CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-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-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Conservation of energy - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-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-sticky-header-enabled 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":"e2344412-9379-4260-9525-54c7aecfd881","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Conservation_of_energy","wgTitle":"Conservation of energy","wgCurRevisionId":1274281973,"wgRevisionId":1274281973,"wgArticleId":67088,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["All articles with dead external links","Articles with dead external links from March 2021","Articles with permanently dead external links","CS1 maint: DOI inactive as of November 2024","Articles with short description","Short description matches Wikidata","Wikipedia pending changes protected pages","Use dmy dates from October 2020","Pages using sidebar with the child parameter","Articles needing additional references from November 2015", "All articles needing additional references","Articles containing German-language text","Articles containing video clips","Conservation laws","Energy (physics)","Laws of thermodynamics"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Conservation_of_energy","wgRelevantArticleId":67088,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgStableRevisionId":1274281973,"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":50000,"wgEditSubmitButtonLabelPublish":true, "wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q11382","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.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.flaggedRevs.basic":"ready","mediawiki.codex.messagebox.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","ext.math.popup","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.flaggedRevs.advanced","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.growthExperiments.SuggestedEditSession"];</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.flaggedRevs.basic%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cmediawiki.codex.messagebox.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.15"> <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 name="viewport" content="width=1120"> <meta property="og:title" content="Conservation of energy - 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/Conservation_of_energy"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Conservation_of_energy&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/Conservation_of_energy"> <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-Conservation_of_energy rootpage-Conservation_of_energy 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" title="Main menu" > <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/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=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=Conservation+of+energy" 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=Conservation+of+energy" 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/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=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=Conservation+of+energy" 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=Conservation+of+energy" 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-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <button aria-controls="toc-History-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 History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Mechanical_equivalent_of_heat" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mechanical_equivalent_of_heat"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Mechanical equivalent of heat</span> </div> </a> <ul id="toc-Mechanical_equivalent_of_heat-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mass–energy_equivalence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mass–energy_equivalence"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Mass–energy equivalence</span> </div> </a> <ul id="toc-Mass–energy_equivalence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conservation_of_energy_in_beta_decay" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Conservation_of_energy_in_beta_decay"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Conservation of energy in beta decay</span> </div> </a> <ul id="toc-Conservation_of_energy_in_beta_decay-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-First_law_of_thermodynamics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#First_law_of_thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>First law of thermodynamics</span> </div> </a> <ul id="toc-First_law_of_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Noether's_theorem" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Noether's_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Noether's theorem</span> </div> </a> <ul id="toc-Noether's_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Special_relativity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Special_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Special relativity</span> </div> </a> <ul id="toc-Special_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-General_relativity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#General_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>General relativity</span> </div> </a> <ul id="toc-General_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Quantum theory</span> </div> </a> <ul id="toc-Quantum_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Status" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Status"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Status</span> </div> </a> <ul id="toc-Status-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">8</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">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Bibliography</span> </div> </a> <button aria-controls="toc-Bibliography-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 Bibliography subsection</span> </button> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-Modern_accounts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modern_accounts"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Modern accounts</span> </div> </a> <ul id="toc-Modern_accounts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History_of_ideas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#History_of_ideas"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>History of ideas</span> </div> </a> <ul id="toc-History_of_ideas-sublist" class="vector-toc-list"> </ul> </li> </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">11</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" title="Table of Contents" > <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">Conservation of energy</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 102 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-102" 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">102 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/Behoud_van_energie" title="Behoud van energie – Afrikaans" lang="af" hreflang="af" data-title="Behoud van energie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Energieerhaltungssatz" title="Energieerhaltungssatz – Alemannic" lang="gsw" hreflang="gsw" data-title="Energieerhaltungssatz" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D9%81%D8%B8_%D8%A7%D9%84%D8%B7%D8%A7%D9%82%D8%A9_(%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1)" title="حفظ الطاقة (فيزياء) – Arabic" lang="ar" hreflang="ar" data-title="حفظ الطاقة (فيزياء)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Conservaci%C3%B3n_d%27a_enerch%C3%ADa" title="Conservación d'a enerchía – Aragonese" lang="an" hreflang="an" data-title="Conservación d'a enerchía" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A7%B0_%E0%A6%B8%E0%A6%82%E0%A7%B0%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%A3%E0%A6%B6%E0%A7%80%E0%A6%B2%E0%A6%A4%E0%A6%BE" title="শক্তিৰ সংৰক্ষণশীলতা – Assamese" lang="as" hreflang="as" data-title="শক্তিৰ সংৰক্ষণশীলতা" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Caltenimientu_de_la_enerx%C3%ADa" title="Caltenimientu de la enerxía – Asturian" lang="ast" hreflang="ast" data-title="Caltenimientu de la enerxía" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Enerjinin_saxlanmas%C4%B1_qanunu" title="Enerjinin saxlanması qanunu – Azerbaijani" lang="az" hreflang="az" data-title="Enerjinin saxlanması qanunu" 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%A7%D9%86%D8%B1%DA%98%DB%8C%E2%80%8C%D9%86%DB%8C%D9%86_%D8%B3%D8%A7%D8%AE%D9%84%D8%A7%D9%86%D9%85%D8%A7%D8%B3%DB%8C_%D9%82%D8%A7%D9%86%D9%88%D9%86%D9%88" title="انرژی‌نین ساخلانماسی قانونو – South Azerbaijani" lang="azb" hreflang="azb" data-title="انرژی‌نین ساخلانماسی قانونو" 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%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%B0_%E0%A6%A8%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%AF%E0%A6%A4%E0%A6%BE" title="শক্তির নিত্যতা – Bangla" lang="bn" hreflang="bn" data-title="শক্তির নিত্যতা" 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/L%C3%AAng-li%C5%8Dng_si%C3%BA-h%C3%AAng_t%C4%93ng-lu%CC%8Dt" title="Lêng-liōng siú-hêng tēng-lu̍t – Minnan" lang="nan" hreflang="nan" data-title="Lêng-liōng siú-hêng tēng-lu̍t" 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-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D2%BB%D0%B0%D2%A1%D0%BB%D0%B0%D0%BD%D1%8B%D1%83_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD%D1%8B" title="Энергия һаҡланыу законы – Bashkir" lang="ba" hreflang="ba" data-title="Энергия һаҡланыу законы" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B7%D0%B0%D1%85%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%96" title="Закон захавання энергіі – Belarusian" lang="be" hreflang="be" data-title="Закон захавання энергіі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B7%D0%B0%D1%85%D0%B0%D0%B2%D0%B0%D0%BD%D1%8C%D0%BD%D1%8F_%D1%8D%D0%BD%D1%8D%D1%80%D0%B3%D1%96%D1%96" title="Закон захаваньня энэргіі – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Закон захаваньня энэргіі" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B7%D0%B0_%D0%B7%D0%B0%D0%BF%D0%B0%D0%B7%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D1%82%D0%B0" title="Закон за запазване на енергията – Bulgarian" lang="bg" hreflang="bg" data-title="Закон за запазване на енергията" 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/Zakon_o%C4%8Duvanja_energije" title="Zakon očuvanja energije – Bosnian" lang="bs" hreflang="bs" data-title="Zakon očuvanja energije" 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/Conservaci%C3%B3_de_l%27energia" title="Conservació de l'energia – Catalan" lang="ca" hreflang="ca" data-title="Conservació de l'energia" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8_%D1%81%D1%8B%D1%85%D0%BB%D0%B0%D0%BD%D0%BD%D0%B8%D0%BD_%D1%81%D0%B0%D0%BA%D0%BA%D1%83%D0%BD%C4%95" title="Энерги сыхланнин саккунĕ – Chuvash" lang="cv" hreflang="cv" data-title="Энерги сыхланнин саккунĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Z%C3%A1kon_zachov%C3%A1n%C3%AD_energie" title="Zákon zachování energie – Czech" lang="cs" hreflang="cs" data-title="Zákon zachování energie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cadwraeth_egni" title="Cadwraeth egni – Welsh" lang="cy" hreflang="cy" data-title="Cadwraeth egni" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Energibevarelse" title="Energibevarelse – Danish" lang="da" hreflang="da" data-title="Energibevarelse" 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/Energieerhaltungssatz" title="Energieerhaltungssatz – German" lang="de" hreflang="de" data-title="Energieerhaltungssatz" 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/Energia_j%C3%A4%C3%A4vuse_seadus" title="Energia jäävuse seadus – Estonian" lang="et" hreflang="et" data-title="Energia jäävuse seadus" 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%91%CF%81%CF%87%CE%AE_%CE%B4%CE%B9%CE%B1%CF%84%CE%AE%CF%81%CE%B7%CF%83%CE%B7%CF%82_%CF%84%CE%B7%CF%82_%CE%B5%CE%BD%CE%AD%CF%81%CE%B3%CE%B5%CE%B9%CE%B1%CF%82" title="Αρχή διατήρησης της ενέργειας – Greek" lang="el" hreflang="el" data-title="Αρχή διατήρησης της ενέργειας" 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/Conservaci%C3%B3n_de_la_energ%C3%ADa" title="Conservación de la energía – Spanish" lang="es" hreflang="es" data-title="Conservación de la energía" 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/Principo_de_konservado_de_energio" title="Principo de konservado de energio – Esperanto" lang="eo" hreflang="eo" data-title="Principo de konservado de energio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Energiaren_kontserbazioaren_printzipioa" title="Energiaren kontserbazioaren printzipioa – Basque" lang="eu" hreflang="eu" data-title="Energiaren kontserbazioaren printzipioa" 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/%D9%BE%D8%A7%DB%8C%D8%B3%D8%AA%DA%AF%DB%8C_%D8%A7%D9%86%D8%B1%DA%98%DB%8C" title="پایستگی انرژی – Persian" lang="fa" hreflang="fa" data-title="پایستگی انرژی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Conservation_of_energy" title="Conservation of energy – Fiji Hindi" lang="hif" hreflang="hif" data-title="Conservation of energy" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Conservation_de_l%27%C3%A9nergie" title="Conservation de l'énergie – French" lang="fr" hreflang="fr" data-title="Conservation de l'énergie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Dl%C3%AD_imchoime%C3%A1d_an_fhuinnimh" title="Dlí imchoimeád an fhuinnimh – Irish" lang="ga" hreflang="ga" data-title="Dlí imchoimeád an fhuinnimh" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Conservaci%C3%B3n_da_enerx%C3%ADa" title="Conservación da enerxía – Galician" lang="gl" hreflang="gl" data-title="Conservación da enerxía" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%90%EB%84%88%EC%A7%80_%EB%B3%B4%EC%A1%B4_%EB%B2%95%EC%B9%99" title="에너지 보존 법칙 – Korean" lang="ko" hreflang="ko" data-title="에너지 보존 법칙" 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/%D4%B7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1%D5%B5%D5%AB_%D5%BA%D5%A1%D5%B0%D5%BA%D5%A1%D5%B6%D5%B4%D5%A1%D5%B6_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Էներգիայի պահպանման օրենք – Armenian" lang="hy" hreflang="hy" data-title="Էներգիայի պահպանման օրենք" 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%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE_%E0%A4%B8%E0%A4%82%E0%A4%B0%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%A3_%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊर्जा संरक्षण का नियम – Hindi" lang="hi" hreflang="hi" data-title="ऊर्जा संरक्षण का नियम" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Zakon_o%C4%8Duvanja_energije" title="Zakon očuvanja energije – Croatian" lang="hr" hreflang="hr" data-title="Zakon očuvanja energije" 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/Kekekalan_energi" title="Kekekalan energi – Indonesian" lang="id" hreflang="id" data-title="Kekekalan energi" 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-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Conservation_de_energia" title="Conservation de energia – Interlingua" lang="ia" hreflang="ia" data-title="Conservation de energia" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Orkuvar%C3%B0veisla" title="Orkuvarðveisla – Icelandic" lang="is" hreflang="is" data-title="Orkuvarðveisla" 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/Legge_di_conservazione_dell%27energia" title="Legge di conservazione dell'energia – Italian" lang="it" hreflang="it" data-title="Legge di conservazione dell'energia" 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%97%D7%95%D7%A7_%D7%A9%D7%99%D7%9E%D7%95%D7%A8_%D7%94%D7%90%D7%A0%D7%A8%D7%92%D7%99%D7%94" title="חוק שימור האנרגיה – Hebrew" lang="he" hreflang="he" data-title="חוק שימור האנרגיה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B6%E0%B2%95%E0%B3%8D%E0%B2%A4%E0%B2%BF%E0%B2%AF_%E0%B2%B8%E0%B2%82%E0%B2%B0%E0%B2%95%E0%B3%8D%E0%B2%B7%E0%B2%A3%E0%B3%86" title="ಶಕ್ತಿಯ ಸಂರಕ್ಷಣೆ – Kannada" lang="kn" hreflang="kn" data-title="ಶಕ್ತಿಯ ಸಂರಕ್ಷಣೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D1%81%D0%B0%D0%BA%D1%8A%D0%BB%D0%B0%D1%83%D0%BD%D1%83_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD%D1%83" title="Энергия сакълауну закону – Karachay-Balkar" lang="krc" hreflang="krc" data-title="Энергия сакълауну закону" data-language-autonym="Къарачай-малкъар" data-language-local-name="Karachay-Balkar" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9C%E1%83%94%E1%83%A0%E1%83%92%E1%83%98%E1%83%98%E1%83%A1_%E1%83%A8%E1%83%94%E1%83%9C%E1%83%90%E1%83%AE%E1%83%95%E1%83%98%E1%83%A1_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="ენერგიის შენახვის კანონი – Georgian" lang="ka" hreflang="ka" data-title="ენერგიის შენახვის კანონი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D0%BD%D1%8B%D2%A3_%D1%81%D0%B0%D2%9B%D1%82%D0%B0%D0%BB%D1%83_%D0%B7%D0%B0%D2%A3%D1%8B" title="Энергияның сақталу заңы – Kazakh" lang="kk" hreflang="kk" data-title="Энергияның сақталу заңы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Hifadhi_ya_nishati" title="Hifadhi ya nishati – Swahili" lang="sw" hreflang="sw" data-title="Hifadhi ya nishati" 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/Lwa_kons%C3%A8vasyon_en%C3%A8ji" title="Lwa konsèvasyon enèji – Haitian Creole" lang="ht" hreflang="ht" data-title="Lwa konsèvasyon enèji" 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-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D0%BD%D1%8B%D0%BD_%D1%81%D0%B0%D0%BA%D1%82%D0%B0%D0%BB%D1%83%D1%83_%D0%BC%D1%8B%D0%B9%D0%B7%D0%B0%D0%BC%D1%8B" title="Энергиянын сакталуу мыйзамы – Kyrgyz" lang="ky" hreflang="ky" data-title="Энергиянын сакталуу мыйзамы" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Conservatio_energiae" title="Conservatio energiae – Latin" lang="la" hreflang="la" data-title="Conservatio energiae" 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/Ener%C4%A3ijas_nez%C5%ABdam%C4%ABbas_likums" title="Enerģijas nezūdamības likums – Latvian" lang="lv" hreflang="lv" data-title="Enerģijas nezūdamības likums" 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/Energijos_tverm%C4%97s_d%C4%97snis" title="Energijos tvermės dėsnis – Lithuanian" lang="lt" hreflang="lt" data-title="Energijos tvermės dėsnis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Conservazzion_de_l%27energia" title="Conservazzion de l'energia – Lombard" lang="lmo" hreflang="lmo" data-title="Conservazzion de l'energia" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Energiamegmarad%C3%A1s" title="Energiamegmaradás – Hungarian" lang="hu" hreflang="hu" data-title="Energiamegmaradás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B7%D0%B0_%D0%B7%D0%B0%D1%87%D1%83%D0%B2%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%98%D0%B0%D1%82%D0%B0" title="Закон за зачувување на енергијата – Macedonian" lang="mk" hreflang="mk" data-title="Закон за зачувување на енергијата" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%8A%E0%B5%BC%E0%B4%9C%E0%B5%8D%E0%B4%9C_%E0%B4%B8%E0%B4%82%E2%80%8C%E0%B4%B0%E0%B4%95%E0%B5%8D%E0%B4%B7%E0%B4%A3_%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="ഊർജ്ജ സം‌രക്ഷണ നിയമം – Malayalam" lang="ml" hreflang="ml" data-title="ഊർജ്ജ സം‌രക്ഷണ നിയമം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%94%E1%83%9C%E1%83%94%E1%83%A0%E1%83%92%E1%83%98%E1%83%90%E1%83%A8_%E1%83%99%E1%83%9D%E1%83%9C%E1%83%A1%E1%83%94%E1%83%A0%E1%83%95%E1%83%90%E1%83%AA%E1%83%98%E1%83%90%E1%83%A8_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="ენერგიაშ კონსერვაციაშ კანონი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ენერგიაშ კონსერვაციაშ კანონი" 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%A8%D9%82%D8%A7%D8%A1_%D8%A7%D9%84%D8%B7%D8%A7%D9%82%D9%87" title="بقاء الطاقه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="بقاء الطاقه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Keabadian_tenaga" title="Keabadian tenaga – Malay" lang="ms" hreflang="ms" data-title="Keabadian tenaga" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8_%D1%85%D0%B0%D0%B4%D0%B3%D0%B0%D0%BB%D0%B0%D0%B3%D0%B4%D0%B0%D1%85_%D1%85%D1%83%D1%83%D0%BB%D1%8C" title="Энерги хадгалагдах хууль – Mongolian" lang="mn" hreflang="mn" data-title="Энерги хадгалагдах хууль" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%BD%E1%80%99%E1%80%BA%E1%80%B8%E1%80%A1%E1%80%84%E1%80%BA_%E1%80%90%E1%80%8A%E1%80%BA%E1%80%99%E1%80%BC%E1%80%B2%E1%80%99%E1%80%BE%E1%80%AF_%E1%80%94%E1%80%AD%E1%80%9A%E1%80%AC%E1%80%99" title="စွမ်းအင် တည်မြဲမှု နိယာမ – Burmese" lang="my" hreflang="my" data-title="စွမ်းအင် တည်မြဲမှု နိယာမ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_van_behoud_van_energie" title="Wet van behoud van energie – Dutch" lang="nl" hreflang="nl" data-title="Wet van behoud van energie" 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%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E4%BF%9D%E5%AD%98%E3%81%AE%E6%B3%95%E5%89%87" title="エネルギー保存の法則 – Japanese" lang="ja" hreflang="ja" data-title="エネルギー保存の法則" 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/Energiprinsippet" title="Energiprinsippet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Energiprinsippet" 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/Energiprinsippet" title="Energiprinsippet – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Energiprinsippet" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Conservacion_de_l%27energia" title="Conservacion de l'energia – Occitan" lang="oc" hreflang="oc" data-title="Conservacion de l'energia" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Gitaa%E2%80%99ummaa_Anniisaa" title="Gitaa’ummaa Anniisaa – Oromo" lang="om" hreflang="om" data-title="Gitaa’ummaa Anniisaa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Energiyaning_saqlanish_va_aylanish_qonuni" title="Energiyaning saqlanish va aylanish qonuni – Uzbek" lang="uz" hreflang="uz" data-title="Energiyaning saqlanish va aylanish qonuni" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%8A%E0%A8%B0%E0%A8%9C%E0%A8%BE_%E0%A8%A6%E0%A9%80_%E0%A8%B8%E0%A9%B0%E0%A8%AD%E0%A8%BE%E0%A8%B2" title="ਊਰਜਾ ਦੀ ਸੰਭਾਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਊਰਜਾ ਦੀ ਸੰਭਾਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D8%B1%D8%AC%DB%8C_%D8%A8%DA%86%D8%AA_%D8%AF%D8%A7_%D9%82%D9%86%D9%88%D9%86" title="انرجی بچت دا قنون – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انرجی بچت دا قنون" 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%AF_%D8%A7%D9%86%D8%B1%DA%98%DB%8D_%D9%BE%D8%A7%DB%8C%DA%9A%D8%AA" title="د انرژۍ پایښت – Pashto" lang="ps" hreflang="ps" data-title="د انرژۍ پایښت" 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/Prinsipi_%C3%ABd_conservassion_%C3%ABd_l%27energ%C3%ACa" title="Prinsipi ëd conservassion ëd l'energìa – Piedmontese" lang="pms" hreflang="pms" data-title="Prinsipi ëd conservassion ëd l'energìa" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Energieprinzip" title="Energieprinzip – Low German" lang="nds" hreflang="nds" data-title="Energieprinzip" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zasada_zachowania_energii" title="Zasada zachowania energii – Polish" lang="pl" hreflang="pl" data-title="Zasada zachowania energii" 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/Lei_da_conserva%C3%A7%C3%A3o_da_energia" title="Lei da conservação da energia – Portuguese" lang="pt" hreflang="pt" data-title="Lei da conservação da energia" 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/Legea_conserv%C4%83rii_energiei" title="Legea conservării energiei – Romanian" lang="ro" hreflang="ro" data-title="Legea conservării energiei" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B2%D1%81%D0%BE%D0%BA%D0%BE%D1%87%D1%96%D0%BD%D1%8F_%D0%B5%D0%BD%D0%B5%D1%80%D2%91%D1%96%D1%97" title="Закон всокочіня енерґії – Rusyn" lang="rue" hreflang="rue" data-title="Закон всокочіня енерґії" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D1%81%D0%BE%D1%85%D1%80%D0%B0%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D0%B8" title="Закон сохранения энергии – Russian" lang="ru" hreflang="ru" data-title="Закон сохранения энергии" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ligji_i_ruajtjes_s%C3%AB_energjis%C3%AB" title="Ligji i ruajtjes së energjisë – Albanian" lang="sq" hreflang="sq" data-title="Ligji i ruajtjes së energjisë" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%81%E0%B6%9A%E0%B7%8A%E0%B6%AD%E0%B7%92_%E0%B7%83%E0%B6%82%E0%B7%83%E0%B7%8A%E0%B6%AE%E0%B7%92%E0%B6%AD%E0%B7%92_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="ශක්ති සංස්ථිති නියමය – Sinhala" lang="si" hreflang="si" data-title="ශක්ති සංස්ථිති නියමය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Conservation_of_energy" title="Conservation of energy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Conservation of energy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Z%C3%A1kon_zachovania_energie" title="Zákon zachovania energie – Slovak" lang="sk" hreflang="sk" data-title="Zákon zachovania energie" 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/Ohranitev_energije" title="Ohranitev energije – Slovenian" lang="sl" hreflang="sl" data-title="Ohranitev energije" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DB%8C%D8%A7%D8%B3%D8%A7%DB%8C_%D9%BE%D8%A7%D8%B1%D8%A7%D8%B3%D8%AA%D9%86%DB%8C_%D9%88%D8%B2%DB%95" title="یاسای پاراستنی وزە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="یاسای پاراستنی وزە" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BE%D1%87%D1%83%D0%B2%D0%B0%D1%9A%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%98%D0%B5" title="Закон очувања енергије – Serbian" lang="sr" hreflang="sr" data-title="Закон очувања енергије" 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/Zakon_o%C4%8Duvanja_energije" title="Zakon očuvanja energije – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Zakon očuvanja energije" 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/Energian_s%C3%A4ilymislaki" title="Energian säilymislaki – Finnish" lang="fi" hreflang="fi" data-title="Energian säilymislaki" 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/Energiprincipen" title="Energiprincipen – Swedish" lang="sv" hreflang="sv" data-title="Energiprincipen" 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%86%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D_%E0%AE%95%E0%AE%BE%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="ஆற்றல் காப்பு – Tamil" lang="ta" hreflang="ta" data-title="ஆற்றல் காப்பு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D1%81%D0%B0%D0%BA%D0%BB%D0%B0%D0%BD%D1%83_%D0%BA%D0%B0%D0%BD%D1%83%D0%BD%D1%8B" title="Энергия саклану кануны – Tatar" lang="tt" hreflang="tt" data-title="Энергия саклану кануны" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B6%E0%B0%95%E0%B1%8D%E0%B0%A4%E0%B0%BF_%E0%B0%A8%E0%B0%BF%E0%B0%A4%E0%B1%8D%E0%B0%AF%E0%B0%A4%E0%B1%8D%E0%B0%B5_%E0%B0%A8%E0%B0%BF%E0%B0%AF%E0%B0%AE%E0%B0%82" title="శక్తి నిత్యత్వ నియమం – Telugu" lang="te" hreflang="te" data-title="శక్తి నిత్యత్వ నియమం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%8E%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%87%E0%B8%B2%E0%B8%99" title="กฎทรงพลังงาน – Thai" lang="th" hreflang="th" data-title="กฎทรงพลังงาน" 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/Enerjinin_korunumu" title="Enerjinin korunumu – Turkish" lang="tr" hreflang="tr" data-title="Enerjinin korunumu" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F%D0%BD%D1%8B%D2%A3_%D0%BA%D0%B0%D0%B4%D0%B0%D0%B3%D0%B0%D0%BB%D0%B0%D1%82%D1%82%D1%8B%D0%BD%D0%B0%D1%80%D1%8B%D0%BD%D1%8B%D2%A3_%D1%85%D0%BE%D0%BE%D0%B9%D0%BB%D1%83%D0%B7%D1%83" title="Энергияның кадагалаттынарының хоойлузу – Tuvinian" lang="tyv" hreflang="tyv" data-title="Энергияның кадагалаттынарының хоойлузу" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B7%D0%B1%D0%B5%D1%80%D0%B5%D0%B6%D0%B5%D0%BD%D0%BD%D1%8F_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%97" title="Закон збереження енергії – Ukrainian" lang="uk" hreflang="uk" data-title="Закон збереження енергії" 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/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%A8%D9%82%D8%A7%D8%A6%DB%92_%D8%AA%D9%88%D8%A7%D9%86%D8%A7%D8%A6%DB%8C" title="قانون بقائے توانائی – Urdu" lang="ur" hreflang="ur" data-title="قانون بقائے توانائی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Energijan_varadusen_k%C3%A4skuz" title="Energijan varadusen käskuz – Veps" lang="vep" hreflang="vep" data-title="Energijan varadusen käskuz" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%E1%BA%A3o_to%C3%A0n_n%C4%83ng_l%C6%B0%E1%BB%A3ng" title="Bảo toàn năng lượng – Vietnamese" lang="vi" hreflang="vi" data-title="Bảo toàn năng lượng" 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-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%83%BD%E9%87%8F%E5%AE%88%E6%81%86%E5%BE%8B" title="能量守恆律 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="能量守恆律" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Konserbasyon_han_enerhiya" title="Konserbasyon han enerhiya – Waray" lang="war" hreflang="war" data-title="Konserbasyon han enerhiya" 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/%E8%83%BD%E9%87%8F%E5%AE%88%E6%81%92%E5%AE%9A%E5%BE%8B" title="能量守恒定律 – Wu" lang="wuu" hreflang="wuu" data-title="能量守恒定律" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%90%D7%A0%D7%A1%D7%A2%D7%A8%D7%95%D7%95%D7%99%D7%A8%D7%95%D7%A0%D7%92_%D7%A4%D7%95%D7%9F_%D7%A2%D7%A0%D7%A2%D7%A8%D7%92%D7%99%D7%A2" title="קאנסערווירונג פון ענערגיע – Yiddish" lang="yi" hreflang="yi" data-title="קאנסערווירונג פון ענערגיע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%83%BD%E9%87%8F%E5%AE%88%E6%81%86%E5%AE%9A%E5%BE%8B" title="能量守恆定律 – Cantonese" lang="yue" hreflang="yue" data-title="能量守恆定律" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%83%BD%E9%87%8F%E5%AE%88%E6%81%92%E5%AE%9A%E5%BE%8B" title="能量守恒定律 – Chinese" lang="zh" hreflang="zh" data-title="能量守恒定律" 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/Q11382#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/Conservation_of_energy" 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:Conservation_of_energy" 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/Conservation_of_energy"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Conservation_of_energy&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=Conservation_of_energy&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/Conservation_of_energy"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Conservation_of_energy&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=Conservation_of_energy&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/Conservation_of_energy" 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/Conservation_of_energy" 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="//en.wikipedia.org/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=Conservation_of_energy&oldid=1274281973" 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=Conservation_of_energy&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=Conservation_of_energy&id=1274281973&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%2FConservation_of_energy"><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%2FConservation_of_energy"><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=Conservation_of_energy&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=Conservation_of_energy&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/Category:Conservation_of_energy" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiversity mw-list-item"><a href="https://en.wikiversity.org/wiki/Conservation_of_energy" hreflang="en"><span>Wikiversity</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/Q11382" 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 id="mw-indicator-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--stable"></span><b>Checked</b></indicator></div> <div id="mw-indicator-pp-autoreview" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedia:Protection_policy#pending" title="All edits by unregistered and new users are subject to review prior to becoming visible to unregistered users"><img alt="Page protected with pending changes" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b7/Pending-protection-shackle.svg/20px-Pending-protection-shackle.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b7/Pending-protection-shackle.svg/30px-Pending-protection-shackle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b7/Pending-protection-shackle.svg/40px-Pending-protection-shackle.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Page version status</h2><p class="cdx-dialog__header__subtitle">This is an accepted version of this page</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
							cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="Close" onclick="document.getElementById("mw-fr-revision-details").style.display = "none";" type="submit"><span class="cdx-icon cdx-icon--medium
							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">This is the <a href="/wiki/Wikipedia:Pending_changes" title="Wikipedia:Pending changes">latest accepted revision</a>, <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Special:Log&type=review&page=Conservation_of_energy">reviewed</a> on <i>6 February 2025</i>.</div></div><div tabindex="0"></div></div></div></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">Law of physics and chemistry</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">This article is about the law of conservation of energy in physics. For sustainable energy resources, see <a href="/wiki/Energy_conservation" title="Energy conservation">Energy conservation</a>.</div> <p class="mw-empty-elt"> </p> <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: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><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=-D{\frac {d\varphi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.874ex; height:5.509ex;" alt="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"></span><div class="sidebar-caption"><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Laws</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Conservations</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Mass</a></li> <li><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">Momentum</a></li> <li><a class="mw-selflink selflink">Energy</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Inequalities</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem (entropy)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Deformation_(physics)" title="Deformation (physics)">Deformation</a></li> <li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a></li> <li><a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">Strain</a> <ul><li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Finite strain</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain</a></li></ul></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li> <li><a href="/wiki/Bending" title="Bending">Bending</a></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">frictional</a></li></ul></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Fluid" title="Fluid">Fluids</a></th></tr><tr><td class="sidebar-content"> <div class="wraplinks"> <ul><li><a href="/wiki/Hydrostatics" title="Hydrostatics">Statics</a> <b>·</b> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Dynamics</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <b>·</b> <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Hagen%E2%80%93Poiseuille_equation" title="Hagen–Poiseuille equation">Poiseuille equation</a> <b>·</b> <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li>(<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> <b>·</b> <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>)</li></ul></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a> <b>·</b> <a href="/wiki/Mixing_(process_engineering)" title="Mixing (process engineering)">Mixing</a> <b>·</b> <a href="/wiki/Pressure" title="Pressure">Pressure</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Liquid" title="Liquid">Liquids</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Adhesion" title="Adhesion">Adhesion</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a></li> <li><a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">Cohesion (chemistry)</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Gas" title="Gas">Gases</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Fick%27s_law" class="mw-redirect" title="Fick's law">Fick's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></th></tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Rheology" title="Rheology">Rheology</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Adolf_Eugen_Fick" title="Adolf Eugen Fick">Fick</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Graham</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Walter_Noll" title="Walter Noll">Noll</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li> <li><a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">Truesdell</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><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:Continuum_mechanics" title="Template:Continuum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Continuum_mechanics" title="Template talk:Continuum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Continuum_mechanics" title="Special:EditPage/Template:Continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>law of conservation of energy</b> states that the total <a href="/wiki/Energy" title="Energy">energy</a> of an <a href="/wiki/Isolated_system" title="Isolated system">isolated system</a> remains constant; it is said to be <a href="/wiki/Conservation_law" title="Conservation law"><i>conserved</i></a> over time.<sup id="cite_ref-Feynman2Ch1S2_1-0" class="reference"><a href="#cite_note-Feynman2Ch1S2-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In the case of a <a href="/wiki/Closed_system#In_thermodynamics" title="Closed system">closed system</a>, the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, <a href="/wiki/Chemical_energy" title="Chemical energy">chemical energy</a> is <a href="/wiki/Energy_conversion" class="mw-redirect" title="Energy conversion">converted</a> to <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> when a stick of <a href="/wiki/Dynamite" title="Dynamite">dynamite</a> explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a> of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. </p><p>Classically, the conservation of energy was distinct from the <a href="/wiki/Conservation_of_mass" title="Conservation of mass">conservation of mass</a>. However, <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> shows that mass is related to energy and vice versa by <span class="mwe-math-element" data-qid="Q35875"><a href="/w/index.php?title=Special:MathWikibase&qid=Q35875" style="color:inherit;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f73dbd37a0cac34406ee89057fa1b36a1e6a18e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.976ex; height:2.676ex;" alt="{\displaystyle E=mc^{2}}"></a></span>, the equation representing <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a>, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that mass can itself be converted to energy, and vice versa. However, this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe <a href="/wiki/Grand_unification_epoch" title="Grand unification epoch">very shortly after the Big Bang</a> or when <a href="/wiki/Black_hole" title="Black hole">black holes</a> emit <a href="/wiki/Hawking_radiation" title="Hawking radiation">Hawking radiation</a>. </p><p>Given the <a href="/wiki/Stationary-action_principle" class="mw-redirect" title="Stationary-action principle">stationary-action principle</a>, the conservation of energy can be rigorously proven by <a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a> as a consequence of <a href="/wiki/Continuous_function" title="Continuous function">continuous</a> <a href="/wiki/Time_translation_symmetry" class="mw-redirect" title="Time translation symmetry">time translation symmetry</a>; that is, from the fact that the laws of physics do not change over time. </p><p>A consequence of the law of conservation of energy is that a <a href="/wiki/Perpetual_motion#Classification" title="Perpetual motion">perpetual motion machine of the first kind</a> cannot exist; that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings.<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> Depending on the definition of energy, the conservation of energy can arguably be violated by <a href="/wiki/General_relativity" title="General relativity">general relativity</a> on the cosmological scale.<sup id="cite_ref-Energy_Is_Not_Conserved_3-0" class="reference"><a href="#cite_note-Energy_Is_Not_Conserved-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, Noether's theorem is known to apply to the <a href="/wiki/Expectation_value_(quantum_mechanics)" title="Expectation value (quantum mechanics)">expected value</a>, making any consistent conservation violation provably impossible, but whether individual conservation-violating events could ever exist or be <a href="/wiki/Observable" title="Observable">observed</a> is subject to some debate.<sup id="cite_ref-quanta-mag_4-0" class="reference"><a href="#cite_note-quanta-mag-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Conservation_of_energy" title="Special:EditPage/Conservation of energy">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">November 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><a href="/wiki/Ancient_philosophy" title="Ancient philosophy">Ancient philosophers</a> as far back as <a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales of Miletus</a> <abbr title="circa">c.</abbr> 550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy" (for example, Thales thought it was water). <a href="/wiki/Empedocles" title="Empedocles">Empedocles</a> (490–430 BCE) wrote that in his universal system, composed of <a href="/wiki/Classical_element" title="Classical element">four roots</a> (earth, air, water, fire), "nothing comes to be or perishes";<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> instead, these elements suffer continual rearrangement. <a href="/wiki/Epicurus" title="Epicurus">Epicurus</a> (<abbr title="circa">c.</abbr> 350 BCE) on the other hand believed everything in the universe to be composed of indivisible units of matter—the ancient precursor to 'atoms'—and he too had some idea of the necessity of conservation, stating that "the sum total of things was always such as it is now, and such it will ever remain."<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In 1605, the Flemish scientist <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> was able to solve a number of problems in statics based on the principle that <a href="/wiki/Perpetual_motion" title="Perpetual motion">perpetual motion</a> was impossible. </p><p>In 1639, <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a> published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height to which a moving body ascends on a frictionless surface does not depend on the shape of the surface. </p><p>In 1669, <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> published a brief account on his laws of collision. Among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their <a href="/wiki/Linear_momentum" class="mw-redirect" title="Linear momentum">linear momenta</a> as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental.<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> In his <i><a href="/wiki/Horologium_Oscillatorium" title="Horologium Oscillatorium">Horologium Oscillatorium</a></i>, Huygens gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of perpetual motion. His study of the dynamics of pendulum motion was based on a single principle, known as <a href="/wiki/Evangelista_Torricelli" title="Evangelista Torricelli">Torricelli's Principle</a>: that the <a href="/wiki/Center_of_mass" title="Center of mass">center of gravity</a> of a heavy object, or collection of objects, cannot lift itself. Using this principle, Huygens was able to derive the formula for the <a href="/wiki/Center_of_percussion" title="Center of percussion">center of oscillation</a> by an "energy" method, without dealing with forces or torques.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Gottfried_Wilhelm_Leibniz.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Gottfried_Wilhelm_Leibniz.jpg/150px-Gottfried_Wilhelm_Leibniz.jpg" decoding="async" width="150" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Gottfried_Wilhelm_Leibniz.jpg/225px-Gottfried_Wilhelm_Leibniz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/3/3b/Gottfried_Wilhelm_Leibniz.jpg 2x" data-file-width="300" data-file-height="346" /></a><figcaption><a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Gottfried Leibniz</a></figcaption></figure> <p>Between 1676 and 1689, <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Gottfried Leibniz</a> first attempted a mathematical formulation of the kind of energy that is associated with <i>motion</i> (kinetic energy). Using Huygens's work on collision, Leibniz noticed that in many mechanical systems (of several <a href="/wiki/Mass" title="Mass">masses</a> <i>m<sub>i</sub></i>, each with <a href="/wiki/Velocity" title="Velocity">velocity</a> <i>v<sub>i</sub></i>), </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}m_{i}v_{i}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}m_{i}v_{i}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0369647e33f4ff129034584a5fa0a68e6bf7f6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.764ex; height:5.509ex;" alt="{\displaystyle \sum _{i}m_{i}v_{i}^{2}}"></span></dd></dl> <p>was conserved so long as the masses did not interact. He called this quantity the <i><a href="/wiki/Vis_viva" title="Vis viva">vis viva</a></i> or <i>living force</i> of the system. The principle represents an accurate statement of the approximate conservation of <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> in situations where there is no friction. Many <a href="/wiki/Physicist" title="Physicist">physicists</a> at that time, including <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>, held that the <a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a>, which holds even in systems with friction, as defined by the <a href="/wiki/Momentum" title="Momentum">momentum</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}m_{i}v_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}m_{i}v_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/182f362fc9dd93f773ee050bfe171d6870175abf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.509ex; height:5.509ex;" alt="{\displaystyle \sum _{i}m_{i}v_{i}}"></span></dd></dl> <p>was the conserved <i>vis viva</i>. It was later shown that both quantities are conserved simultaneously given the proper conditions, such as in an <a href="/wiki/Elastic_collision" title="Elastic collision">elastic collision</a>. </p><p>In 1687, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> published his <i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a></i>, which set out his <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">laws of motion</a>. It was organized around the concept of force and momentum. However, the researchers were quick to recognize that the principles set out in the book, while fine for point masses, were not sufficient to tackle the motions of rigid and fluid bodies. Some other principles were also required. </p><p>By the 1690s, Leibniz was arguing that conservation of <i>vis viva</i> and conservation of momentum undermined the then-popular philosophical doctrine of <a href="/wiki/Interactionist_dualism" class="mw-redirect" title="Interactionist dualism">interactionist dualism</a>. (During the 19th century, when conservation of energy was better understood, Leibniz's basic argument would gain widespread acceptance. Some modern scholars continue to champion specifically conservation-based attacks on dualism, while others subsume the argument into a more general argument about <a href="/wiki/Causal_closure" title="Causal closure">causal closure</a>.)<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> </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Daniel_Bernoulli_001.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Daniel_Bernoulli_001.jpg/150px-Daniel_Bernoulli_001.jpg" decoding="async" width="150" height="245" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Daniel_Bernoulli_001.jpg/225px-Daniel_Bernoulli_001.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Daniel_Bernoulli_001.jpg/300px-Daniel_Bernoulli_001.jpg 2x" data-file-width="613" data-file-height="1000" /></a><figcaption><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></figcaption></figure> <p>The law of conservation of vis viva was championed by the father and son duo, <a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann</a> and <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>. The former enunciated the principle of <a href="/wiki/Virtual_work" title="Virtual work">virtual work</a> as used in statics in its full generality in 1715, while the latter based his <i><a href="/wiki/Hydrodynamica" title="Hydrodynamica">Hydrodynamica</a></i>, published in 1738, on this single vis viva conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a>, which asserts the loss to be proportional to the change in hydrodynamic pressure. Daniel also formulated the notion of <a href="/wiki/Work_(physics)" title="Work (physics)">work</a> and efficiency for <a href="/wiki/Hydraulic" class="mw-redirect" title="Hydraulic">hydraulic</a> machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas. </p><p>This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the <a href="/wiki/D%27Alembert%27s_principle" title="D'Alembert's principle">D'Alembert's principle</a>, <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian</a>, and <a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian</a> formulations of mechanics. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Emilie_Chatelet_portrait_by_Latour.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Emilie_Chatelet_portrait_by_Latour.jpg/150px-Emilie_Chatelet_portrait_by_Latour.jpg" decoding="async" width="150" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Emilie_Chatelet_portrait_by_Latour.jpg/225px-Emilie_Chatelet_portrait_by_Latour.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Emilie_Chatelet_portrait_by_Latour.jpg/300px-Emilie_Chatelet_portrait_by_Latour.jpg 2x" data-file-width="866" data-file-height="1037" /></a><figcaption><a href="/wiki/Emilie_du_Chatelet" class="mw-redirect" title="Emilie du Chatelet">Emilie du Chatelet</a></figcaption></figure> <p><a href="/wiki/%C3%89milie_du_Ch%C3%A2telet" title="Émilie du Châtelet">Émilie du Châtelet</a> (1706–1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by <a href="/wiki/Willem_%27s_Gravesande" title="Willem 's Gravesande">Willem 's Gravesande</a> in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy—as indicated by the quantity of material displaced—was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height from which the balls were dropped, equal to the initial potential energy. Some earlier workers, including Newton and Voltaire, had believed that "energy" was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped. In classical physics, the correct formula is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{k}={\frac {1}{2}}mv^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{k}={\frac {1}{2}}mv^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83f03039a1f0b8aa7076737f5dccb36fb002995c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.123ex; height:5.176ex;" alt="{\displaystyle E_{k}={\frac {1}{2}}mv^{2}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7587849b44d775263271e89499f4327eeac5dc81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.804ex; height:2.509ex;" alt="{\displaystyle E_{k}}"></span> is the kinetic energy of an object, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> its mass and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> its <a href="/wiki/Speed" title="Speed">speed</a>. On this basis, du Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to consider it in different forms (kinetic, potential, heat, ...).<sup id="cite_ref-Hagengruber_10-0" class="reference"><a href="#cite_note-Hagengruber-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Arianrhod_11-0" class="reference"><a href="#cite_note-Arianrhod-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Engineer" title="Engineer">Engineers</a> such as <a href="/wiki/John_Smeaton" title="John Smeaton">John Smeaton</a>, <a href="/wiki/Peter_Ewart" title="Peter Ewart">Peter Ewart</a>, <a href="/w/index.php?title=Carl_Holtzmann&action=edit&redlink=1" class="new" title="Carl Holtzmann (page does not exist)">Carl Holtzmann</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Carl_Holtzmann" class="extiw" title="de:Carl Holtzmann">de</a>; <a href="https://ar.wikipedia.org/wiki/%D9%83%D8%A7%D8%B1%D9%84_%D9%87%D9%88%D9%84%D8%AA%D8%B2%D9%85%D8%A7%D9%86" class="extiw" title="ar:كارل هولتزمان">ar</a>]</span>, <a href="/wiki/Gustave-Adolphe_Hirn" title="Gustave-Adolphe Hirn">Gustave-Adolphe Hirn</a>, and <a href="/wiki/Marc_Seguin" title="Marc Seguin">Marc Seguin</a> recognized that conservation of momentum alone was not adequate for practical calculation and made use of Leibniz's principle. The principle was also championed by some <a href="/wiki/Chemist" title="Chemist">chemists</a> such as <a href="/wiki/William_Hyde_Wollaston" title="William Hyde Wollaston">William Hyde Wollaston</a>. Academics such as <a href="/wiki/John_Playfair" title="John Playfair">John Playfair</a> were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, but in the 18th and 19th centuries, the fate of the lost energy was still unknown. </p><p>Gradually it came to be suspected that the heat inevitably generated by motion under friction was another form of <i>vis viva</i>. In 1783, <a href="/wiki/Antoine_Lavoisier" title="Antoine Lavoisier">Antoine Lavoisier</a> and <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> reviewed the two competing theories of <i>vis viva</i> and <a href="/wiki/Caloric_theory" title="Caloric theory">caloric theory</a>.<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> <a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Count Rumford</a>'s 1798 observations of heat generation during the <a href="/wiki/Boring_(manufacturing)" title="Boring (manufacturing)">boring</a> of <a href="/wiki/Cannon" title="Cannon">cannons</a> added more weight to the view that mechanical motion could be converted into heat and (that it was important) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). <i>Vis viva</i> then started to be known as <i>energy</i>, after the term was first used in that sense by <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> in 1807. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Gaspard-Gustave_de_Coriolis.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Gaspard-Gustave_de_Coriolis.jpg/150px-Gaspard-Gustave_de_Coriolis.jpg" decoding="async" width="150" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Gaspard-Gustave_de_Coriolis.jpg/225px-Gaspard-Gustave_de_Coriolis.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Gaspard-Gustave_de_Coriolis.jpg/300px-Gaspard-Gustave_de_Coriolis.jpg 2x" data-file-width="396" data-file-height="465" /></a><figcaption><a href="/wiki/Gaspard-Gustave_Coriolis" class="mw-redirect" title="Gaspard-Gustave Coriolis">Gaspard-Gustave Coriolis</a></figcaption></figure> <p>The recalibration of <i>vis viva</i> to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fcae198c9fadd4eeffe75d891e4a05b6e5b95cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:11.15ex; height:6.343ex;" alt="{\displaystyle {\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}"></span></dd></dl> <p>which can be understood as converting kinetic energy to <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a>, was largely the result of <a href="/wiki/Gaspard-Gustave_Coriolis" class="mw-redirect" title="Gaspard-Gustave Coriolis">Gaspard-Gustave Coriolis</a> and <a href="/wiki/Jean-Victor_Poncelet" title="Jean-Victor Poncelet">Jean-Victor Poncelet</a> over the period 1819–1839. The former called the quantity <i>quantité de travail</i> (quantity of work) and the latter, <i>travail mécanique</i> (mechanical work), and both championed its use in engineering calculations. </p><p>In the paper <i>Über die Natur der Wärme</i> (German "On the Nature of Heat/Warmth"), published in the <span title="German-language text"><i lang="de"><a href="/wiki/Zeitschrift_f%C3%BCr_Physik" title="Zeitschrift für Physik">Zeitschrift für Physik</a></i></span> in 1837, <a href="/wiki/Karl_Friedrich_Mohr" title="Karl Friedrich Mohr">Karl Friedrich Mohr</a> gave one of the earliest general statements of the doctrine of the conservation of energy: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called <i>Kraft</i> [energy or work]. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others." </p> <div class="mw-heading mw-heading3"><h3 id="Mechanical_equivalent_of_heat">Mechanical equivalent of heat</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=2" title="Edit section: Mechanical equivalent of heat"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A key stage in the development of the modern conservation principle was the demonstration of the <i><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">mechanical equivalent of heat</a></i>. The <a href="/wiki/Caloric_theory" title="Caloric theory">caloric theory</a> maintained that heat could neither be created nor destroyed, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable. </p><p>In the middle of the eighteenth century, <a href="/wiki/Mikhail_Lomonosov" title="Mikhail Lomonosov">Mikhail Lomonosov</a>, a Russian scientist, postulated his corpusculo-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid. </p><p>In 1798, Count Rumford (<a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Benjamin Thompson</a>) performed measurements of the frictional heat generated in boring cannons and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt. </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:SS-joule.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/SS-joule.jpg/130px-SS-joule.jpg" decoding="async" width="130" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/SS-joule.jpg/195px-SS-joule.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/SS-joule.jpg/260px-SS-joule.jpg 2x" data-file-width="702" data-file-height="1059" /></a><figcaption><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a></figcaption></figure> <p>The mechanical <a href="/wiki/Equivalence_principle" title="Equivalence principle">equivalence principle</a> was first stated in its modern form by the German surgeon <a href="/wiki/Julius_Robert_von_Mayer" class="mw-redirect" title="Julius Robert von Mayer">Julius Robert von Mayer</a> in 1842.<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> Mayer reached his conclusion on a voyage to the <a href="/wiki/Dutch_East_Indies" title="Dutch East Indies">Dutch East Indies</a>, where he found that his patients' blood was a deeper red because they were consuming less <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, and therefore less energy, to maintain their body temperature in the hotter climate. He discovered that <a href="/wiki/Heat" title="Heat">heat</a> and <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">mechanical work</a> were both forms of energy, and in 1845, after improving his knowledge of physics, he published a monograph that stated a quantitative relationship between them.<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> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Joule%27s_Apparatus_(Harper%27s_Scan).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Joule%27s_Apparatus_%28Harper%27s_Scan%29.png/220px-Joule%27s_Apparatus_%28Harper%27s_Scan%29.png" decoding="async" width="220" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Joule%27s_Apparatus_%28Harper%27s_Scan%29.png/330px-Joule%27s_Apparatus_%28Harper%27s_Scan%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Joule%27s_Apparatus_%28Harper%27s_Scan%29.png/440px-Joule%27s_Apparatus_%28Harper%27s_Scan%29.png 2x" data-file-width="1684" data-file-height="1387" /></a><figcaption><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a>'s apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.</figcaption></figure> <p>Meanwhile, in 1843, <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> independently discovered the mechanical equivalent in a series of experiments. In one of them, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the <a href="/wiki/Gravitational_energy" title="Gravitational energy">gravitational potential energy</a> lost by the weight in descending was equal to the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> gained by the water through <a href="/wiki/Friction" title="Friction">friction</a> with the paddle. </p><p>Over the period 1840–1843, similar work was carried out by engineer <a href="/wiki/Ludwig_A._Colding" title="Ludwig A. Colding">Ludwig A. Colding</a>, although it was little known outside his native Denmark. </p><p>Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For the dispute between Joule and Mayer over priority, see <a href="/wiki/Mechanical_equivalent_of_heat:_Priority" class="mw-redirect" title="Mechanical equivalent of heat: Priority">Mechanical equivalent of heat: Priority</a>.</div> <p>In 1844, the Welsh scientist <a href="/wiki/William_Robert_Grove" title="William Robert Grove">William Robert Grove</a> postulated a relationship between mechanics, heat, <a href="/wiki/Light" title="Light">light</a>, <a href="/wiki/Electricity" title="Electricity">electricity</a>, and <a href="/wiki/Magnetism" title="Magnetism">magnetism</a> by treating them all as manifestations of a single "force" (<i>energy</i> in modern terms). In 1846, Grove published his theories in his book <i>The Correlation of Physical Forces</i>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In 1847, drawing on the earlier work of Joule, <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a>, and <a href="/wiki/%C3%89mile_Clapeyron" title="Émile Clapeyron">Émile Clapeyron</a>, <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> arrived at conclusions similar to Grove's and published his theories in his book <i>Über die Erhaltung der Kraft</i> (<i>On the Conservation of Force</i>, 1847).<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> The general modern acceptance of the principle stems from this publication. </p><p>In 1850, the Scottish mathematician <a href="/wiki/William_Rankine" title="William Rankine">William Rankine</a> first used the phrase <i>the law of the conservation of energy</i> for the principle.<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> </p><p>In 1877, <a href="/wiki/Peter_Guthrie_Tait" title="Peter Guthrie Tait">Peter Guthrie Tait</a> claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the <i><a href="/wiki/Philosophiae_Naturalis_Principia_Mathematica" class="mw-redirect" title="Philosophiae Naturalis Principia Mathematica">Philosophiae Naturalis Principia Mathematica</a></i>. This is now regarded as an example of <a href="/wiki/Whig_history" title="Whig history">Whig history</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mass–energy_equivalence"><span id="Mass.E2.80.93energy_equivalence"></span>Mass–energy equivalence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=3" title="Edit section: Mass–energy equivalence"><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/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Conservation_of_energy" title="Special:EditPage/Conservation of energy">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">November 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Matter is composed of atoms and what makes up atoms. Matter has <a href="/wiki/Rest_mass" class="mw-redirect" title="Rest mass"><i>intrinsic</i> or <i>rest</i> mass</a>. In the limited range of recognized experience of the nineteenth century, it was found that such rest mass is conserved. Einstein's 1905 theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> showed that rest mass corresponds to an equivalent amount of <i>rest energy</i>. This means that <i>rest mass</i> can be converted to or from equivalent amounts of (non-material) forms of energy, for example, kinetic energy, potential energy, and electromagnetic <a href="/wiki/Radiant_energy" title="Radiant energy">radiant energy</a>. When this happens, as recognized in twentieth-century experience, rest mass is not conserved, unlike the <a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity"><i>total</i> mass</a> or <i>total</i> energy. All forms of energy contribute to the total mass and total energy. </p><p>For example, an <a href="/wiki/Electron" title="Electron">electron</a> and a <a href="/wiki/Positron" title="Positron">positron</a> each have rest mass. They can perish together, converting their combined rest energy into <a href="/wiki/Photon" title="Photon">photons</a> which have electromagnetic radiant energy but no rest mass. If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total <i>mass</i> nor the total <i>energy</i> of the system will change. The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Likewise, non-material forms of energy can perish into matter, which has rest mass. </p><p>Thus, conservation of energy (<i>total</i>, including material or <i>rest</i> energy) and <a href="/wiki/Conservation_of_mass" title="Conservation of mass">conservation of mass</a> (<i>total</i>, not just <i>rest</i>) are one (equivalent) law. In the 18th century, these had appeared as two seemingly-distinct laws. </p> <div class="mw-heading mw-heading3"><h3 id="Conservation_of_energy_in_beta_decay">Conservation of energy in beta decay</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=4" title="Edit section: Conservation of energy in beta decay"><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/Beta_decay#Neutrinos" title="Beta decay">Beta decay § Neutrinos</a></div> <p>The discovery in 1911 that electrons emitted in <a href="/wiki/Beta_decay" title="Beta decay">beta decay</a> have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This problem was eventually resolved in 1933 by <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> who proposed the correct <a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">description of beta-decay</a> as the emission of both an electron and an <a href="/wiki/Antineutrino" class="mw-redirect" title="Antineutrino">antineutrino</a>, which carries away the apparently missing energy.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="First_law_of_thermodynamics">First law of thermodynamics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=5" title="Edit section: First law of thermodynamics"><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/First_law_of_thermodynamics" title="First law of thermodynamics">First law of thermodynamics</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/First_law_of_thermodynamics_(fluid_mechanics)" title="First law of thermodynamics (fluid mechanics)">First law of thermodynamics (fluid mechanics)</a></div> <p>For a <a href="/wiki/Closed_system#In_thermodynamics" title="Closed system">closed thermodynamic system</a>, the first law of thermodynamics may be stated as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=\mathrm {d} U+\delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q=\mathrm {d} U+\delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2b2ec583c3d49153ea73afaf917f6f4f542ce92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.385ex; height:2.676ex;" alt="{\displaystyle \delta Q=\mathrm {d} U+\delta W}"></span>, or equivalently, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=\delta Q-\delta W,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>δ</mi> <mi>W</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=\delta Q-\delta W,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60fada72885619f961416a97c87fdb93dc3e76fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.032ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} U=\delta Q-\delta W,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf715eece146c816847a8c5d56eae97798453d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.887ex; height:2.676ex;" alt="{\displaystyle \delta Q}"></span> is the quantity of <a href="/wiki/Energy" title="Energy">energy</a> added to the system by a <a href="/wiki/Heat" title="Heat">heating</a> process, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973e6b089758466f338610e76ab50fd4093efbc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.484ex; height:2.343ex;" alt="{\displaystyle \delta W}"></span> is the quantity of energy lost by the system due to <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a> done by the system on its surroundings, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d25429855f05fe5da1e4beadb321ed305633e4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.075ex; height:2.176ex;" alt="{\displaystyle \mathrm {d} U}"></span> is the change in the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of the system. </p><p>The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d25429855f05fe5da1e4beadb321ed305633e4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.075ex; height:2.176ex;" alt="{\displaystyle \mathrm {d} U}"></span> increment of internal energy (see <a href="/wiki/Inexact_differential" title="Inexact differential">Inexact differential</a>). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf715eece146c816847a8c5d56eae97798453d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.887ex; height:2.676ex;" alt="{\displaystyle \delta Q}"></span> means "that amount of energy added as a result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973e6b089758466f338610e76ab50fd4093efbc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.484ex; height:2.343ex;" alt="{\displaystyle \delta W}"></span> means "that amount of energy lost as a result of work". Thus one can state the amount of internal energy possessed by a thermodynamic system that one knows is presently in a given state, but one cannot tell, just from knowledge of the given present state, how much energy has in the past flowed into or out of the system as a result of its being heated or cooled, nor as a result of work being performed on or by the system. </p><p><a href="/wiki/Entropy_(classical_thermodynamics)" title="Entropy (classical thermodynamics)">Entropy</a> is a function of the state of a system which tells of limitations of the possibility of conversion of heat into work. </p><p>For a simple compressible system, the work performed by the system may be written: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W=P\,\mathrm {d} V,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>W</mi> <mo>=</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W=P\,\mathrm {d} V,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84e0adddc647be4f80ec6abc5d1b9b32757587a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.441ex; height:2.676ex;" alt="{\displaystyle \delta W=P\,\mathrm {d} V,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> is the <a href="/wiki/Pressure" title="Pressure">pressure</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21c3a0961325e164fddf3f56b30add5bce2f37f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle dV}"></span> is a small change in the <a href="/wiki/Volume" title="Volume">volume</a> of the system, each of which are system variables. In the fictive case in which the process is idealized and infinitely slow, so as to be called <i>quasi-static</i>, and regarded as reversible, the heat being transferred from a source with temperature infinitesimally above the system temperature, the heat energy may be written </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=T\,\mathrm {d} S,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q=T\,\mathrm {d} S,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/904a7133818cb02f4a50a0e1f2d45de2e5c7cc32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.447ex; height:2.676ex;" alt="{\displaystyle \delta Q=T\,\mathrm {d} S,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> is the <a href="/wiki/Temperature" title="Temperature">temperature</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72ba425d7d7a0f229457dea3c0be4a47ea303cc3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.792ex; height:2.176ex;" alt="{\displaystyle \mathrm {d} S}"></span> is a small change in the entropy of the system. Temperature and entropy are variables of the state of a system. </p><p>If an open system (in which mass may be exchanged with the environment) has several walls such that the mass transfer is through rigid walls separate from the heat and work transfers, then the first law may be written as<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=\delta Q-\delta W+\sum _{i}h_{i}\,dM_{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>δ</mi> <mi>W</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=\delta Q-\delta W+\sum _{i}h_{i}\,dM_{i},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1980b02ac1f480b867154fec65a29b9ba131da5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:29.41ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} U=\delta Q-\delta W+\sum _{i}h_{i}\,dM_{i},}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dM_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dM_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4aba62c651c0e6c93f50c99a0caa1cf03df045ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.27ex; height:2.509ex;" alt="{\displaystyle dM_{i}}"></span> is the added mass of species <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d535f210cbd9b9fe6689e61427b3e213e5b2d547" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.139ex; height:2.509ex;" alt="{\displaystyle h_{i}}"></span> is the corresponding enthalpy per unit mass. Note that generally <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dS\neq \delta Q/T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>S</mi> <mo>≠</mo> <mi>δ</mi> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dS\neq \delta Q/T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36dba88c524b9c43cca3e07d9cd2852d71ff3243" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.499ex; height:2.843ex;" alt="{\displaystyle dS\neq \delta Q/T}"></span> in this case, as matter carries its own entropy. Instead, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dS=\delta Q/T+\textstyle {\sum _{i}}s_{i}\,dM_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>S</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> </mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dS=\delta Q/T+\textstyle {\sum _{i}}s_{i}\,dM_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/673d19bec4e13e8d777c80ea7d9ad3f2bb7c1b04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.14ex; height:3.009ex;" alt="{\displaystyle dS=\delta Q/T+\textstyle {\sum _{i}}s_{i}\,dM_{i}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfda82668232cbdc0874ed28ab8b6079420d1ffe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.89ex; height:2.009ex;" alt="{\displaystyle s_{i}}"></span> is the entropy per unit mass of type <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>, from which we recover the <a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">fundamental thermodynamic relation</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=T\,dS-P\,dV+\sum _{i}\mu _{i}\,dN_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>S</mi> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=T\,dS-P\,dV+\sum _{i}\mu _{i}\,dN_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a4cf709bb048c035ea9b62bc829b2313d136849" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.941ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} U=T\,dS-P\,dV+\sum _{i}\mu _{i}\,dN_{i}}"></span></dd></dl> <p>because the chemical potential <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dea0a0293841cce9eef98b55e53a92b82ae59ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.201ex; height:2.176ex;" alt="{\displaystyle \mu _{i}}"></span> is the partial molar Gibbs free energy of species <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> and the Gibbs free energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G\equiv H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>≡</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G\equiv H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4506984a79b23be2e2174c7909b6e185ce944d30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.965ex; height:2.343ex;" alt="{\displaystyle G\equiv H-TS}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Noether's_theorem"><span id="Noether.27s_theorem"></span>Noether's theorem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=6" title="Edit section: Noether's theorem"><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/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Noether.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Noether.jpg/200px-Noether.jpg" decoding="async" width="200" height="305" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Noether.jpg/300px-Noether.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Noether.jpg/400px-Noether.jpg 2x" data-file-width="1208" data-file-height="1840" /></a><figcaption><a href="/wiki/Emmy_Noether" title="Emmy Noether">Emmy Noether</a> (1882-1935) was an influential <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> known for her groundbreaking contributions to <a href="/wiki/Abstract_algebra" title="Abstract algebra">abstract algebra</a> and <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>.</figcaption></figure> <p>The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of <a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a>, developed by <a href="/wiki/Emmy_Noether" title="Emmy Noether">Emmy Noether</a> in 1915 and first published in 1918. In any physical theory that obeys the stationary-action principle, the theorem states that every continuous symmetry has an associated conserved quantity; if the theory's symmetry is time invariance, then the conserved quantity is called "energy".<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> The energy conservation law is a consequence of the shift <a href="/wiki/Symmetry_(physics)" title="Symmetry (physics)">symmetry</a> of time; energy conservation is implied by the empirical fact that the <a href="/wiki/Laws_of_physics" class="mw-redirect" title="Laws of physics">laws of physics</a> do not change with time itself. Philosophically this can be stated as "nothing depends on time per se". In other words, if the physical system is invariant under the <a href="/wiki/Continuous_symmetry" title="Continuous symmetry">continuous symmetry</a> of <a href="/wiki/Time_translation" class="mw-redirect" title="Time translation">time translation</a>, then its energy (which is the <a href="/wiki/Canonical_conjugate" class="mw-redirect" title="Canonical conjugate">canonical conjugate</a> quantity to time) is conserved. Conversely, systems that are not invariant under shifts in time (e.g. systems with time-dependent potential energy) do not exhibit conservation of energy – unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time-invariant again. Conservation of energy for finite systems is valid in physical theories such as special relativity and quantum theory (including <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">QED</a>) in the flat <a href="/wiki/Space-time" class="mw-redirect" title="Space-time">space-time</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Special_relativity">Special relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=7" title="Edit section: Special relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>With the discovery of special relativity by <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> and <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, the energy was proposed to be a component of an <a href="/wiki/Four-momentum" title="Four-momentum">energy-momentum 4-vector</a>. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given <a href="/wiki/Inertial_reference_frame" class="mw-redirect" title="Inertial reference frame">inertial reference frame</a>. Also conserved is the vector length (<a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski norm</a>), which is the <a href="/wiki/Rest_mass" class="mw-redirect" title="Rest mass">rest mass</a> for single particles, and the <a href="/wiki/Invariant_mass" title="Invariant mass">invariant mass</a> for systems of particles (where momenta and energy are separately summed before the length is calculated). </p><p>The relativistic energy of a single <a href="/wiki/Mass" title="Mass">massive</a> particle contains a term related to its rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the <a href="/wiki/Rest_frame" title="Rest frame">rest frame</a>) of a massive particle, or else in the <a href="/wiki/Center_of_momentum_frame" class="mw-redirect" title="Center of momentum frame">center of momentum frame</a> for objects or systems which retain kinetic energy, the <a href="/wiki/Total_energy" class="mw-redirect" title="Total energy">total energy</a> of a particle or object (including internal kinetic energy in systems) is proportional to the rest mass or invariant mass, as described by the equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f73dbd37a0cac34406ee89057fa1b36a1e6a18e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.976ex; height:2.676ex;" alt="{\displaystyle E=mc^{2}}"></span>. </p><p>Thus, the rule of <a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity"><i>conservation of energy</i> over time in special relativity</a> continues to hold, so long as the <a href="/wiki/Frame_of_reference" title="Frame of reference">reference frame</a> of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the invariant mass, which is the minimal system mass and energy that can be seen by any observer, and which is defined by the <a href="/wiki/Energy%E2%80%93momentum_relation" title="Energy–momentum relation">energy–momentum relation</a>. </p> <div class="mw-heading mw-heading2"><h2 id="General_relativity">General relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=8" title="Edit section: General relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim that energy is no longer meaningfully conserved in any identifiable form.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-leaking_27-0" class="reference"><a href="#cite_note-leaking-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/John_Baez" class="mw-redirect" title="John Baez">John Baez</a>'s view is that energy–momentum conservation is not well-defined except in certain special cases. Energy-momentum is typically expressed with the aid of a <a href="/wiki/Stress%E2%80%93energy%E2%80%93momentum_pseudotensor" title="Stress–energy–momentum pseudotensor">stress–energy–momentum pseudotensor</a>. However, since pseudotensors are not tensors, they do not transform cleanly between reference frames. If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker metric</a> that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Besides being dependent on the coordinate system, pseudotensor energy is dependent on the type of pseudotensor in use; for example, the energy exterior to a <a href="/wiki/Kerr%E2%80%93Newman_black_hole" class="mw-redirect" title="Kerr–Newman black hole">Kerr–Newman black hole</a> is twice as large when calculated from Møller's pseudotensor as it is when calculated using the <a href="/wiki/Einstein_pseudotensor" class="mw-redirect" title="Einstein pseudotensor">Einstein pseudotensor</a>.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>For asymptotically flat universes, Einstein and others salvage conservation of energy by introducing a specific global gravitational potential energy that cancels out mass-energy changes triggered by spacetime expansion or contraction. This global energy has no well-defined density and cannot technically be applied to a non-asymptotically flat universe; however, for practical purposes this can be finessed, and so by this view, energy is conserved in our universe.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Energy_Is_Not_Conserved_3-1" class="reference"><a href="#cite_note-Energy_Is_Not_Conserved-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Alan_Guth" title="Alan Guth">Alan Guth</a> stated that the universe might be "the ultimate free lunch", and theorized that, when accounting for gravitational potential energy, the net energy of the Universe is <a href="/wiki/Zero-energy_universe" title="Zero-energy universe">zero</a>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_theory">Quantum theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=9" title="Edit section: Quantum theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, the energy of a quantum system is described by a <a href="/wiki/Self-adjoint_operator" title="Self-adjoint operator">self-adjoint</a> (or Hermitian) operator called the <a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a>, which acts on the <a href="/wiki/Hilbert_space" title="Hilbert space">Hilbert space</a> (or a space of <a href="/wiki/Wave_function" title="Wave function">wave functions</a>) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum <a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a> for the energy-momentum tensor operator. Thus energy is conserved by the normal unitary evolution of a quantum system. </p><p>However, when the non-unitary <a href="/wiki/Born_rule" title="Born rule">Born rule</a> is applied, the system's energy is <a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">measured</a> with an energy that can be below or above the expectation value, if the system was not in an energy eigenstate. (For macroscopic systems, this effect is usually too small to measure.) The disposition of this energy gap is not well-understood; most physicists believe that the energy is transferred to or from the macroscopic environment in the course of the measurement process,<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> while others believe that the observable energy is only conserved "on average".<sup id="cite_ref-quanta-mag_4-1" class="reference"><a href="#cite_note-quanta-mag-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Energy_Non-conservation_in_Quantum_33-0" class="reference"><a href="#cite_note-Energy_Non-conservation_in_Quantum-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> No experiment has been confirmed as definitive evidence of violations of the conservation of energy principle in quantum mechanics, but that does not rule out that some newer experiments, as proposed, may find evidence of violations of the conservation of energy principle in quantum mechanics.<sup id="cite_ref-Energy_Non-conservation_in_Quantum_33-1" class="reference"><a href="#cite_note-Energy_Non-conservation_in_Quantum-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Status">Status</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=10" title="Edit section: Status"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the context of perpetual motion machines such as the <a href="/wiki/Orbo" class="mw-redirect" title="Orbo">Orbo</a>, Professor <a href="/wiki/Eric_Ash" title="Eric Ash">Eric Ash</a> has argued at the <a href="/wiki/BBC" title="BBC">BBC</a>: "Denying [conservation of energy] would undermine not just little bits of science - the whole edifice would be no more. All of the technology on which we built the modern world would lie in ruins". It is because of conservation of energy that "we know - without having to examine details of a particular device - that Orbo cannot work."<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Energy conservation has been a foundational physical principle for about two hundred years. From the point of view of modern general relativity, the lab environment can be well approximated by <a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a>, where energy is exactly conserved. The entire Earth can be well approximated by the <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild metric</a>, where again energy is exactly conserved. Given all the experimental evidence, any new theory (such as <a href="/wiki/Quantum_gravity" title="Quantum gravity">quantum gravity</a>), in order to be successful, will have to explain why energy has appeared to always be exactly conserved in terrestrial experiments.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> In some speculative theories, corrections to quantum mechanics are too small to be detected at anywhere near the current <a href="/wiki/TeV" class="mw-redirect" title="TeV">TeV</a> level accessible through particle accelerators. <a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a> models may argue for a breakdown in energy-momentum conservation for sufficiently energetic particles; such models are constrained by observations that cosmic rays appear to travel for billions of years without displaying anomalous non-conservation behavior.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Some interpretations of quantum mechanics claim that observed energy tends to increase when the Born rule is applied due to localization of the wave function. If true, objects could be expected to spontaneously heat up; thus, such models are constrained by observations of large, cool astronomical objects as well as the observation of (often supercooled) laboratory experiments.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Milton_A._Rothman" title="Milton A. Rothman">Milton A. Rothman</a> wrote that the law of conservation of energy has been verified by nuclear physics experiments to an accuracy of one part in a thousand million million (10<sup>15</sup>). He then defines its precision as "perfect for all practical purposes".<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <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=Conservation_of_energy&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Crystal_energy.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/29px-Crystal_energy.svg.png" decoding="async" width="29" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/44px-Crystal_energy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/59px-Crystal_energy.svg.png 2x" data-file-width="130" data-file-height="124" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Energy" title="Portal:Energy">Energy portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Energy_quality" title="Energy quality">Energy quality</a></li> <li><a href="/wiki/Energy_transformation" title="Energy transformation">Energy transformation</a></li> <li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a></li> <li><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws of thermodynamics</a></li> <li><a href="/wiki/Zero-energy_universe" title="Zero-energy universe">Zero-energy universe</a></li></ul> </div> <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=Conservation_of_energy&action=edit&section=12" 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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Feynman2Ch1S2-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Feynman2Ch1S2_1-0">^</a></b></span> <span class="reference-text"><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="CITEREFRichard_Feynman1970" class="citation book cs1">Richard Feynman (1970). <a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/I_04.html"><i>The Feynman Lectures on Physics Vol I</i></a>. Addison Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-02115-8" title="Special:BookSources/978-0-201-02115-8"><bdi>978-0-201-02115-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Feynman+Lectures+on+Physics+Vol+I&rft.pub=Addison+Wesley&rft.date=1970&rft.isbn=978-0-201-02115-8&rft.au=Richard+Feynman&rft_id=https%3A%2F%2Ffeynmanlectures.caltech.edu%2FI_04.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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">Planck, M. (1923/1927). <i>Treatise on Thermodynamics</i>, third English edition translated by A. Ogg from the seventh German edition, Longmans, Green & Co., London, page 40.</span> </li> <li id="cite_note-Energy_Is_Not_Conserved-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Energy_Is_Not_Conserved_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Energy_Is_Not_Conserved_3-1"><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 class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.discovermagazine.com/the-sciences/energy-is-not-conserved">"Energy Is Not Conserved"</a>. <i>Discover Magazine</i>. 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Discover+Magazine&rft.atitle=Energy+Is+Not+Conserved&rft.date=2010&rft_id=https%3A%2F%2Fwww.discovermagazine.com%2Fthe-sciences%2Fenergy-is-not-conserved&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-quanta-mag-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-quanta-mag_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-quanta-mag_4-1"><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 class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.quantamagazine.org/puzzling-quantum-scenario-appears-not-to-conserve-energy-20220516/">"Puzzling Quantum Scenario Appears Not to Conserve Energy"</a>. <i><a href="/wiki/Quanta_Magazine" title="Quanta Magazine">Quanta Magazine</a></i>. 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quanta+Magazine&rft.atitle=Puzzling+Quantum+Scenario+Appears+Not+to+Conserve+Energy&rft.date=2022&rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fpuzzling-quantum-scenario-appears-not-to-conserve-energy-20220516%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></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="CITEREFJanko2004" class="citation journal cs1">Janko, Richard (2004). <a rel="nofollow" class="external text" href="http://ancphil.lsa.umich.edu/-/downloads/faculty/janko/empedocles-nature.pdf">"Empedocles, "On Nature"<span class="cs1-kern-right"></span>"</a> <span class="cs1-format">(PDF)</span>. <i>Zeitschrift für Papyrologie und Epigraphik</i>. <b>150</b>: <span class="nowrap">1–</span>26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Papyrologie+und+Epigraphik&rft.atitle=Empedocles%2C+%22On+Nature%22&rft.volume=150&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E26&rft.date=2004&rft.aulast=Janko&rft.aufirst=Richard&rft_id=http%3A%2F%2Fancphil.lsa.umich.edu%2F-%2Fdownloads%2Ffaculty%2Fjanko%2Fempedocles-nature.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLaertius" class="citation book cs1">Laertius, Diogenes. <a rel="nofollow" class="external text" href="https://www-loebclassics.com/view/diogenes_laertius-lives_eminent_philosophers_book_x_epicurus/1925/pb_LCL185.569.xml?result=1&rskey=YoU4V6"><i>Lives of Eminent Philosophers: Epicurus</i></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lives+of+Eminent+Philosophers%3A+Epicurus&rft.aulast=Laertius&rft.aufirst=Diogenes&rft_id=https%3A%2F%2Fwww-loebclassics.com%2Fview%2Fdiogenes_laertius-lives_eminent_philosophers_book_x_epicurus%2F1925%2Fpb_LCL185.569.xml%3Fresult%3D1%26rskey%3DYoU4V6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged March 2021">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup>. This passage comes from a letter quoted in full by Diogenes, and purportedly written by Epicurus himself in which he lays out the tenets of his philosophy.</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 id="CITEREFErlichson1997" class="citation journal cs1">Erlichson, Herman (1 February 1997). <a rel="nofollow" class="external text" href="https://pubs.aip.org/aapt/ajp/article-abstract/65/2/149/1054978/The-young-Huygens-solves-the-problem-of-elastic?redirectedFrom=fulltext">"The young Huygens solves the problem of elastic collisions"</a>. <i>American Journal of Physics</i>. <b>65</b> (2): <span class="nowrap">149–</span>154. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.18659">10.1119/1.18659</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/0002-9505">0002-9505</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=The+young+Huygens+solves+the+problem+of+elastic+collisions&rft.volume=65&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E149-%3C%2Fspan%3E154&rft.date=1997-02-01&rft_id=info%3Adoi%2F10.1119%2F1.18659&rft.issn=0002-9505&rft.aulast=Erlichson&rft.aufirst=Herman&rft_id=https%3A%2F%2Fpubs.aip.org%2Faapt%2Fajp%2Farticle-abstract%2F65%2F2%2F149%2F1054978%2FThe-young-Huygens-solves-the-problem-of-elastic%3FredirectedFrom%3Dfulltext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFErlichson1996" class="citation journal cs1">Erlichson, Herman (1 May 1996). <a rel="nofollow" class="external text" href="https://pubs.aip.org/aapt/ajp/article-abstract/64/5/571/1045484/Christiaan-Huygens-discovery-of-the-center-of?redirectedFrom=fulltext">"Christiaan Huygens' discovery of the center of oscillation formula"</a>. <i>American Journal of Physics</i>. <b>64</b> (5): <span class="nowrap">571–</span>574. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.18156">10.1119/1.18156</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/0002-9505">0002-9505</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Christiaan+Huygens%E2%80%99+discovery+of+the+center+of+oscillation+formula&rft.volume=64&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E571-%3C%2Fspan%3E574&rft.date=1996-05-01&rft_id=info%3Adoi%2F10.1119%2F1.18156&rft.issn=0002-9505&rft.aulast=Erlichson&rft.aufirst=Herman&rft_id=https%3A%2F%2Fpubs.aip.org%2Faapt%2Fajp%2Farticle-abstract%2F64%2F5%2F571%2F1045484%2FChristiaan-Huygens-discovery-of-the-center-of%3FredirectedFrom%3Dfulltext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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="CITEREFPitts2021" class="citation journal cs1">Pitts, J. Brian (September 2021). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8570307">"Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter"</a>. <i>Foundations of Science</i>. <b>26</b> (3): <span class="nowrap">559–</span>584. <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%2Fs10699-020-09657-1">10.1007/s10699-020-09657-1</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8570307">8570307</a></span>. <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/34759713">34759713</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Science&rft.atitle=Conservation+of+Energy%3A+Missing+Features+in+Its+Nature+and+Justification+and+Why+They+Matter&rft.volume=26&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E559-%3C%2Fspan%3E584&rft.date=2021-09&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8570307%23id-name%3DPMC&rft_id=info%3Apmid%2F34759713&rft_id=info%3Adoi%2F10.1007%2Fs10699-020-09657-1&rft.aulast=Pitts&rft.aufirst=J.+Brian&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8570307&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-Hagengruber-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hagengruber_10-0">^</a></b></span> <span class="reference-text">Hagengruber, Ruth, editor (2011) <i>Émilie du Chatelet between Leibniz and Newton</i>. Springer. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-94-007-2074-9" title="Special:BookSources/978-94-007-2074-9">978-94-007-2074-9</a>.</span> </li> <li id="cite_note-Arianrhod-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Arianrhod_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArianrhod2012" class="citation book cs1">Arianrhod, Robyn (2012). <a rel="nofollow" class="external text" href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9444991"><i>Seduced by logic : Émilie du Châtelet, Mary Somerville, and the Newtonian revolution</i></a> (US ed.). New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-993161-3" title="Special:BookSources/978-0-19-993161-3"><bdi>978-0-19-993161-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Seduced+by+logic+%3A+%C3%89milie+du+Ch%C3%A2telet%2C+Mary+Somerville%2C+and+the+Newtonian+revolution&rft.place=New+York&rft.edition=US&rft.pub=Oxford+University+Press&rft.date=2012&rft.isbn=978-0-19-993161-3&rft.aulast=Arianrhod&rft.aufirst=Robyn&rft_id=http%3A%2F%2Fjournals.cambridge.org%2Faction%2FdisplayAbstract%3FfromPage%3Donline%26aid%3D9444991&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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">Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", <i>Académie Royale des Sciences</i> pp. 4–355</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="CITEREFGuerlac1976" class="citation journal cs1">Guerlac, Henry (1976). <a rel="nofollow" class="external text" href="https://online.ucpress.edu/hsns/article-abstract/doi/10.2307/27757357/47949/Chemistry-as-a-Branch-of-Physics-Laplace-s?redirectedFrom=fulltext">"Chemistry as a Branch of Physics: Laplace's Collaboration with Lavoisier"</a>. <i>Historical Studies in the Physical Sciences</i>. <b>7</b>. University of California Press: <span class="nowrap">193–</span>276. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F27757357">10.2307/27757357</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/27757357">27757357</a><span class="reference-accessdate">. Retrieved <span class="nowrap">24 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historical+Studies+in+the+Physical+Sciences&rft.atitle=Chemistry+as+a+Branch+of+Physics%3A+Laplace%27s+Collaboration+with+Lavoisier&rft.volume=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E193-%3C%2Fspan%3E276&rft.date=1976&rft_id=info%3Adoi%2F10.2307%2F27757357&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F27757357%23id-name%3DJSTOR&rft.aulast=Guerlac&rft.aufirst=Henry&rft_id=https%3A%2F%2Fonline.ucpress.edu%2Fhsns%2Farticle-abstract%2Fdoi%2F10.2307%2F27757357%2F47949%2FChemistry-as-a-Branch-of-Physics-Laplace-s%3FredirectedFrom%3Dfulltext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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">von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in <i>Annalen der Chemie und Pharmacie</i>, <b>43</b>, 233</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">Mayer, J.R. (1845). <i>Die organische Bewegung in ihrem Zusammenhange mit dem Stoffwechsel. Ein Beitrag zur Naturkunde</i>, Dechsler, Heilbronn.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrove,_W._R.1874" class="citation book cs1">Grove, W. R. (1874). <a rel="nofollow" class="external text" href="https://archive.org/details/correlationphys06grovgoog"><i>The Correlation of Physical Forces</i></a> (6th ed.). London: Longmans, Green.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Correlation+of+Physical+Forces&rft.place=London&rft.edition=6th&rft.pub=Longmans%2C+Green&rft.date=1874&rft.au=Grove%2C+W.+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcorrelationphys06grovgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.bartleby.com/30/125.html">"On the Conservation of Force"</a>. Bartleby<span class="reference-accessdate">. Retrieved <span class="nowrap">6 April</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=On+the+Conservation+of+Force&rft.pub=Bartleby&rft_id=http%3A%2F%2Fwww.bartleby.com%2F30%2F125.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" 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">William John Macquorn Rankine (1853) "On the General Law of the Transformation of Energy," <i>Proceedings of the Philosophical Society of Glasgow</i>, vol. 3, no. 5, pages 276-280; reprinted in: (1) <i>Philosophical Magazine</i>, series 4, vol. 5, no. 30, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3Ov22-gFMnEC&pg=PA106">pages 106-117</a> (February 1853); and (2) W. J. Millar, ed., <i>Miscellaneous Scientific Papers: by W. J. Macquorn Rankine</i>, ... (London, England: Charles Griffin and Co., 1881), part II, <a rel="nofollow" class="external text" href="https://archive.org/stream/miscellaneoussci00rank#page/203/mode/1up">pages 203-208</a>: "The law of the <i>Conservation of Energy</i> is already known—viz. that the sum of all the energies of the universe, actual and potential, is unchangeable."</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHadden1994" class="citation book cs1">Hadden, Richard W. (1994). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7IxtC4Jw1YoC"><i>On the shoulders of merchants: exchange and the mathematical conception of nature in early modern Europe</i></a>. SUNY Press. p. 13. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7914-2011-9" title="Special:BookSources/978-0-7914-2011-9"><bdi>978-0-7914-2011-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+shoulders+of+merchants%3A+exchange+and+the+mathematical+conception+of+nature+in+early+modern+Europe&rft.pages=13&rft.pub=SUNY+Press&rft.date=1994&rft.isbn=978-0-7914-2011-9&rft.aulast=Hadden&rft.aufirst=Richard+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7IxtC4Jw1YoC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7IxtC4Jw1YoC&pg=PA13">Chapter 1, p. 13</a></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJensen2000" class="citation book cs1">Jensen, Carsten (2000). <a rel="nofollow" class="external text" href="https://www.springer.com/birkhauser/physics/book/978-3-7643-5313-1"><i>Controversy and Consensus: Nuclear Beta Decay 1911-1934</i></a>. Birkhäuser Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7643-5313-1" title="Special:BookSources/978-3-7643-5313-1"><bdi>978-3-7643-5313-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Controversy+and+Consensus%3A+Nuclear+Beta+Decay+1911-1934&rft.pub=Birkh%C3%A4user+Verlag&rft.date=2000&rft.isbn=978-3-7643-5313-1&rft.aulast=Jensen&rft.aufirst=Carsten&rft_id=https%3A%2F%2Fwww.springer.com%2Fbirkhauser%2Fphysics%2Fbook%2F978-3-7643-5313-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrown1978" class="citation journal cs1">Brown, Laurie M. (1978). "The idea of the neutrino". <i>Physics Today</i>. <b>31</b> (9): <span class="nowrap">23–</span>8. <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/1978PhT....31i..23B">1978PhT....31i..23B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.2995181">10.1063/1.2995181</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=The+idea+of+the+neutrino&rft.volume=31&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E23-%3C%2Fspan%3E8&rft.date=1978&rft_id=info%3Adoi%2F10.1063%2F1.2995181&rft_id=info%3Abibcode%2F1978PhT....31i..23B&rft.aulast=Brown&rft.aufirst=Laurie+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson1968" class="citation journal cs1">Wilson, F. L. (1968). <a rel="nofollow" class="external text" href="http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1">"Fermi's Theory of Beta Decay"</a>. <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>36</b> (12): <span class="nowrap">1150–</span>1160. <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/1968AmJPh..36.1150W">1968AmJPh..36.1150W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1974382">10.1119/1.1974382</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Fermi%27s+Theory+of+Beta+Decay&rft.volume=36&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1150-%3C%2Fspan%3E1160&rft.date=1968&rft_id=info%3Adoi%2F10.1119%2F1.1974382&rft_id=info%3Abibcode%2F1968AmJPh..36.1150W&rft.aulast=Wilson&rft.aufirst=F.+L.&rft_id=http%3A%2F%2Fmicroboone-docdb.fnal.gov%2Fcgi-bin%2FRetrieveFile%3Fdocid%3D953%3Bfilename%3DFermiBetaDecay1934.pdf%3Bversion%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriffiths2009" class="citation book cs1">Griffiths, D. (2009). <i>Introduction to Elementary Particles</i> (2nd ed.). pp. <span class="nowrap">314–</span>315. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-40601-2" title="Special:BookSources/978-3-527-40601-2"><bdi>978-3-527-40601-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Elementary+Particles&rft.pages=%3Cspan+class%3D%22nowrap%22%3E314-%3C%2Fspan%3E315&rft.edition=2nd&rft.date=2009&rft.isbn=978-3-527-40601-2&rft.aulast=Griffiths&rft.aufirst=D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnuimanBarneveldBesseling2012" class="citation journal cs1">Knuiman, Jan T.; Barneveld, Peter A.; Besseling, Nicolaas A. M. (2012). <a rel="nofollow" class="external text" href="https://pubs.acs.org/doi/full/10.1021/ed200405k">"On the Relation between the Fundamental Equation of Thermodynamics and the Energy Balance Equation in the Context of Closed and Open Systems"</a>. <i>Journal of Chemical Education</i>. <b>89</b> (8): <span class="nowrap">968–</span>972. <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/2012JChEd..89..968K">2012JChEd..89..968K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed200405k">10.1021/ed200405k</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+Chemical+Education&rft.atitle=On+the+Relation+between+the+Fundamental+Equation+of+Thermodynamics+and+the+Energy+Balance+Equation+in+the+Context+of+Closed+and+Open+Systems&rft.volume=89&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E968-%3C%2Fspan%3E972&rft.date=2012&rft_id=info%3Adoi%2F10.1021%2Fed200405k&rft_id=info%3Abibcode%2F2012JChEd..89..968K&rft.aulast=Knuiman&rft.aufirst=Jan+T.&rft.au=Barneveld%2C+Peter+A.&rft.au=Besseling%2C+Nicolaas+A.+M.&rft_id=https%3A%2F%2Fpubs.acs.org%2Fdoi%2Ffull%2F10.1021%2Fed200405k&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">Hanc, J., Tuleja, S., & Hancova, M. (2004). Symmetries and conservation laws: Consequences of Noether’s theorem. American Journal of Physics, 72(4), 428-435.</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">Harrison, E. R. (1995). Mining energy in an expanding universe. The Astrophysical Journal, 446, 63.</span> </li> <li id="cite_note-leaking-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-leaking_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTamara_M._Davis2010" class="citation news cs1">Tamara M. Davis (2010). <a rel="nofollow" class="external text" href="https://www.scientificamerican.com/article/is-the-universe-leaking-energy/">"Is the Universe Leaking Energy?"</a>. <i>Scientific American</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Is+the+Universe+Leaking+Energy%3F&rft.date=2010&rft.au=Tamara+M.+Davis&rft_id=https%3A%2F%2Fwww.scientificamerican.com%2Farticle%2Fis-the-universe-leaking-energy%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichael_WeissJohn_Baez" class="citation web cs1">Michael Weiss; John Baez. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070605041426/http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html">"Is Energy Conserved in General Relativity?"</a>. Archived from <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html">the original</a> on 5 June 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">5 January</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Is+Energy+Conserved+in+General+Relativity%3F&rft.au=Michael+Weiss&rft.au=John+Baez&rft_id=http%3A%2F%2Fmath.ucr.edu%2Fhome%2Fbaez%2Fphysics%2FRelativity%2FGR%2Fenergy_gr.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuerr2019" class="citation journal cs1">Duerr, Patrick M. (February 2019). "Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity". <i>Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics</i>. <b>65</b>: <span class="nowrap">1–</span>14. <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/2019SHPMP..65....1D">2019SHPMP..65....1D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.shpsb.2018.07.002">10.1016/j.shpsb.2018.07.002</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:126366668">126366668</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Science+Part+B%3A+Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=Fantastic+Beasts+and+where+%28not%29+to+find+them%3A+Local+gravitational+energy+and+energy+conservation+in+general+relativity&rft.volume=65&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E14&rft.date=2019-02&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A126366668%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.shpsb.2018.07.002&rft_id=info%3Abibcode%2F2019SHPMP..65....1D&rft.aulast=Duerr&rft.aufirst=Patrick+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoskowitz2014" class="citation news cs1">Moskowitz, Clara (2014). <a rel="nofollow" class="external text" href="https://www.scientificamerican.com/article/energy-can-neither-be-created-nor-destroyed/">"Fact or Fiction?: Energy Can Neither Be Created Nor Destroyed"</a>. <i>Scientific American</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Fact+or+Fiction%3F%3A+Energy+Can+Neither+Be+Created+Nor+Destroyed&rft.date=2014&rft.aulast=Moskowitz&rft.aufirst=Clara&rft_id=https%3A%2F%2Fwww.scientificamerican.com%2Farticle%2Fenergy-can-neither-be-created-nor-destroyed%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.space.com/31465-is-our-universe-just-one-of-many-in-a-multiverse.html">"Confronting the Multiverse: What 'Infinite Universes' Would Mean"</a>. <i>Space.com</i>. 23 December 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Space.com&rft.atitle=Confronting+the+Multiverse%3A+What+%27Infinite+Universes%27+Would+Mean&rft.date=2015-12-23&rft_id=https%3A%2F%2Fwww.space.com%2F31465-is-our-universe-just-one-of-many-in-a-multiverse.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarroll2021" class="citation web cs1">Carroll, Sean (28 January 2021). <a rel="nofollow" class="external text" href="https://www.preposterousuniverse.com/blog/2021/01/28/energy-conservation-and-non-conservation-in-quantum-mechanics/">"Energy Conservation and Non-Conservation in Quantum Mechanics"</a>. <i>Preposterousuniverse</i><span class="reference-accessdate">. Retrieved <span class="nowrap">26 May</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Preposterousuniverse&rft.atitle=Energy+Conservation+and+Non-Conservation+in+Quantum+Mechanics&rft.date=2021-01-28&rft.aulast=Carroll&rft.aufirst=Sean&rft_id=https%3A%2F%2Fwww.preposterousuniverse.com%2Fblog%2F2021%2F01%2F28%2Fenergy-conservation-and-non-conservation-in-quantum-mechanics%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-Energy_Non-conservation_in_Quantum-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-Energy_Non-conservation_in_Quantum_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Energy_Non-conservation_in_Quantum_33-1"><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="CITEREFCarrollLodman2021" class="citation journal cs1">Carroll, Sean M.; Lodman, Jackie (August 2021). "Energy Non-conservation in Quantum Mechanics". <i>Foundations of Physics</i>. <b>51</b> (4): 83. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2101.11052">2101.11052</a></span>. <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/2021FoPh...51...83C">2021FoPh...51...83C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10701-021-00490-5">10.1007/s10701-021-00490-5</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:226664820">226664820</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Physics&rft.atitle=Energy+Non-conservation+in+Quantum+Mechanics&rft.volume=51&rft.issue=4&rft.pages=83&rft.date=2021-08&rft_id=info%3Aarxiv%2F2101.11052&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A226664820%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10701-021-00490-5&rft_id=info%3Abibcode%2F2021FoPh...51...83C&rft.aulast=Carroll&rft.aufirst=Sean+M.&rft.au=Lodman%2C+Jackie&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAharonov2023" class="citation journal cs1">Aharonov, Yakir (October 2023). "Conservation laws and the foundations of quantum mechanics". <i>Proceedings of the National Academy of Sciences</i>. <b>41</b> (120). <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2401.14261">2401.14261</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.22208101201of9">10.1073/pnas.22208101201of9</a> (inactive 1 November 2024).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=Conservation+laws+and+the+foundations+of+quantum+mechanics&rft.volume=41&rft.issue=120&rft.date=2023-10&rft_id=info%3Aarxiv%2F2401.14261&rft_id=info%3Adoi%2F10.1073%2Fpnas.22208101201of9&rft.aulast=Aharonov&rft.aufirst=Yakir&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: DOI inactive as of November 2024 (<a href="/wiki/Category:CS1_maint:_DOI_inactive_as_of_November_2024" title="Category:CS1 maint: DOI inactive as of November 2024">link</a>)</span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://news.bbc.co.uk/2/hi/technology/6283374.stm">"The perpetual myth of free energy"</a>. <i>BBC</i>. 9 July 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BBC&rft.atitle=The+perpetual+myth+of+free+energy&rft.date=2007-07-09&rft_id=http%3A%2F%2Fnews.bbc.co.uk%2F2%2Fhi%2Ftechnology%2F6283374.stm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaudlinOkonSudarsky2020" class="citation journal cs1">Maudlin, Tim; Okon, Elias; Sudarsky, Daniel (February 2020). "On the status of conservation laws in physics: Implications for semiclassical gravity". <i>Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics</i>. <b>69</b>: <span class="nowrap">67–</span>81. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1910.06473">1910.06473</a></span>. <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/2020SHPMP..69...67M">2020SHPMP..69...67M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.shpsb.2019.10.004">10.1016/j.shpsb.2019.10.004</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:204575731">204575731</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Science+Part+B%3A+Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=On+the+status+of+conservation+laws+in+physics%3A+Implications+for+semiclassical+gravity&rft.volume=69&rft.pages=%3Cspan+class%3D%22nowrap%22%3E67-%3C%2Fspan%3E81&rft.date=2020-02&rft_id=info%3Aarxiv%2F1910.06473&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A204575731%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.shpsb.2019.10.004&rft_id=info%3Abibcode%2F2020SHPMP..69...67M&rft.aulast=Maudlin&rft.aufirst=Tim&rft.au=Okon%2C+Elias&rft.au=Sudarsky%2C+Daniel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAmelino-Camelia2013" class="citation journal cs1">Amelino-Camelia, Giovanni (12 June 2013). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255913">"Quantum-Spacetime Phenomenology"</a>. <i>Living Reviews in Relativity</i>. <b>16</b> (1): 5. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0806.0339">0806.0339</a></span>. <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/2013LRR....16....5A">2013LRR....16....5A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.12942%2Flrr-2013-5">10.12942/lrr-2013-5</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255913">5255913</a></span>. <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/28179844">28179844</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Living+Reviews+in+Relativity&rft.atitle=Quantum-Spacetime+Phenomenology&rft.volume=16&rft.issue=1&rft.pages=5&rft.date=2013-06-12&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5255913%23id-name%3DPMC&rft_id=info%3Abibcode%2F2013LRR....16....5A&rft_id=info%3Aarxiv%2F0806.0339&rft_id=info%3Apmid%2F28179844&rft_id=info%3Adoi%2F10.12942%2Flrr-2013-5&rft.aulast=Amelino-Camelia&rft.aufirst=Giovanni&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5255913&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarlessoDonadiFerialdiPaternostro2022" class="citation journal cs1">Carlesso, Matteo; Donadi, Sandro; Ferialdi, Luca; Paternostro, Mauro; Ulbricht, Hendrik; Bassi, Angelo (March 2022). "Present status and future challenges of non-interferometric tests of collapse models". <i>Nature Physics</i>. <b>18</b> (3): <span class="nowrap">243–</span>250. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2203.04231">2203.04231</a></span>. <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/2022NatPh..18..243C">2022NatPh..18..243C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41567-021-01489-5">10.1038/s41567-021-01489-5</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:246949254">246949254</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Physics&rft.atitle=Present+status+and+future+challenges+of+non-interferometric+tests+of+collapse+models&rft.volume=18&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E243-%3C%2Fspan%3E250&rft.date=2022-03&rft_id=info%3Aarxiv%2F2203.04231&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A246949254%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2Fs41567-021-01489-5&rft_id=info%3Abibcode%2F2022NatPh..18..243C&rft.aulast=Carlesso&rft.aufirst=Matteo&rft.au=Donadi%2C+Sandro&rft.au=Ferialdi%2C+Luca&rft.au=Paternostro%2C+Mauro&rft.au=Ulbricht%2C+Hendrik&rft.au=Bassi%2C+Angelo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRothman1989" class="citation journal cs1">Rothman, Milton (1989). "Myths About Science... And Belief in the Paranormal". <i>The Skeptical Inquirer</i>. <b>14</b> (1): 28.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Skeptical+Inquirer&rft.atitle=Myths+About+Science...+And+Belief+in+the+Paranormal&rft.volume=14&rft.issue=1&rft.pages=28&rft.date=1989&rft.aulast=Rothman&rft.aufirst=Milton&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=13" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Modern_accounts">Modern accounts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=14" title="Edit section: Modern accounts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Goldstein, Martin, and Inge F., (1993). <i>The Refrigerator and the Universe</i>. Harvard Univ. Press. A gentle introduction.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKroemer,_HerbertKittel,_Charles1980" class="citation book cs1">Kroemer, Herbert; Kittel, Charles (1980). <i>Thermal Physics (2nd ed.)</i>. W. H. Freeman Company. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-1088-2" title="Special:BookSources/978-0-7167-1088-2"><bdi>978-0-7167-1088-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermal+Physics+%282nd+ed.%29&rft.pub=W.+H.+Freeman+Company&rft.date=1980&rft.isbn=978-0-7167-1088-2&rft.au=Kroemer%2C+Herbert&rft.au=Kittel%2C+Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNolan,_Peter_J.1996" class="citation book cs1">Nolan, Peter J. (1996). <i>Fundamentals of College Physics, 2nd ed</i>. William C. Brown Publishers.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+College+Physics%2C+2nd+ed.&rft.pub=William+C.+Brown+Publishers&rft.date=1996&rft.au=Nolan%2C+Peter+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOxtoby_&_Nachtrieb1996" class="citation book cs1">Oxtoby & Nachtrieb (1996). <i>Principles of Modern Chemistry, 3rd ed</i>. Saunders College Publishing.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Modern+Chemistry%2C+3rd+ed.&rft.pub=Saunders+College+Publishing&rft.date=1996&rft.au=Oxtoby+%26+Nachtrieb&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPapineau,_D.2002" class="citation book cs1">Papineau, D. (2002). <i>Thinking about Consciousness</i>. Oxford: Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thinking+about+Consciousness&rft.place=Oxford&rft.pub=Oxford+University+Press&rft.date=2002&rft.au=Papineau%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSerway,_Raymond_A.Jewett,_John_W.2004" class="citation book cs1">Serway, Raymond A.; Jewett, John W. (2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/physicssciengv2p00serw"><i>Physics for Scientists and Engineers (6th ed.)</i></a></span>. Brooks/Cole. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-534-40842-8" title="Special:BookSources/978-0-534-40842-8"><bdi>978-0-534-40842-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers+%286th+ed.%29&rft.pub=Brooks%2FCole&rft.date=2004&rft.isbn=978-0-534-40842-8&rft.au=Serway%2C+Raymond+A.&rft.au=Jewett%2C+John+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysicssciengv2p00serw&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li>Stenger, Victor J. (2000). <i>Timeless Reality</i>. Prometheus Books. Especially chpt. 12. Nontechnical.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTipler,_Paul2004" class="citation book cs1">Tipler, Paul (2004). <i>Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.)</i>. W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0809-4" title="Special:BookSources/978-0-7167-0809-4"><bdi>978-0-7167-0809-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers%3A+Mechanics%2C+Oscillations+and+Waves%2C+Thermodynamics+%285th+ed.%29&rft.pub=W.+H.+Freeman&rft.date=2004&rft.isbn=978-0-7167-0809-4&rft.au=Tipler%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLanczos,_Cornelius1970" class="citation book cs1"><a href="/wiki/Lanczos" class="mw-redirect" title="Lanczos">Lanczos</a>, Cornelius (1970). <i>The Variational Principles of Mechanics</i>. Toronto: University of Toronto Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8020-1743-7" title="Special:BookSources/978-0-8020-1743-7"><bdi>978-0-8020-1743-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Variational+Principles+of+Mechanics&rft.place=Toronto&rft.pub=University+of+Toronto+Press&rft.date=1970&rft.isbn=978-0-8020-1743-7&rft.au=Lanczos%2C+Cornelius&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="History_of_ideas">History of ideas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Conservation_of_energy&action=edit&section=15" title="Edit section: History of ideas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrown,_T.M.1965" class="citation journal cs1">Brown, T.M. (1965). "Resource letter EEC-1 on the evolution of energy concepts from Galileo to Helmholtz". <i>American Journal of Physics</i>. <b>33</b> (10): <span class="nowrap">759–</span>765. <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/1965AmJPh..33..759B">1965AmJPh..33..759B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1970980">10.1119/1.1970980</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Resource+letter+EEC-1+on+the+evolution+of+energy+concepts+from+Galileo+to+Helmholtz&rft.volume=33&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E759-%3C%2Fspan%3E765&rft.date=1965&rft_id=info%3Adoi%2F10.1119%2F1.1970980&rft_id=info%3Abibcode%2F1965AmJPh..33..759B&rft.au=Brown%2C+T.M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCardwell,_D.S.L.1971" class="citation book cs1">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%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuillen,_M.1999" class="citation book cs1">Guillen, M. (1999). <i><a href="/wiki/Five_Equations_That_Changed_the_World" title="Five Equations That Changed the World">Five Equations That Changed the World</a></i>. New York: Abacus. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-349-11064-6" title="Special:BookSources/978-0-349-11064-6"><bdi>978-0-349-11064-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Five+Equations+That+Changed+the+World&rft.place=New+York&rft.pub=Abacus&rft.date=1999&rft.isbn=978-0-349-11064-6&rft.au=Guillen%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHiebert,_E.N.1981" class="citation book cs1">Hiebert, E.N. (1981). <i>Historical Roots of the Principle of Conservation of Energy</i>. Madison, Wis.: Ayer Co Pub. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-405-13880-5" title="Special:BookSources/978-0-405-13880-5"><bdi>978-0-405-13880-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Historical+Roots+of+the+Principle+of+Conservation+of+Energy&rft.place=Madison%2C+Wis.&rft.pub=Ayer+Co+Pub&rft.date=1981&rft.isbn=978-0-405-13880-5&rft.au=Hiebert%2C+E.N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><a href="/wiki/Thomas_Kuhn" title="Thomas Kuhn">Kuhn, T.S.</a> (1957) "Energy conservation as an example of simultaneous discovery", in M. Clagett (ed.) <i>Critical Problems in the History of Science</i> <i>pp.</i>321–56</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSarton,_G.JouleCarnot1929" class="citation journal cs1">Sarton, G.; Joule, J. P.; Carnot, Sadi (1929). "The discovery of the law of conservation of energy". <i>Isis</i>. <b>13</b>: <span class="nowrap">18–</span>49. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F346430">10.1086/346430</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:145585492">145585492</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=The+discovery+of+the+law+of+conservation+of+energy&rft.volume=13&rft.pages=%3Cspan+class%3D%22nowrap%22%3E18-%3C%2Fspan%3E49&rft.date=1929&rft_id=info%3Adoi%2F10.1086%2F346430&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A145585492%23id-name%3DS2CID&rft.au=Sarton%2C+G.&rft.au=Joule%2C+J.+P.&rft.au=Carnot%2C+Sadi&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith,_C.1998" class="citation book cs1">Smith, C. (1998). <i>The Science of Energy: Cultural History of Energy Physics in Victorian Britain</i>. London: Heinemann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-485-11431-7" title="Special:BookSources/978-0-485-11431-7"><bdi>978-0-485-11431-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Science+of+Energy%3A+Cultural+History+of+Energy+Physics+in+Victorian+Britain&rft.place=London&rft.pub=Heinemann&rft.date=1998&rft.isbn=978-0-485-11431-7&rft.au=Smith%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMach,_E.1872" class="citation book cs1"><a href="/wiki/Ernst_Mach" title="Ernst Mach">Mach, E.</a> (1872). <a rel="nofollow" class="external text" href="https://archive.org/details/historyandrootp00machgoog"><i>History and Root of the Principles of the Conservation of Energy</i></a>. Open Court Pub. Co., Illinois.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=History+and+Root+of+the+Principles+of+the+Conservation+of+Energy&rft.pub=Open+Court+Pub.+Co.%2C+Illinois&rft.date=1872&rft.au=Mach%2C+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryandrootp00machgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.1905" class="citation book cs1"><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré, H.</a> (1905). <a rel="nofollow" class="external text" href="https://archive.org/details/scienceandhypoth00poinuoft"><i>Science and Hypothesis</i></a>. Walter Scott Publishing Co. Ltd; Dover reprint, 1952. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60221-9" title="Special:BookSources/978-0-486-60221-9"><bdi>978-0-486-60221-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+Hypothesis&rft.pub=Walter+Scott+Publishing+Co.+Ltd%3B+Dover+reprint%2C+1952&rft.date=1905&rft.isbn=978-0-486-60221-9&rft.au=Poincar%C3%A9%2C+H.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fscienceandhypoth00poinuoft&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConservation+of+energy" class="Z3988"></span>, Chapter 8, "Energy and Thermo-dynamics"</li></ul> <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=Conservation_of_energy&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.physnet.org/modules/pdf_modules/m158.pdf"><small>MISN-0-158</small> <i>The First Law of Thermodynamics</i></a> (<a href="/wiki/Portable_Document_Format" class="mw-redirect" title="Portable Document Format">PDF file</a>) by Jerzy Borysowicz for <a rel="nofollow" class="external text" href="http://www.physnet.org">Project PHYSNET</a>.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><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><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox1618" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q11382#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></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://d-nb.info/gnd/4152219-9">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Energy conservation"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85043124">United States</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Énergie -- Conservation"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11969457b">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Énergie -- Conservation"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11969457b">BnF data</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="zákon zachování energie"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph984753&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000052998&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007543207805171">Israel</a></span></li></ul></div></td></tr></tbody></table></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" 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=Conservation_of_energy&oldid=1274281973">https://en.wikipedia.org/w/index.php?title=Conservation_of_energy&oldid=1274281973</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:Conservation_laws" title="Category:Conservation laws">Conservation laws</a></li><li><a href="/wiki/Category:Energy_(physics)" title="Category:Energy (physics)">Energy (physics)</a></li><li><a href="/wiki/Category:Laws_of_thermodynamics" title="Category:Laws of thermodynamics">Laws of thermodynamics</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:All_articles_with_dead_external_links" title="Category:All articles with dead external links">All articles with dead external links</a></li><li><a href="/wiki/Category:Articles_with_dead_external_links_from_March_2021" title="Category:Articles with dead external links from March 2021">Articles with dead external links from March 2021</a></li><li><a href="/wiki/Category:Articles_with_permanently_dead_external_links" title="Category:Articles with permanently dead external links">Articles with permanently dead external links</a></li><li><a href="/wiki/Category:CS1_maint:_DOI_inactive_as_of_November_2024" title="Category:CS1 maint: DOI inactive as of November 2024">CS1 maint: DOI inactive as of November 2024</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_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_pending_changes_protected_pages" title="Category:Wikipedia pending changes protected pages">Wikipedia pending changes protected pages</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_October_2020" title="Category:Use dmy dates from October 2020">Use dmy dates from October 2020</a></li><li><a href="/wiki/Category:Pages_using_sidebar_with_the_child_parameter" title="Category:Pages using sidebar with the child parameter">Pages using sidebar with the child parameter</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_November_2015" title="Category:Articles needing additional references from November 2015">Articles needing additional references from November 2015</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:Articles_containing_German-language_text" title="Category:Articles containing German-language text">Articles containing German-language text</a></li><li><a href="/wiki/Category:Articles_containing_video_clips" title="Category:Articles containing video clips">Articles containing video clips</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 6 February 2025, at 13:30<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=Conservation_of_energy&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" lang="en" 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-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div 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"> <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> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-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-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Conservation of energy</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>102 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </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-6665bcd6cc-wr77s","wgBackendResponseTime":129,"wgPageParseReport":{"limitreport":{"cputime":"0.857","walltime":"1.080","ppvisitednodes":{"value":4400,"limit":1000000},"postexpandincludesize":{"value":134522,"limit":2097152},"templateargumentsize":{"value":3133,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":15,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":228647,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 864.667 1 -total"," 30.81% 266.395 1 Template:Reflist"," 17.60% 152.159 20 Template:Cite_book"," 12.68% 109.664 1 Template:Continuum_mechanics"," 11.10% 95.984 1 Template:Lang"," 9.63% 83.290 17 Template:Cite_journal"," 6.99% 60.445 1 Template:Short_description"," 6.98% 60.319 1 Template:Authority_control"," 6.34% 54.793 3 Template:Sidebar"," 5.79% 50.047 1 Template:Pp-pc"]},"scribunto":{"limitreport-timeusage":{"value":"0.572","limit":"10.000"},"limitreport-memusage":{"value":23007891,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-7878cd4448-gdl79","timestamp":"20250211200137","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Conservation of energy","url":"https:\/\/en.wikipedia.org\/wiki\/Conservation_of_energy","sameAs":"http:\/\/www.wikidata.org\/entity\/Q11382","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q11382","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":"2002-08-02T23:30:07Z","headline":"law of physics and chemistry"}</script> </body> </html>