%B6%CE%B9%CE%BF%CF%85%CF%82" title="Ρούντολφ Κλαούζιους – Greek" lang="el" hreflang="el" data-title="Ρούντολφ Κλαούζιους" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Spanish" lang="es" hreflang="es" data-title="Rudolf Clausius" data-language-autonym="Español" data-language-local-name="Spanish" 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/Rudolf_Clausius" title="Rudolf Clausius – Esperanto" lang="eo" hreflang="eo" data-title="Rudolf Clausius" 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/Rudolf_Clausius" title="Rudolf Clausius – Basque" lang="eu" hreflang="eu" data-title="Rudolf Clausius" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D9%88%D8%AF%D9%84%D9%81_%DA%A9%D9%84%D8%A7%D9%88%D8%B2%DB%8C%D9%88%D8%B3" title="رودلف کلاوزیوس – Persian" lang="fa" hreflang="fa" data-title="رودلف کلاوزیوس" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Rudolf_Clausius" title="Rudolf Clausius – French" lang="fr" hreflang="fr" data-title="Rudolf Clausius" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A3%A8%EB%8F%8C%ED%94%84_%ED%81%B4%EB%9D%BC%EC%9A%B0%EC%A7%80%EC%9A%B0%EC%8A%A4" title="루돌프 클라우지우스 – Korean" lang="ko" hreflang="ko" data-title="루돌프 클라우지우스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%B8%D6%82%D5%A4%D5%B8%D5%AC%D6%86_%D4%BF%D5%AC%D5%A1%D5%B8%D6%82%D5%A6%D5%AB%D5%B8%D6%82%D5%BD" title="Ռուդոլֆ Կլաուզիուս – Armenian" lang="hy" hreflang="hy" data-title="Ռուդոլֆ Կլաուզիուս" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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%B0%E0%A5%81%E0%A4%A1%E0%A5%89%E0%A4%B2%E0%A5%8D%E0%A4%AB_%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%B8%E0%A4%BF%E0%A4%85%E0%A4%B8" title="रुडॉल्फ क्लासिअस – Hindi" lang="hi" hreflang="hi" data-title="रुडॉल्फ क्लासिअस" 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/Rudolf_Clausius" title="Rudolf Clausius – Croatian" lang="hr" hreflang="hr" data-title="Rudolf Clausius" data-language-autonym="Hrvatski" data-language-local-name="Croatian" 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/Rudolf_Clausius" title="Rudolf Clausius – Indonesian" lang="id" hreflang="id" data-title="Rudolf Clausius" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Icelandic" lang="is" hreflang="is" data-title="Rudolf Clausius" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Italian" lang="it" hreflang="it" data-title="Rudolf Clausius" data-language-autonym="Italiano" data-language-local-name="Italian" 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%A8%D7%95%D7%93%D7%95%D7%9C%D7%A3_%D7%A7%D7%9C%D7%90%D7%95%D7%96%D7%99%D7%95%D7%A1" title="רודולף קלאוזיוס – Hebrew" lang="he" hreflang="he" data-title="רודולף קלאוזיוס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Swahili" lang="sw" hreflang="sw" data-title="Rudolf Clausius" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Haitian Creole" lang="ht" hreflang="ht" data-title="Rudolf Clausius" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Rudolphus_Clausius" title="Rudolphus Clausius – Latin" lang="la" hreflang="la" data-title="Rudolphus Clausius" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/R%C5%ABdolfs_Klauziuss" title="Rūdolfs Klauziuss – Latvian" lang="lv" hreflang="lv" data-title="Rūdolfs Klauziuss" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Lithuanian" lang="lt" hreflang="lt" data-title="Rudolf Clausius" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Hungarian" lang="hu" hreflang="hu" data-title="Rudolf Clausius" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Malagasy" lang="mg" hreflang="mg" data-title="Rudolf Clausius" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B1%E0%B5%81%E0%B4%A1%E0%B5%8B%E0%B5%BE%E0%B4%AB%E0%B5%8D_%E0%B4%95%E0%B5%8D%E0%B4%B2%E0%B5%8B%E0%B4%B7%E0%B5%8D%E0%B4%AF%E0%B4%B8%E0%B5%8D" title="റുഡോൾഫ് ക്ലോഷ്യസ് – Malayalam" lang="ml" hreflang="ml" data-title="റുഡോൾഫ് ക്ലോഷ്യസ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Maltese" lang="mt" hreflang="mt" data-title="Rudolf Clausius" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A0%E1%83%A3%E1%83%93%E1%83%9D%E1%83%9A%E1%83%A4_%E1%83%99%E1%83%9A%E1%83%90%E1%83%A3%E1%83%96%E1%83%98%E1%83%A3%E1%83%A1%E1%83%98" title="რუდოლფ კლაუზიუსი – Mingrelian" lang="xmf" hreflang="xmf" data-title="რუდოლფ კლაუზიუსი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B1%D9%88%D8%AF%D9%88%D9%84%D9%81_%D9%83%D9%84%D8%A7%D9%88%D8%B2%D9%8A%D9%88%D8%B3" title="رودولف كلاوزيوس – Egyptian Arabic" lang="arz" hreflang="arz" data-title="رودولف كلاوزيوس" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Dutch" lang="nl" hreflang="nl" data-title="Rudolf Clausius" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/%E3%83%AB%E3%83%89%E3%83%AB%E3%83%95%E3%83%BB%E3%82%AF%E3%83%A9%E3%82%A6%E3%82%B8%E3%82%A6%E3%82%B9" title="ルドルフ・クラウジウス – Japanese" lang="ja" hreflang="ja" data-title="ルドルフ・クラウジウス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Rudolf Clausius" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Rudolf Clausius" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Uzbek" lang="uz" hreflang="uz" data-title="Rudolf Clausius" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%D9%88%DA%88%D9%84%D9%81_%DA%A9%D9%84%D8%A7%D8%B3%DB%8C%D8%B3" title="روڈلف کلاسیس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="روڈلف کلاسیس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B1%D9%88%D8%AF%D9%88%D9%84%D9%81_%DA%A9%D9%84%D8%A7%D9%88%D8%B2%D9%8A%D9%88%D8%B3" title="رودولف کلاوزيوس – Pashto" lang="ps" hreflang="ps" data-title="رودولف کلاوزيوس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Piedmontese" lang="pms" hreflang="pms" data-title="Rudolf Clausius" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Polish" lang="pl" hreflang="pl" data-title="Rudolf Clausius" data-language-autonym="Polski" data-language-local-name="Polish" 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/Rudolf_Clausius" title="Rudolf Clausius – Portuguese" lang="pt" hreflang="pt" data-title="Rudolf Clausius" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Rudolf_Julius_Emanuel_Clausius" title="Rudolf Julius Emanuel Clausius – Romanian" lang="ro" hreflang="ro" data-title="Rudolf Julius Emanuel Clausius" data-language-autonym="Română" data-language-local-name="Romanian" 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%9A%D0%BB%D0%B0%D1%83%D0%B7%D0%B8%D1%83%D1%81,_%D0%A0%D1%83%D0%B4%D0%BE%D0%BB%D1%8C%D1%84_%D0%AE%D0%BB%D0%B8%D1%83%D1%81_%D0%AD%D0%BC%D0%B0%D0%BD%D1%83%D1%8D%D0%BB%D1%8C" title="Клаузиус, Рудольф Юлиус Эмануэль – Russian" lang="ru" hreflang="ru" data-title="Клаузиус, Рудольф Юлиус Эмануэль" data-language-autonym="Русский" data-language-local-name="Russian" 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/Rudolf_Clausius" title="Rudolf Clausius – Scots" lang="sco" hreflang="sco" data-title="Rudolf Clausius" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Slovak" lang="sk" hreflang="sk" data-title="Rudolf Clausius" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Rudolf_Julius_Emmanuel_Clausius" title="Rudolf Julius Emmanuel Clausius – Slovenian" lang="sl" hreflang="sl" data-title="Rudolf Julius Emmanuel Clausius" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D1%83%D0%B4%D0%BE%D0%BB%D1%84_%D0%9A%D0%BB%D0%B0%D1%83%D0%B7%D0%B8%D1%98%D1%83%D1%81" title="Рудолф Клаузијус – Serbian" lang="sr" hreflang="sr" data-title="Рудолф Клаузијус" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Rudolf_Clausius" title="Rudolf Clausius – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Rudolf Clausius" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Finnish" lang="fi" hreflang="fi" data-title="Rudolf Clausius" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Swedish" lang="sv" hreflang="sv" data-title="Rudolf Clausius" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B0%E0%AF%81%E0%AE%9F%E0%AE%BE%E0%AE%B2%E0%AF%8D%E0%AE%AA%E0%AF%8D_%E0%AE%95%E0%AE%BF%E0%AE%B3%E0%AE%BE%E0%AE%9A%E0%AE%BF%E0%AE%AF%E0%AE%9A%E0%AF%81" title="ருடால்ப் கிளாசியசு – Tamil" lang="ta" hreflang="ta" data-title="ருடால்ப் கிளாசியசு" 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%A3%E0%B8%B9%E0%B8%94%E0%B9%87%E0%B8%AD%E0%B8%A5%E0%B9%8C%E0%B8%9F_%E0%B9%80%E0%B8%84%E0%B8%A5%E0%B8%B2%E0%B8%8B%E0%B8%B5%E0%B8%AD%E0%B8%B8%E0%B8%AA" title="รูด็อล์ฟ เคลาซีอุส – Thai" lang="th" hreflang="th" data-title="รูด็อล์ฟ เคลาซีอุส" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Turkish" lang="tr" hreflang="tr" data-title="Rudolf Clausius" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D1%83%D0%B4%D0%BE%D0%BB%D1%8C%D1%84_%D0%9A%D0%BB%D0%B0%D1%83%D0%B7%D1%96%D1%83%D1%81" title="Рудольф Клаузіус – Ukrainian" lang="uk" hreflang="uk" data-title="Рудольф Клаузіус" data-language-autonym="Українська" data-language-local-name="Ukrainian" 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%B1%DA%88%D9%88%D9%84%D9%81_%DA%A9%D9%84%D8%A7%D8%B3%D8%A6%DB%8C%D8%B3" title="رڈولف کلاسئیس – Urdu" lang="ur" hreflang="ur" data-title="رڈولف کلاسئیس" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Vietnamese" lang="vi" hreflang="vi" data-title="Rudolf Clausius" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Waray" lang="war" hreflang="war" data-title="Rudolf Clausius" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%B2%81%E9%81%93%E5%A4%AB%C2%B7%E5%85%8B%E5%8A%B3%E4%BF%AE%E6%96%AF" title="鲁道夫·克劳修斯 – Wu" lang="wuu" hreflang="wuu" data-title="鲁道夫·克劳修斯" 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-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Rudolf_Clausius" title="Rudolf Clausius – Samogitian" lang="sgs" hreflang="sgs" data-title="Rudolf Clausius" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%AD%AF%E9%81%93%E5%A4%AB%C2%B7%E5%85%8B%E5%8B%9E%E4%BF%AE%E6%96%AF" title="魯道夫·克勞修斯 – Chinese" lang="zh" hreflang="zh" data-title="魯道夫·克勞修斯" data-language-autonym="中文" data-language-local-name="Chinese" 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/Q30693#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</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="Namespaces"> <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/Rudolf_Clausius" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Rudolf_Clausius" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</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="Change language variant" > <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">English</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="Views"> <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/Rudolf_Clausius"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Tools" > <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">Tools</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">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </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/Rudolf_Clausius"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Rudolf_Clausius" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Rudolf_Clausius" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&oldid=1259907066" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Rudolf_Clausius&id=1259907066&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRudolf_Clausius"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRudolf_Clausius"><span>Download QR code</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"> Print/export </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=Special:DownloadAsPdf&page=Rudolf_Clausius&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Rudolf_Clausius&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</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"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Rudolf_Clausius" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://en.wikiquote.org/wiki/Rudolf_Clausius" hreflang="en"><span>Wikiquote</span></a></li><li class="wb-otherproject-link wb-otherproject-wikisource mw-list-item"><a href="https://en.wikisource.org/wiki/Author:Rudolf_Julius_Emanuel_Clausius" hreflang="en"><span>Wikisource</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q30693" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <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">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</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">From Wikipedia, the free encyclopedia</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="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">German physicist and mathematician (1822–1888)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Clausius" redirects here. For the lunar crater, see <a href="/wiki/Clausius_(crater)" title="Clausius (crater)">Clausius (crater)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Rudolf Clausius</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Rudolf_Clausius_01.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/220px-Rudolf_Clausius_01.jpg" decoding="async" width="220" height="337" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/330px-Rudolf_Clausius_01.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Rudolf_Clausius_01.jpg/440px-Rudolf_Clausius_01.jpg 2x" data-file-width="1335" data-file-height="2048" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Rudolf Julius Emanuel Clausius</div><br /><span style="display:none">(<span class="bday">1822-01-02</span>)</span>2 January 1822<br /><div style="display:inline" class="birthplace"><a href="/wiki/Koszalin" title="Koszalin">Köslin</a>, <a href="/wiki/Province_of_Pomerania_(1815%E2%80%931945)" title="Province of Pomerania (1815–1945)">Province of Pomerania</a>, <a href="/wiki/Kingdom_of_Prussia" title="Kingdom of Prussia">Prussia</a><br /><span style="font-size:85%;">(present-day Koszalin, Poland)</span></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">24 August 1888<span style="display:none">(1888-08-24)</span> (aged 66)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Bonn" title="Bonn">Bonn</a>, <a href="/wiki/Rhine_Province" title="Rhine Province">Rhine Province</a>, Prussia, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/Germans" title="Germans">German</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li><li><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First law of thermodynamics</a></li><li><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second law of thermodynamics</a></li><li>Originator of the concept of <a href="/wiki/Entropy" title="Entropy">entropy</a></li><li><a href="/wiki/Entropy_production" title="Entropy production">Entropy production</a></li><li><a href="/wiki/Disgregation" title="Disgregation">Disgregation</a></li><li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li><li><a href="/wiki/Kinetic_theory_of_gases" title="Kinetic theory of gases">Kinetic theory of gases</a></li><li><a href="/wiki/Virial_theorem" title="Virial theorem">Virial theorem</a></li><li><a href="/wiki/Real_gas#Clausius_model" title="Real gas">Clausius model</a></li><li><a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li><li><a href="/wiki/Clausius%E2%80%93Mossotti_relation" title="Clausius–Mossotti relation">Clausius–Mossotti relation</a></li><li><a href="/wiki/Clausius%E2%80%93Clapeyron_relation" title="Clausius–Clapeyron relation">Clausius–Clapeyron relation</a></li><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem inequality</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Poncelet_Prize" title="Poncelet Prize">Poncelet Prize</a> (1882)</li><li><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> (1879)</li><li><a href="/wiki/List_of_fellows_of_the_Royal_Society_A,_B,_C" title="List of fellows of the Royal Society A, B, C">ForMemRS</a> (1868)</li></ul></div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Physics" title="Physics">Physics</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><span class="infobox-signature skin-invert" typeof="mw:File"><a href="/wiki/File:Rudolf_Clausius_signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rudolf_Clausius_signature.svg/150px-Rudolf_Clausius_signature.svg.png" decoding="async" width="150" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rudolf_Clausius_signature.svg/225px-Rudolf_Clausius_signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rudolf_Clausius_signature.svg/300px-Rudolf_Clausius_signature.svg.png 2x" data-file-width="729" data-file-height="250" /></a></span></td></tr></tbody></table> <p><b>Rudolf Julius Emanuel Clausius</b> (<style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">German pronunciation:</span> <span class="IPA nowrap" lang="de-Latn-fonipa"><a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[ˈʁuːdɔlf<span class="wrap"> </span>ˈklaʊzi̯ʊs]</a></span>;<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> 2 January 1822 – 24 August 1888) was a German <a href="/wiki/Physicist" title="Physicist">physicist</a> and <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and is considered one of the central founding fathers of the science of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> By his restatement of <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a>'s principle known as the <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a>, he gave the <a href="/wiki/Theory_of_heat" class="mw-redirect" title="Theory of heat">theory of heat</a> a truer and sounder basis. His most important paper, "On the Moving Force of Heat",<sup id="cite_ref-Theory_of_Heat_4-0" class="reference"><a href="#cite_note-Theory_of_Heat-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> published in 1850, first stated the basic ideas of the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>. In 1865 he introduced the concept of <a href="/wiki/Entropy" title="Entropy">entropy</a>. In 1870 he introduced the <a href="/wiki/Virial_theorem" title="Virial theorem">virial theorem</a>, which applied to <a href="/wiki/Heat" title="Heat">heat</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=1" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Clausius was born in <a href="/wiki/Koszalin" title="Koszalin">Köslin</a> (now <a href="/wiki/Koszalin" title="Koszalin">Koszalin</a>, Poland) in the <a href="/wiki/Province_of_Pomerania_(1815%E2%80%931945)" title="Province of Pomerania (1815–1945)">Province of Pomerania</a> in <a href="/wiki/Prussia" title="Prussia">Prussia</a>. His father was a <a href="/wiki/Protestant" class="mw-redirect" title="Protestant">Protestant</a> pastor and school inspector,<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> and Rudolf studied in the school of his father. In 1838, he went to the <a href="/wiki/Gymnasium_(school)" title="Gymnasium (school)">Gymnasium</a> in <a href="/wiki/Szczecin" title="Szczecin">Stettin</a>. Clausius graduated from the <a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a> in 1844 where he had studied mathematics and physics since 1840 with, among others, <a href="/wiki/Heinrich_Gustav_Magnus" title="Heinrich Gustav Magnus">Gustav Magnus</a>, <a href="/wiki/Peter_Gustav_Lejeune_Dirichlet" title="Peter Gustav Lejeune Dirichlet">Peter Gustav Lejeune Dirichlet</a>, and <a href="/wiki/Jakob_Steiner" title="Jakob Steiner">Jakob Steiner</a>. He also studied history with <a href="/wiki/Leopold_von_Ranke" title="Leopold von Ranke">Leopold von Ranke</a>. During 1848, he got his doctorate from the <a href="/wiki/University_of_Halle" class="mw-redirect" title="University of Halle">University of Halle</a> on optical effects in Earth's atmosphere. In 1850 he became professor of physics at the <a href="/wiki/TU_Berlin" class="mw-redirect" title="TU Berlin">Royal Artillery and Engineering School in Berlin</a> and Privatdozent at the Berlin University. In 1855 he became professor at the <a href="/wiki/ETH_Z%C3%BCrich" class="mw-redirect" title="ETH Zürich">ETH Zürich</a>, the Swiss Federal Institute of Technology in <a href="/wiki/Z%C3%BCrich" class="mw-redirect" title="Zürich">Zürich</a>, where he stayed until 1867. During that year, he moved to <a href="/wiki/University_of_W%C3%BCrzburg" title="University of Würzburg">Würzburg</a> and two years later, in 1869 to <a href="/wiki/University_of_Bonn" title="University of Bonn">Bonn</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In 1870 Clausius organized an ambulance corps in the <a href="/wiki/Franco-Prussian_War" title="Franco-Prussian War">Franco-Prussian War</a>. He was wounded in battle, leaving him with a lasting disability. He was awarded the <a href="/wiki/Iron_Cross" title="Iron Cross">Iron Cross</a> for his services. </p><p>His wife, Adelheid Rimpau died in 1875, leaving him to raise their six children. In 1886, he married Sophie Sack, and then had another child. Two years later, on 24 August 1888, he died in <a href="/wiki/Bonn" title="Bonn">Bonn</a>, Germany.<sup id="cite_ref-Cropper2004_8-0" class="reference"><a href="#cite_note-Cropper2004-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=2" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Clausius's PhD thesis concerning the refraction of light proposed that we see a blue sky during the day, and various shades of red at sunrise and sunset (among other phenomena) due to reflection and refraction of light. Later, <a href="/wiki/Lord_Rayleigh" class="mw-redirect" title="Lord Rayleigh">Lord Rayleigh</a> would show that it was in fact due to the scattering of light. </p><p>His most famous paper, <i>Ueber die bewegende Kraft der Wärme</i> ("On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom")<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> was published in 1850, and dealt with the mechanical theory of heat. In this paper, he showed there was a contradiction between <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a>'s principle and the concept of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>. Clausius restated the two <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a> to overcome this contradiction. This paper made him famous among scientists. (The <a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">third law</a> was developed by <a href="/wiki/Walther_Nernst" title="Walther Nernst">Walther Nernst</a>, during the years 1906–1912). </p><p>Clausius's most famous statement of the second law of thermodynamics was published in German in 1854,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and in English in 1856.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p> Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.</p></blockquote> <p>During 1857, Clausius contributed to the field of <a href="/wiki/Kinetic_theory_of_gases" title="Kinetic theory of gases">kinetic theory</a> after refining <a href="/wiki/August_Kr%C3%B6nig" title="August Krönig">August Krönig</a>'s very simple gas-kinetic model to include translational, rotational and vibrational molecular motions. In this same work he introduced the concept of '<a href="/wiki/Mean_free_path" title="Mean free path">Mean free path</a>' of a particle.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p> Clausius deduced the <a href="/wiki/Clausius%E2%80%93Clapeyron_relation" title="Clausius–Clapeyron relation">Clausius–Clapeyron relation</a> from thermodynamics. This relation, which is a way of characterizing the <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> between two states of matter such as <a href="/wiki/Solid" title="Solid">solid</a> and <a href="/wiki/Liquid" title="Liquid">liquid</a>, had originally been developed in 1834 by <a href="/wiki/%C3%89mile_Clapeyron" title="Émile Clapeyron">Émile Clapeyron</a>.</p><ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clausius-1-1.jpg" class="mw-file-description" title="1864 edition of Clausius' Abhandlungen über die mechanische Wärmetheorie, volume I"><img alt="1864 edition of Clausius' Abhandlungen über die mechanische Wärmetheorie, volume I" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clausius-1-1.jpg/76px-Clausius-1-1.jpg" decoding="async" width="76" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clausius-1-1.jpg/114px-Clausius-1-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clausius-1-1.jpg/151px-Clausius-1-1.jpg 2x" data-file-width="3324" data-file-height="5260" /></a></span></div> <div class="gallerytext">1864 edition of Clausius' <i>Abhandlungen über die mechanische Wärmetheorie</i>, volume I</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clausius-1-2.jpg" class="mw-file-description" title="Title page of an 1864 edition of Clausius' Abhandlungen über die mechanische Wärmetheorie, volume I"><img alt="Title page of an 1864 edition of Clausius' Abhandlungen über die mechanische Wärmetheorie, volume I" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Clausius-1-2.jpg/78px-Clausius-1-2.jpg" decoding="async" width="78" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Clausius-1-2.jpg/117px-Clausius-1-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Clausius-1-2.jpg/156px-Clausius-1-2.jpg 2x" data-file-width="2994" data-file-height="4593" /></a></span></div> <div class="gallerytext">Title page of an 1864 edition of Clausius' <i>Abhandlungen über die mechanische Wärmetheorie</i>, volume I</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clausius-2-1.jpg" class="mw-file-description" title="1879 English translation of Clausius' The Mechanical Theory of Heat"><img alt="1879 English translation of Clausius' The Mechanical Theory of Heat" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Clausius-2-1.jpg/71px-Clausius-2-1.jpg" decoding="async" width="71" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Clausius-2-1.jpg/107px-Clausius-2-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Clausius-2-1.jpg/142px-Clausius-2-1.jpg 2x" data-file-width="2214" data-file-height="3732" /></a></span></div> <div class="gallerytext">1879 English translation of Clausius' <i>The Mechanical Theory of Heat</i></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clausius-2-2.jpg" class="mw-file-description" title="Title page of an 1879 English translation of Clausius' The Mechanical Theory of Heat"><img alt="Title page of an 1879 English translation of Clausius' The Mechanical Theory of Heat" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Clausius-2-2.jpg/87px-Clausius-2-2.jpg" decoding="async" width="87" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Clausius-2-2.jpg/130px-Clausius-2-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Clausius-2-2.jpg/173px-Clausius-2-2.jpg 2x" data-file-width="2872" data-file-height="3973" /></a></span></div> <div class="gallerytext">Title page of an 1879 English translation of Clausius' <i>The Mechanical Theory of Heat</i></div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Entropy">Entropy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=3" title="Edit section: Entropy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_entropy" title="History of entropy">History of entropy</a></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/History_of_thermodynamics#Rudolf_Clausius" title="History of thermodynamics">History of thermodynamics § Rudolf Clausius</a></div><p> In 1865, Clausius gave the first mathematical version of the concept of <a href="/wiki/Entropy" title="Entropy">entropy</a>, and also gave it its name.<sup id="cite_ref-Cropper2004_8-1" class="reference"><a href="#cite_note-Cropper2004-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Clausius chose the word because the meaning (from <a href="/wiki/Ancient_Greek" title="Ancient Greek">Greek</a> ἐν <i>en</i> "in" and τροπή <i>tropē</i> "transformation") is "<i>content transformative</i>" or "<i>transformation content</i>" ("<i>Verwandlungsinhalt</i>").<sup id="cite_ref-Theory_of_Heat_4-1" class="reference"><a href="#cite_note-Theory_of_Heat-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Cooper_16-0" class="reference"><a href="#cite_note-Cooper-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, accordingly, to call S the entropy of a body, after the Greek word 'transformation'. I have designedly coined the word entropy to be similar to 'energy', for these two quantities are so analogous in their physical significance, that an analogy of denomination seemed to me helpful.</p><div class="templatequotecite">— <cite>Rudolf Clausius, Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie</cite></div></blockquote><p>He used the now abandoned unit 'Clausius' (symbol: <b>Cl</b>) for entropy.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><dl><dd>1 Clausius (Cl) = 1 <a href="/wiki/Calorie" title="Calorie">calorie</a>/<a href="/wiki/Degree_Celsius" class="mw-redirect" title="Degree Celsius">degree Celsius</a> (cal/°C) = 4.1868 <a href="/wiki/Joule" title="Joule">joules</a> per <a href="/wiki/Kelvin" title="Kelvin">kelvin</a> (J/K)</dd></dl> <p>The landmark 1865 paper in which he introduced the concept of entropy ends with the following summary of the first and second laws of thermodynamics:<sup id="cite_ref-Theory_of_Heat_4-2" class="reference"><a href="#cite_note-Theory_of_Heat-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The energy of the universe is constant.<br /> The entropy of the universe tends to a maximum.</p></blockquote> <p><a href="/wiki/Leon_Cooper" title="Leon Cooper">Leon Cooper</a><sup id="cite_ref-Cooper_16-1" class="reference"><a href="#cite_note-Cooper-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> added that in this way he succeeded in coining a word that meant the same thing to everybody: nothing. </p> <div class="mw-heading mw-heading2"><h2 id="Tributes">Tributes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=4" title="Edit section: Tributes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Prawa_termodynamiki_clausiusa_pk.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Prawa_termodynamiki_clausiusa_pk.jpg/220px-Prawa_termodynamiki_clausiusa_pk.jpg" decoding="async" width="220" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Prawa_termodynamiki_clausiusa_pk.jpg/330px-Prawa_termodynamiki_clausiusa_pk.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Prawa_termodynamiki_clausiusa_pk.jpg/440px-Prawa_termodynamiki_clausiusa_pk.jpg 2x" data-file-width="1581" data-file-height="1323" /></a><figcaption>Memorial stone in front of <a href="/wiki/Koszalin_University_of_Technology" title="Koszalin University of Technology">Koszalin University of Technology</a>, with the laws of thermodynamics as formulated by Clausius</figcaption></figure> <ul><li>Honorary Membership of the <a href="/wiki/Institution_of_Engineers_and_Shipbuilders_in_Scotland" class="mw-redirect" title="Institution of Engineers and Shipbuilders in Scotland">Institution of Engineers and Shipbuilders in Scotland</a> in 1859.<a rel="nofollow" class="external text" href="http://www.iesis.org/honorary-fellows.html">IESIS Institution of Engineers and Shipbuilders in Scotland</a></li> <li><a href="/wiki/Iron_Cross" title="Iron Cross">Iron Cross</a> of 1870</li> <li>Fellow of the <a href="/wiki/Royal_Society_of_London" class="mw-redirect" title="Royal Society of London">Royal Society of London</a> in 1868 and received its <a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> in 1879.</li> <li>Member of the <a href="/wiki/Royal_Swedish_Academy_of_Sciences" title="Royal Swedish Academy of Sciences">Royal Swedish Academy of Sciences</a> in 1878.</li> <li><a href="/wiki/Huygens" title="Huygens">Huygens</a> Medal in 1870.</li> <li>Foreign Member of the <a href="/wiki/Accademia_Nazionale_dei_Lincei" class="mw-redirect" title="Accademia Nazionale dei Lincei">Accademia Nazionale dei Lincei</a> in Rome in 1880</li> <li>Member of the <a href="/wiki/German_Academy_of_Sciences_Leopoldina" class="mw-redirect" title="German Academy of Sciences Leopoldina">German Academy of Sciences Leopoldina</a> in 1880</li> <li><a href="/wiki/Poncelet_Prize" title="Poncelet Prize">Poncelet Prize</a> in 1883.</li> <li>Honorary doctorate from the <a href="/wiki/University_of_W%C3%BCrzburg" title="University of Würzburg">University of Würzburg</a> in 1882.</li> <li>Foreign Member of the <a href="/wiki/Royal_Netherlands_Academy_of_Arts_and_Sciences" title="Royal Netherlands Academy of Arts and Sciences">Royal Netherlands Academy of Arts and Sciences</a> in 1886.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Pour_le_M%C3%A9rite_for_Arts_and_Sciences" class="mw-redirect" title="Pour le Mérite for Arts and Sciences">Pour le Mérite for Arts and Sciences</a> in 1888</li> <li>The lunar crater <a href="/wiki/Clausius_(crater)" title="Clausius (crater)">Clausius</a> named in his honor.</li> <li>A memorial in his home town of <a href="/wiki/Koszalin" title="Koszalin">Koszalin</a> in 2009</li></ul> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=5" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFClausius1867" class="citation book cs1">Clausius, R. (1867). <a rel="nofollow" class="external text" href="https://archive.org/details/mechanicaltheor04claugoog"><i>The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies</i></a>. London: John van Voorst. <q>editions:PwR_Sbkwa8IC.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mechanical+Theory+of+Heat+%E2%80%93+with+its+Applications+to+the+Steam+Engine+and+to+Physical+Properties+of+Bodies&rft.place=London&rft.pub=John+van+Voorst&rft.date=1867&rft.aulast=Clausius&rft.aufirst=R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmechanicaltheor04claugoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span> English translations of nine papers.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6830494"><i>Abhandlungen über die Anwendung der mechanischen Wärmetheorie auf die elektrischen Erscheinungen, nebst einer Einleitung in die mathematische Behandlung der Elektricität</i></a> (in French). Vol. 2. Bruxelles: Société belge d'éditions. 1898.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Abhandlungen+%C3%BCber+die+Anwendung+der+mechanischen+W%C3%A4rmetheorie+auf+die+elektrischen+Erscheinungen%2C+nebst+einer+Einleitung+in+die+mathematische+Behandlung+der+Elektricit%C3%A4t&rft.place=Bruxelles&rft.pub=Soci%C3%A9t%C3%A9+belge+d%27%C3%A9ditions&rft.date=1898&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6830494&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hans_Peter_J%C3%B8rgen_Julius_Thomsen" title="Hans Peter Jørgen Julius Thomsen">Hans Peter Jørgen Julius Thomsen</a>, one of the founders of the <a href="/wiki/Thermochemistry" title="Thermochemistry">thermochemistry</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDudenredaktionKleinerKnöbl2015" class="citation book cs1 cs1-prop-foreign-lang-source">Dudenredaktion; Kleiner, Stefan; Knöbl, Ralf (2015) [First published 1962]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=T6vWCgAAQBAJ"><i>Das Aussprachewörterbuch</i></a> [<i>The Pronunciation Dictionary</i>] (in German) (7th ed.). Berlin: Dudenverlag. pp. 280, 744. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-411-04067-4" title="Special:BookSources/978-3-411-04067-4"><bdi>978-3-411-04067-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Das+Aussprachew%C3%B6rterbuch&rft.place=Berlin&rft.pages=280%2C+744&rft.edition=7th&rft.pub=Dudenverlag&rft.date=2015&rft.isbn=978-3-411-04067-4&rft.au=Dudenredaktion&rft.au=Kleiner%2C+Stefan&rft.au=Kn%C3%B6bl%2C+Ralf&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DT6vWCgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrechStockHirschfeldAnders2009" class="citation book cs1 cs1-prop-foreign-lang-source">Krech, Eva-Maria; Stock, Eberhard; Hirschfeld, Ursula; Anders, Lutz Christian (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E-1tr_oVkW4C&q=deutsches+ausspracheworterbuch"><i>Deutsches Aussprachewörterbuch</i></a> [<i>German Pronunciation Dictionary</i>] (in German). Berlin: Walter de Gruyter. pp. 416, 884. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-11-018202-6" title="Special:BookSources/978-3-11-018202-6"><bdi>978-3-11-018202-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Deutsches+Aussprachew%C3%B6rterbuch&rft.place=Berlin&rft.pages=416%2C+884&rft.pub=Walter+de+Gruyter&rft.date=2009&rft.isbn=978-3-11-018202-6&rft.aulast=Krech&rft.aufirst=Eva-Maria&rft.au=Stock%2C+Eberhard&rft.au=Hirschfeld%2C+Ursula&rft.au=Anders%2C+Lutz+Christian&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE-1tr_oVkW4C%26q%3Ddeutsches%2Bausspracheworterbuch&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCardwell,_D.S.L.1971" class="citation cs2">Cardwell, D.S.L. (1971), <i>From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age</i>, London: Heinemann, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-435-54150-7" title="Special:BookSources/978-0-435-54150-7"><bdi>978-0-435-54150-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Watt+to+Clausius%3A+The+Rise+of+Thermodynamics+in+the+Early+Industrial+Age&rft.place=London&rft.pub=Heinemann&rft.date=1971&rft.isbn=978-0-435-54150-7&rft.au=Cardwell%2C+D.S.L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-Theory_of_Heat-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Theory_of_Heat_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Theory_of_Heat_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Theory_of_Heat_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1867" class="citation book cs1">Clausius, R. (1867). <a rel="nofollow" class="external text" href="https://archive.org/details/mechanicaltheor04claugoog"><i>The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies</i></a>. London: John van Voorst<span class="reference-accessdate">. Retrieved <span class="nowrap">19 June</span> 2012</span>. <q>editions:PwR_Sbkwa8IC.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mechanical+Theory+of+Heat+%E2%80%93+with+its+Applications+to+the+Steam+Engine+and+to+Physical+Properties+of+Bodies&rft.place=London&rft.pub=John+van+Voorst&rft.date=1867&rft.aulast=Clausius&rft.aufirst=R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmechanicaltheor04claugoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span> Contains English translations of many of his other works.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1870" class="citation journal cs1">Clausius, RJE (1870). "On a Mechanical Theorem Applicable to Heat". <i>Philosophical Magazine</i>. 4th Series. <b>40</b>: 122–127.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=On+a+Mechanical+Theorem+Applicable+to+Heat&rft.volume=40&rft.pages=122-127&rft.date=1870&rft.aulast=Clausius&rft.aufirst=RJE&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Emilio Segrè (2012). <i>From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries</i>. Courier Dover Publications. p. 228</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://www.physik.uzh.ch/de/institut/emeriti/RudolfClausius.html">"Rudolf Clausius, Prof. Dr"</a>. <i>physik.uzh.ch</i> (in German). Universität Zürich<span class="reference-accessdate">. Retrieved <span class="nowrap">18 June</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=physik.uzh.ch&rft.atitle=Rudolf+Clausius%2C+Prof.+Dr.&rft_id=https%3A%2F%2Fwww.physik.uzh.ch%2Fde%2Finstitut%2Femeriti%2FRudolfClausius.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-Cropper2004-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cropper2004_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cropper2004_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCropper2004" class="citation book cs1">Cropper, William H. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UqbxZpELwHYC&pg=PA93">"The Road to Entropy Rudolf Clausius"</a>. <i>Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking</i>. Oxford University Press. pp. 93–105. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-517324-6" title="Special:BookSources/978-0-19-517324-6"><bdi>978-0-19-517324-6</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">25 March</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Road+to+Entropy+Rudolf+Clausius&rft.btitle=Great+Physicists%3A+The+Life+and+Times+of+Leading+Physicists+from+Galileo+to+Hawking&rft.pages=93-105&rft.pub=Oxford+University+Press&rft.date=2004&rft.isbn=978-0-19-517324-6&rft.aulast=Cropper&rft.aufirst=William+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUqbxZpELwHYC%26pg%3DPA93&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1850" class="citation journal cs1">Clausius, R. (1850). <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15164w/f518.table">"Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen"</a>. <i>Annalen der Physik</i>. <b>79</b> (4): 368–397, 500–524. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1850AnP...155..500C">1850AnP...155..500C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18501550403">10.1002/andp.18501550403</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fuc1.%24b242250">2027/uc1.$b242250</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Ueber+die+bewegende+Kraft+der+W%C3%A4rme+und+die+Gesetze%2C+welche+sich+daraus+f%C3%BCr+die+W%C3%A4rmelehre+selbst+ableiten+lassen&rft.volume=79&rft.issue=4&rft.pages=368-397%2C+500-524&rft.date=1850&rft_id=info%3Ahdl%2F2027%2Fuc1.%24b242250&rft_id=info%3Adoi%2F10.1002%2Fandp.18501550403&rft_id=info%3Abibcode%2F1850AnP...155..500C&rft.aulast=Clausius&rft.aufirst=R.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k15164w%2Ff518.table&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span>. See English Translation: <a rel="nofollow" class="external text" href="https://archive.org/details/londonedinburghd02lond">On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom</a>. Phil. Mag. (1851), series 4, <b>2</b>, 1–21, 102–119. Also available on <a rel="nofollow" class="external text" href="https://books.google.com/books?id=JbwdWbbM1KgC&pg=RA1-PA1">Google Books</a>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1854" class="citation journal cs1">Clausius, R. (1854). <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15178k/f499.image">"Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheoriein"</a>. <i><a href="/wiki/Annalen_der_Physik" title="Annalen der Physik">Annalen der Physik und Chemie</a></i>. <b>93</b> (12): 481–506. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1854AnP...169..481C">1854AnP...169..481C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18541691202">10.1002/andp.18541691202</a><span class="reference-accessdate">. Retrieved <span class="nowrap">25 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik+und+Chemie&rft.atitle=Ueber+eine+ver%C3%A4nderte+Form+des+zweiten+Hauptsatzes+der+mechanischen+W%C3%A4rmetheoriein&rft.volume=93&rft.issue=12&rft.pages=481-506&rft.date=1854&rft_id=info%3Adoi%2F10.1002%2Fandp.18541691202&rft_id=info%3Abibcode%2F1854AnP...169..481C&rft.aulast=Clausius&rft.aufirst=R.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k15178k%2Ff499.image&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius1856" class="citation journal cs1">Clausius, R. (August 1856). <a rel="nofollow" class="external text" href="https://archive.org/stream/londonedinburghd12lond#page/80/mode/2up">"On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat"</a>. <i><a href="/wiki/Philosophical_Magazine" title="Philosophical Magazine">Phil. Mag.</a></i> 4. <b>12</b> (77): 81–98. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786445608642141">10.1080/14786445608642141</a><span class="reference-accessdate">. Retrieved <span class="nowrap">25 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phil.+Mag.&rft.atitle=On+a+Modified+Form+of+the+Second+Fundamental+Theorem+in+the+Mechanical+Theory+of+Heat&rft.volume=12&rft.issue=77&rft.pages=81-98&rft.date=1856-08&rft_id=info%3Adoi%2F10.1080%2F14786445608642141&rft.aulast=Clausius&rft.aufirst=R.&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Flondonedinburghd12lond%23page%2F80%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius,_R.1857" class="citation cs2">Clausius, R. (1857), <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15185v/f371.table">"Über die Art der Bewegung, die wir Wärme nennen"</a>, <i>Annalen der Physik</i>, <b>100</b> (3): 353–379, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1857AnP...176..353C">1857AnP...176..353C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18571760302">10.1002/andp.18571760302</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+die+Art+der+Bewegung%2C+die+wir+W%C3%A4rme+nennen&rft.volume=100&rft.issue=3&rft.pages=353-379&rft.date=1857&rft_id=info%3Adoi%2F10.1002%2Fandp.18571760302&rft_id=info%3Abibcode%2F1857AnP...176..353C&rft.au=Clausius%2C+R.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k15185v%2Ff371.table&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius,_R.1862" class="citation cs2">Clausius, R. (1862), <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15200x/f13.table">"Ueber die Wärmeleitung gasförmiger Körper"</a>, <i>Annalen der Physik</i>, <b>115</b> (1): 1–57, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1862AnP...191....1C">1862AnP...191....1C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18621910102">10.1002/andp.18621910102</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Ueber+die+W%C3%A4rmeleitung+gasf%C3%B6rmiger+K%C3%B6rper&rft.volume=115&rft.issue=1&rft.pages=1-57&rft.date=1862&rft_id=info%3Adoi%2F10.1002%2Fandp.18621910102&rft_id=info%3Abibcode%2F1862AnP...191....1C&rft.au=Clausius%2C+R.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k15200x%2Ff13.table&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Clausius, R. (1864), <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/notice?N=FRBNF37278069"><i>Abhandlungen über die Mechanische Wärmetheorie</i></a>. Electronic manuscript from the <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">Bibliothèque nationale de France</a>.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius,_R.1865" class="citation cs2">Clausius, R. (1865), <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k152107/f369.table">"Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie"</a>, <i>Annalen der Physik</i>, <b>125</b> (7): 353–400, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1865AnP...201..353C">1865AnP...201..353C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18652010702">10.1002/andp.18652010702</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Ueber+verschiedene+f%C3%BCr+die+Anwendung+bequeme+Formen+der+Hauptgleichungen+der+mechanischen+W%C3%A4rmetheorie&rft.volume=125&rft.issue=7&rft.pages=353-400&rft.date=1865&rft_id=info%3Adoi%2F10.1002%2Fandp.18652010702&rft_id=info%3Abibcode%2F1865AnP...201..353C&rft.au=Clausius%2C+R.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k152107%2Ff369.table&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-Cooper-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cooper_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cooper_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCooper1968" class="citation book cs1">Cooper, Leon N. (1968). <i>An Introduction to the Meaning and Structure of Physics</i>. Harper. p. 331.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+the+Meaning+and+Structure+of+Physics&rft.pages=331&rft.pub=Harper&rft.date=1968&rft.aulast=Cooper&rft.aufirst=Leon+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuangHungChen2010" class="citation journal cs1">Huang, Mei-Ling; Hung, Yung-Hsiang; Chen, Wei-Yu (2010-10-01). "Neural Network Classifier with Entropy Based Feature Selection on Breast Cancer Diagnosis". <i>Journal of Medical Systems</i>. <b>34</b> (5): 865–873. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10916-009-9301-x">10.1007/s10916-009-9301-x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1573-689X">1573-689X</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20703622">20703622</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6658005">6658005</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Medical+Systems&rft.atitle=Neural+Network+Classifier+with+Entropy+Based+Feature+Selection+on+Breast+Cancer+Diagnosis&rft.volume=34&rft.issue=5&rft.pages=865-873&rft.date=2010-10-01&rft.issn=1573-689X&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6658005%23id-name%3DS2CID&rft_id=info%3Apmid%2F20703622&rft_id=info%3Adoi%2F10.1007%2Fs10916-009-9301-x&rft.aulast=Huang&rft.aufirst=Mei-Ling&rft.au=Hung%2C+Yung-Hsiang&rft.au=Chen%2C+Wei-Yu&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00004619">"R.J.E. Clausius (1822–1888)"</a>. Royal Netherlands Academy of Arts and Sciences<span class="reference-accessdate">. Retrieved <span class="nowrap">21 July</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=R.J.E.+Clausius+%281822%E2%80%931888%29&rft.pub=Royal+Netherlands+Academy+of+Arts+and+Sciences&rft_id=http%3A%2F%2Fwww.dwc.knaw.nl%2Fbiografie%2Fpmknaw%2F%3Fpagetype%3DauthorDetail%26aId%3DPE00004619&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rudolf_Clausius&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Rudolf_Clausius" class="extiw" title="q:Special:Search/Rudolf Clausius">Rudolf Clausius</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Rudolf_Clausius" class="extiw" title="commons:Category:Rudolf Clausius">Rudolf Clausius</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.math.umd.edu/~lvrmr/History/Revival.html">Revival of Kinetic Theory by Clausius</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Clausius.html">"Rudolf Clausius"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Rudolf+Clausius&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FClausius.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Clausius, Rudolf Julius Emmanuel"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Clausius,_Rudolf_Julius_Emmanuel">"Clausius, Rudolf Julius Emmanuel" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i> (11th ed.). Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Clausius%2C+Rudolf+Julius+Emmanuel&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARudolf+Clausius" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/author/35970">Works by Rudolf Clausius</a> at <a href="/wiki/Project_Gutenberg" title="Project Gutenberg">Project Gutenberg</a></li> <li><a rel="nofollow" class="external text" href="https://archive.org/search.php?query=%28%28subject%3A%22Clausius%2C%20Rudolf%22%20OR%20subject%3A%22Rudolf%20Clausius%22%20OR%20creator%3A%22Clausius%2C%20Rudolf%22%20OR%20creator%3A%22Rudolf%20Clausius%22%20OR%20creator%3A%22Clausius%2C%20R%2E%22%20OR%20title%3A%22Rudolf%20Clausius%22%20OR%20description%3A%22Clausius%2C%20Rudolf%22%20OR%20description%3A%22Rudolf%20Clausius%22%29%20OR%20%28%221822-1888%22%20AND%20Clausius%29%29%20AND%20%28-mediatype:software%29">Works by or about Rudolf Clausius</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.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:r1236075235">.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}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Copley_Medallists_(1851–1900)" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Copley_Medallists_1851%E2%80%931900" title="Template:Copley Medallists 1851–1900"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Copley_Medallists_1851%E2%80%931900" title="Template talk:Copley Medallists 1851–1900"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Copley_Medallists_1851%E2%80%931900" title="Special:EditPage/Template:Copley Medallists 1851–1900"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Copley_Medallists_(1851–1900)" style="font-size:114%;margin:0 4em"><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medallists</a> (1851–1900)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Richard_Owen" title="Richard Owen">Richard Owen</a> (1851)</span></li> <li><span class="nowrap"><a href="/wiki/Alexander_von_Humboldt" title="Alexander von Humboldt">Alexander von Humboldt</a> (1852)</span></li> <li><span class="nowrap"><a href="/wiki/Heinrich_Wilhelm_Dove" title="Heinrich Wilhelm Dove">Heinrich Wilhelm Dove</a> (1853)</span></li> <li><span class="nowrap"><a href="/wiki/Johannes_Peter_M%C3%BCller" title="Johannes Peter Müller">Johannes Peter Müller</a> (1854)</span></li> <li><span class="nowrap"><a href="/wiki/L%C3%A9on_Foucault" title="Léon Foucault">Léon Foucault</a> (1855)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Milne-Edwards" title="Henri Milne-Edwards">Henri Milne-Edwards</a> (1856)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Eug%C3%A8ne_Chevreul" title="Michel Eugène Chevreul">Michel Eugène Chevreul</a> (1857)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Lyell" title="Charles Lyell">Charles Lyell</a> (1858)</span></li> <li><span class="nowrap"><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Wilhelm Eduard Weber</a> (1859)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a> (1860)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Agassiz" title="Louis Agassiz">Louis Agassiz</a> (1861)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Thomas Graham</a> (1862)</span></li> <li><span class="nowrap"><a href="/wiki/Adam_Sedgwick" title="Adam Sedgwick">Adam Sedgwick</a> (1863)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Darwin" title="Charles Darwin">Charles Darwin</a> (1864)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Chasles" title="Michel Chasles">Michel Chasles</a> (1865)</span></li> <li><span class="nowrap"><a href="/wiki/Julius_Pl%C3%BCcker" title="Julius Plücker">Julius Plücker</a> (1866)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Ernst_von_Baer" title="Karl Ernst von Baer">Karl Ernst von Baer</a> (1867)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Wheatstone" title="Charles Wheatstone">Charles Wheatstone</a> (1868)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Victor_Regnault" title="Henri Victor Regnault">Henri Victor Regnault</a> (1869)</span></li> <li><span class="nowrap"><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> (1870)</span></li> <li><span class="nowrap"><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">Julius Robert von Mayer</a> (1871)</span></li> <li><span class="nowrap"><a href="/wiki/Friedrich_W%C3%B6hler" title="Friedrich Wöhler">Friedrich Wöhler</a> (1872)</span></li> <li><span class="nowrap"><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> (1873)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Pasteur" title="Louis Pasteur">Louis Pasteur</a> (1874)</span></li> <li><span class="nowrap"><a href="/wiki/August_Wilhelm_von_Hofmann" title="August Wilhelm von Hofmann">August Wilhelm von Hofmann</a> (1875)</span></li> <li><span class="nowrap"><a href="/wiki/Claude_Bernard" title="Claude Bernard">Claude Bernard</a> (1876)</span></li> <li><span class="nowrap"><a href="/wiki/James_Dwight_Dana" title="James Dwight Dana">James Dwight Dana</a> (1877)</span></li> <li><span class="nowrap"><a href="/wiki/Jean-Baptiste_Boussingault" title="Jean-Baptiste Boussingault">Jean-Baptiste Boussingault</a> (1878)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">Rudolf Clausius</a> (1879)</span></li> <li><span class="nowrap"><a href="/wiki/James_Joseph_Sylvester" title="James Joseph Sylvester">James Joseph Sylvester</a> (1880)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Adolphe_Wurtz" title="Charles Adolphe Wurtz">Charles Adolphe Wurtz</a> (1881)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Cayley" title="Arthur Cayley">Arthur Cayley</a> (1882)</span></li> <li><span class="nowrap"><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">William Thomson</a> (1883)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Ludwig" title="Carl Ludwig">Carl Ludwig</a> (1884)</span></li> <li><span class="nowrap"><a href="/wiki/August_Kekul%C3%A9" title="August Kekulé">Friedrich August Kekulé von Stradonitz</a> (1885)</span></li> <li><span class="nowrap"><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Franz Ernst Neumann</a> (1886)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_Dalton_Hooker" title="Joseph Dalton Hooker">Joseph Dalton Hooker</a> (1887)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Henry_Huxley" title="Thomas Henry Huxley">Thomas Henry Huxley</a> (1888)</span></li> <li><span class="nowrap"><a href="/wiki/George_Salmon" title="George Salmon">George Salmon</a> (1889)</span></li> <li><span class="nowrap"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a> (1890)</span></li> <li><span class="nowrap"><a href="/wiki/Stanislao_Cannizzaro" title="Stanislao Cannizzaro">Stanislao Cannizzaro</a> (1891)</span></li> <li><span class="nowrap"><a href="/wiki/Rudolf_Virchow" title="Rudolf Virchow">Rudolf Virchow</a> (1892)</span></li> <li><span class="nowrap"><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">George Gabriel Stokes</a> (1893)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Frankland" title="Edward Frankland">Edward Frankland</a> (1894)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> (1895)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Gegenbaur" title="Carl Gegenbaur">Carl Gegenbaur</a> (1896)</span></li> <li><span class="nowrap"><a href="/wiki/Albert_von_K%C3%B6lliker" title="Albert von Kölliker">Albert von Kölliker</a> (1897)</span></li> <li><span class="nowrap"><a href="/wiki/William_Huggins" title="William Huggins">William Huggins</a> (1898)</span></li> <li><span class="nowrap"><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">John William Strutt</a> (1899)</span></li> <li><span class="nowrap"><a href="/wiki/Marcellin_Berthelot" title="Marcellin Berthelot">Marcellin Berthelot</a> (1900)</span></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="image" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/17px-Newton%27s_reflecting_telescope.jpg" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/26px-Newton%27s_reflecting_telescope.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/34px-Newton%27s_reflecting_telescope.jpg 2x" data-file-width="1140" data-file-height="1276" /></span></span> </span><a href="/wiki/Portal:History_of_science" title="Portal:History of science">History of science</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li><li class="portal-bar-item"><span class="nowrap"><span class="mw-image-border" typeof="mw:File"><span><img alt="flag" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Flag_of_Scotland.svg/21px-Flag_of_Scotland.svg.png" decoding="async" width="21" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Flag_of_Scotland.svg/32px-Flag_of_Scotland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Flag_of_Scotland.svg/42px-Flag_of_Scotland.svg.png 2x" data-file-width="1000" data-file-height="600" /></span></span> </span><a href="/wiki/Portal:Scotland" title="Portal:Scotland">Scotland</a></li><li class="portal-bar-item"><span class="nowrap"><span class="mw-image-border" typeof="mw:File"><span><img alt="flag" src="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Flag_of_Germany.svg/21px-Flag_of_Germany.svg.png" decoding="async" width="21" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/ba/Flag_of_Germany.svg/32px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/ba/Flag_of_Germany.svg/42px-Flag_of_Germany.svg.png 2x" data-file-width="1000" data-file-height="600" /></span></span> </span><a href="/wiki/Portal:Germany" title="Portal:Germany">Germany</a></li></ul></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q30693#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q30693#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q30693#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000108880610">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/36968732">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/141156/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJyxpgDYyXYyD9gWD7hj4q">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/116540486">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n85800208">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12221741z">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12221741z">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/001148302">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Clausius, Rudolf"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/REAV096503">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35230052">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ola2002158980&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1460021">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p074276026">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=156975">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/c9prt9zw4jh781c">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810693866805606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007259590705171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058511806206706">Catalonia</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA03079368?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=124908">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:clausius.r">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/49845">MathSciNet</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.leopoldina.org/mitgliederverzeichnis/mitglieder/member/Member/show/rudolf-clausius/">Leopoldina</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/874094">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd116540486.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/116540486">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/030892872">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://hls-dhs-dss.ch/fr/articles/041690">Historical Dictionary of Switzerland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6j40wtp">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Rudolf_Clausius&oldid=1259907066">https://en.wikipedia.org/w/index.php?title=Rudolf_Clausius&oldid=1259907066</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:1822_births" title="Category:1822 births">1822 births</a></li><li><a href="/wiki/Category:1888_deaths" title="Category:1888 deaths">1888 deaths</a></li><li><a href="/wiki/Category:People_from_Koszalin" title="Category:People from Koszalin">People from Koszalin</a></li><li><a href="/wiki/Category:Academic_staff_of_ETH_Zurich" title="Category:Academic staff of ETH Zurich">Academic staff of ETH Zurich</a></li><li><a href="/wiki/Category:Thermodynamicists" title="Category:Thermodynamicists">Thermodynamicists</a></li><li><a href="/wiki/Category:German_military_personnel_of_the_Franco-Prussian_War" title="Category:German military personnel of the Franco-Prussian War">German military personnel of the Franco-Prussian War</a></li><li><a href="/wiki/Category:19th-century_German_physicists" title="Category:19th-century German physicists">19th-century German physicists</a></li><li><a href="/wiki/Category:German_fluid_dynamicists" title="Category:German fluid dynamicists">German fluid dynamicists</a></li><li><a href="/wiki/Category:People_from_the_Province_of_Pomerania" title="Category:People from the Province of Pomerania">People from the Province of Pomerania</a></li><li><a href="/wiki/Category:Recipients_of_the_Iron_Cross_(1870)" title="Category:Recipients of the Iron Cross (1870)">Recipients of the Iron Cross (1870)</a></li><li><a href="/wiki/Category:Recipients_of_the_Copley_Medal" title="Category:Recipients of the Copley Medal">Recipients of the Copley Medal</a></li><li><a href="/wiki/Category:Recipients_of_the_Pour_le_M%C3%A9rite_(civil_class)" title="Category:Recipients of the Pour le Mérite (civil class)">Recipients of the Pour le Mérite (civil class)</a></li><li><a href="/wiki/Category:Humboldt_University_of_Berlin_alumni" title="Category:Humboldt University of Berlin alumni">Humboldt University of Berlin alumni</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_Bonn" title="Category:Academic staff of the University of Bonn">Academic staff of the University of Bonn</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_W%C3%BCrzburg" title="Category:Academic staff of the University of Würzburg">Academic staff of the University of Würzburg</a></li><li><a href="/wiki/Category:Foreign_members_of_the_Royal_Society" title="Category:Foreign members of the Royal Society">Foreign members of the Royal Society</a></li><li><a href="/wiki/Category:Foreign_associates_of_the_National_Academy_of_Sciences" title="Category:Foreign associates of the National Academy of Sciences">Foreign associates of the National Academy of Sciences</a></li><li><a href="/wiki/Category:Members_of_the_Royal_Netherlands_Academy_of_Arts_and_Sciences" title="Category:Members of the Royal Netherlands Academy of Arts and Sciences">Members of the Royal Netherlands Academy of Arts and Sciences</a></li><li><a href="/wiki/Category:Members_of_the_Royal_Swedish_Academy_of_Sciences" title="Category:Members of the Royal Swedish Academy of Sciences">Members of the Royal Swedish Academy of Sciences</a></li><li><a href="/wiki/Category:German_theoretical_physicists" title="Category:German theoretical physicists">German theoretical physicists</a></li><li><a href="/wiki/Category:Prussian_Army_personnel" title="Category:Prussian Army personnel">Prussian Army personnel</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_German-language_sources_(de)" title="Category:CS1 German-language sources (de)">CS1 German-language sources (de)</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Biography_with_signature" title="Category:Biography with signature">Biography with signature</a></li><li><a href="/wiki/Category:Articles_with_hCards" title="Category:Articles with hCards">Articles with hCards</a></li><li><a href="/wiki/Category:Pages_with_German_IPA" title="Category:Pages with German IPA">Pages with German IPA</a></li><li><a href="/wiki/Category:CS1_French-language_sources_(fr)" title="Category:CS1 French-language sources (fr)">CS1 French-language sources (fr)</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_a_citation_from_the_1911_Encyclopaedia_Britannica_with_Wikisource_reference" title="Category:Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference">Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference</a></li><li><a href="/wiki/Category:Articles_with_Project_Gutenberg_links" title="Category:Articles with Project Gutenberg links">Articles with Project Gutenberg links</a></li><li><a href="/wiki/Category:Articles_with_Internet_Archive_links" title="Category:Articles with Internet Archive links">Articles with Internet Archive links</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"> This page was last edited on 27 November 2024, at 19:12<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Rudolf_Clausius&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</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-6b8d669998-gmlpl","wgBackendResponseTime":146,"wgPageParseReport":{"limitreport":{"cputime":"0.790","walltime":"1.056","ppvisitednodes":{"value":4047,"limit":1000000},"postexpandincludesize":{"value":92546,"limit":2097152},"templateargumentsize":{"value":5468,"limit":2097152},"expansiondepth":{"value":14,"limit":100},"expensivefunctioncount":{"value":9,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":98163,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 973.597 1 -total"," 19.62% 191.064 1 Template:Infobox_scientist"," 14.01% 136.422 1 Template:Short_description"," 13.02% 126.727 1 Template:IPA"," 11.39% 110.929 7 Template:Cite_book"," 11.00% 107.139 1 Template:Reflist"," 9.58% 93.284 22 Template:Main_other"," 8.24% 80.244 1 Template:Copley_Medallists_1851–1900"," 8.20% 79.837 1 Template:SDcat"," 7.88% 76.703 1 Template:Navbox"]},"scribunto":{"limitreport-timeusage":{"value":"0.563","limit":"10.000"},"limitreport-memusage":{"value":26267066,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-57488d5c7d-4nwvr","timestamp":"20241128031736","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Rudolf Clausius","url":"https:\/\/en.wikipedia.org\/wiki\/Rudolf_Clausius","sameAs":"http:\/\/www.wikidata.org\/entity\/Q30693","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q30693","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-01-27T12:34:50Z","dateModified":"2024-11-27T19:12:38Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/d\/d4\/Rudolf_Clausius_01.jpg","headline":"German mathematical physicist and professor (1822-1888)"}</script> </body> </html>