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class="vector-toc-numb">2</span> <span>Development of ideas</span> </div> </a> <ul id="toc-Development_of_ideas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mayer's_place_in_the_history_of_physics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mayer's_place_in_the_history_of_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Mayer's place in the history of physics</span> </div> </a> <button aria-controls="toc-Mayer's_place_in_the_history_of_physics-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 Mayer's place in the history of physics subsection</span> </button> <ul id="toc-Mayer's_place_in_the_history_of_physics-sublist" class="vector-toc-list"> <li id="toc-Mayer's_relation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mayer's_relation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Mayer's relation</span> </div> </a> <ul id="toc-Mayer's_relation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Later_life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Later_life"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Later life</span> </div> </a> <ul id="toc-Later_life-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Honors" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Honors"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Honors</span> </div> </a> <ul id="toc-Honors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Works" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Works"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Works</span> </div> </a> <ul id="toc-Works-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">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Julius von Mayer: Difference between revisions</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 44 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-44" 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">44 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%8A%D9%88%D9%84%D9%8A%D9%88%D8%B3_%D9%85%D8%A7%D9%8A%D8%B1" title="يوليوس ماير – Arabic" lang="ar" hreflang="ar" data-title="يوليوس ماير" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DB%8C%D9%88%D9%84%DB%8C%D9%88%D8%B3_%D8%B1%D9%88%D8%A8%D8%B1%D8%AA_%D9%81%D9%88%D9%86_%D9%85%D8%A7%DB%8C%D8%B1" title="یولیوس روبرت فون مایر – South Azerbaijani" lang="azb" hreflang="azb" data-title="یولیوس روبرت فون مایر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AE%D0%BB%D1%96%D1%83%D1%81_%D0%A0%D0%BE%D0%B1%D0%B5%D1%80%D1%82_%D0%9C%D0%B0%D0%B5%D1%80" title="Юліус Роберт Маер – Belarusian" lang="be" hreflang="be" data-title="Юліус Роберт Маер" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%AE%D0%BB%D0%B8%D1%83%D1%81_%D0%A0%D0%BE%D0%B1%D0%B5%D1%80%D1%82_%D1%84%D0%BE%D0%BD_%D0%9C%D0%B0%D0%B9%D0%B5%D1%80" title="Юлиус Роберт фон Майер – Bulgarian" lang="bg" hreflang="bg" data-title="Юлиус Роберт фон Майер" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Catalan" lang="ca" hreflang="ca" data-title="Julius Robert von Mayer" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Czech" lang="cs" hreflang="cs" data-title="Julius Robert von Mayer" 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/Julius_von_Mayer" title="Julius von Mayer – Welsh" lang="cy" hreflang="cy" data-title="Julius von Mayer" 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/Robert_von_Mayer" title="Robert von Mayer – Danish" lang="da" hreflang="da" data-title="Robert von Mayer" 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/Robert_Mayer" title="Robert Mayer – German" lang="de" hreflang="de" data-title="Robert Mayer" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B9%CE%BF%CF%8D%CE%BB%CE%B9%CE%BF%CF%85%CF%82_%CF%86%CE%BF%CE%BD_%CE%9C%CE%AC%CE%B3%CE%B9%CE%B5%CF%81" title="Γιούλιους φον Μάγιερ – Greek" lang="el" hreflang="el" data-title="Γιούλιους φον Μάγιερ" 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/Julius_von_Mayer" title="Julius von Mayer – Spanish" lang="es" hreflang="es" data-title="Julius von Mayer" 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/Julius_von_Mayer" title="Julius von Mayer – Esperanto" lang="eo" hreflang="eo" data-title="Julius von Mayer" 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/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Basque" lang="eu" hreflang="eu" data-title="Julius Robert von Mayer" 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/%DB%8C%D9%88%D9%84%DB%8C%D9%88%D8%B3_%D8%B1%D9%88%D8%A8%D8%B1%D8%AA_%D9%81%D9%88%D9%86_%D9%85%D8%A7%DB%8C%D8%B1" title="یولیوس روبرت فون مایر – Persian" lang="fa" hreflang="fa" data-title="یولیوس روبرت فون مایر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – French" lang="fr" hreflang="fr" data-title="Julius Robert von Mayer" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A8%EB%A6%AC%EC%9A%B0%EC%8A%A4_%EB%A1%9C%EB%B2%A0%EB%A5%B4%ED%8A%B8_%ED%8F%B0_%EB%A7%88%EC%9D%B4%EC%96%B4" title="율리우스 로베르트 폰 마이어 – Korean" lang="ko" hreflang="ko" data-title="율리우스 로베르트 폰 마이어" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%85%D5%B8%D6%82%D5%AC%D5%AB%D5%B8%D6%82%D5%BD_%D5%8C%D5%B8%D5%A2%D5%A5%D6%80%D5%BF_%D5%84%D5%A1%D5%B5%D5%A5%D6%80" title="Յուլիուս Ռոբերտ Մայեր – Armenian" lang="hy" hreflang="hy" data-title="Յուլիուս Ռոբերտ Մայեր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Robert_Mayer" title="Robert Mayer – Croatian" lang="hr" hreflang="hr" data-title="Robert Mayer" 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/Julius_von_Mayer" title="Julius von Mayer – Indonesian" lang="id" hreflang="id" data-title="Julius von Mayer" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Italian" lang="it" hreflang="it" data-title="Julius Robert von Mayer" 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%99%D7%95%D7%9C%D7%99%D7%95%D7%A1_%D7%A8%D7%95%D7%91%D7%A8%D7%98_%D7%A4%D7%95%D7%9F_%D7%9E%D7%90%D7%99%D7%99%D7%A8" title="יוליוס רוברט פון מאייר – Hebrew" lang="he" hreflang="he" data-title="יוליוס רוברט פון מאייר" 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%9C%E0%B3%82%E0%B2%B2%E0%B2%BF%E0%B2%AF%E0%B2%B8%E0%B3%8D_%E0%B2%B0%E0%B2%BE%E0%B2%AC%E0%B2%B0%E0%B3%8D%E0%B2%9F%E0%B3%8D_%E0%B2%AE%E0%B3%87%E0%B2%AF%E0%B2%B0%E0%B3%8D" title="ಜೂಲಿಯಸ್ ರಾಬರ್ಟ್ ಮೇಯರ್ – Kannada" lang="kn" hreflang="kn" data-title="ಜೂಲಿಯಸ್ ರಾಬರ್ಟ್ ಮೇಯರ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%9D%E1%83%91%E1%83%94%E1%83%A0%E1%83%A2_%E1%83%98%E1%83%A3%E1%83%9A%E1%83%98%E1%83%A3%E1%83%A1_%E1%83%9B%E1%83%90%E1%83%98%E1%83%94%E1%83%A0%E1%83%98" title="რობერტ იულიუს მაიერი – Georgian" lang="ka" hreflang="ka" data-title="რობერტ იულიუს მაიერი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Hungarian" lang="hu" hreflang="hu" data-title="Julius Robert von Mayer" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Malagasy" lang="mg" hreflang="mg" data-title="Julius Robert von Mayer" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%8A%D9%88%D9%84%D9%8A%D9%88%D8%B3_%D9%85%D8%A7%D9%8A%D8%B1_(%D8%AF%D9%83%D8%AA%D9%88%D8%B1_%D9%85%D9%86_%D9%85%D9%85%D9%84%D9%83%D8%A9_%DA%A4%D9%88%D8%B1%D8%AA%D9%8A%D9%85%D8%A8%D9%8A%D8%B1%D8%AC)" title="يوليوس ماير (دكتور من مملكة ڤورتيمبيرج) – Egyptian Arabic" lang="arz" hreflang="arz" data-title="يوليوس ماير (دكتور من مملكة ڤورتيمبيرج)" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Dutch" lang="nl" hreflang="nl" data-title="Julius Robert von Mayer" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ja.wikipedia.org/wiki/%E3%83%A6%E3%83%AA%E3%82%A6%E3%82%B9%E3%83%BB%E3%83%AD%E3%83%99%E3%83%AB%E3%83%88%E3%83%BB%E3%83%95%E3%82%A9%E3%83%B3%E3%83%BB%E3%83%9E%E3%82%A4%E3%83%A4%E3%83%BC" title="ユリウス・ロベルト・フォン・マイヤー – Japanese" lang="ja" hreflang="ja" data-title="ユリウス・ロベルト・フォン・マイヤー" 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 badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://no.wikipedia.org/wiki/Robert_Mayer" title="Robert Mayer – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Robert Mayer" 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/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Julius Robert von Mayer" 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-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Julius_Robert_Mayer" title="Julius Robert Mayer – Piedmontese" lang="pms" hreflang="pms" data-title="Julius Robert Mayer" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Polish" lang="pl" hreflang="pl" data-title="Julius Robert von Mayer" 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/Julius_von_Mayer" title="Julius von Mayer – Portuguese" lang="pt" hreflang="pt" data-title="Julius von Mayer" 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/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Romanian" lang="ro" hreflang="ro" data-title="Julius Robert von Mayer" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%B5%D1%80,_%D0%AE%D0%BB%D0%B8%D1%83%D1%81_%D0%A0%D0%BE%D0%B1%D0%B5%D1%80%D1%82_%D1%84%D0%BE%D0%BD" title="Майер, Юлиус Роберт фон – Russian" lang="ru" hreflang="ru" data-title="Майер, Юлиус Роберт фон" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Slovak" lang="sk" hreflang="sk" data-title="Julius Robert von Mayer" 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/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Slovenian" lang="sl" hreflang="sl" data-title="Julius Robert von Mayer" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Robert_Mayer" title="Robert Mayer – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Robert Mayer" 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/Julius_Robert_von_Mayer" title="Julius Robert von Mayer – Finnish" lang="fi" hreflang="fi" data-title="Julius Robert von Mayer" 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/Robert_Mayer" title="Robert Mayer – Swedish" lang="sv" hreflang="sv" data-title="Robert Mayer" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A2%E0%B8%B9%E0%B8%A5%E0%B8%B5%E0%B8%AD%E0%B8%B8%E0%B8%AA_%E0%B8%9F%E0%B9%87%E0%B8%AD%E0%B8%99_%E0%B9%84%E0%B8%A1%E0%B9%80%E0%B8%AD%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="ยูลีอุส ฟ็อน ไมเออร์ – Thai" lang="th" hreflang="th" data-title="ยูลีอุส ฟ็อน ไมเออร์" data-language-autonym="ไทย" 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He grew up in Heilbronn. After completing his ''[[Abitur]]'', he studied medicine at the [[University of Tübingen]], where he was a member of the ''Corps Guestphalia'', a [[German Student Corps]]. During 1838 he attained his doctorate as well as passing the ''[[Education in Germany|Staatsexamen]]''. After a stay in Paris (1839/40) he left as a ship's physician on a [[Netherlands|Dutch]] three-mast [[sailing ship]] for a journey to [[Jakarta]].</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>Von Mayer was born on November 25, 1814 in [[Heilbronn]], [[Württemberg]] ([[Baden-Württemberg]], modern day Germany), the son of a [[pharmacist]]. He grew up in Heilbronn. After completing his ''[[Abitur]]'', he studied medicine at the [[University of Tübingen]], where he was a member of the ''Corps Guestphalia'', a [[German Student Corps]]. During 1838 he attained his doctorate as well as passing the ''[[Education in Germany|Staatsexamen]]''. After a stay in Paris (1839/40) he left as a ship's physician on a [[Netherlands|Dutch]] three-mast [[sailing ship]] for a journey to [[Jakarta]].</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Revision as of 21:40, 12 May 2019</h2> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Julius Robert von Mayer</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Julius_Robert_Mayer_von_Friedrich_Berrer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Julius_Robert_Mayer_von_Friedrich_Berrer.jpg/220px-Julius_Robert_Mayer_von_Friedrich_Berrer.jpg" decoding="async" width="220" height="355" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Julius_Robert_Mayer_von_Friedrich_Berrer.jpg/330px-Julius_Robert_Mayer_von_Friedrich_Berrer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Julius_Robert_Mayer_von_Friedrich_Berrer.jpg/440px-Julius_Robert_Mayer_von_Friedrich_Berrer.jpg 2x" data-file-width="650" data-file-height="1050" /></a></span><div class="infobox-caption">Julius Robert von Mayer</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">November 25, 1814<br /><div style="display:inline" class="birthplace"><a href="/wiki/Heilbronn" title="Heilbronn">Heilbronn</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">March 20, 1878<span style="display:none">(1878-03-20)</span> (aged 63)<br /><div style="display:inline" class="deathplace">Heilbronn</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category">Germany</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_T%C3%BCbingen" title="University of Tübingen">University of Tübingen</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First law of thermodynamics</a> <a href="/wiki/Mayer%27s_reagent" title="Mayer's reagent">Mayer's Reagent</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> (1871)</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Physics" title="Physics">Physics</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Julius Robert Mayer</b> (November 25, 1814 – March 20, 1878) was a German <a href="/wiki/Physician" title="Physician">physician</a>, <a href="/wiki/Chemist" title="Chemist">chemist</a> and <a href="/wiki/Physicist" title="Physicist">physicist</a> and one of the founders of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>. He is best known for enunciating in 1841 one of the original statements of the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> or what is now known as one of the first versions of the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a>, namely that "energy can be neither created nor destroyed".<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In 1842, Mayer described the vital <a href="/wiki/Chemistry" title="Chemistry">chemical process</a> now referred to as <a href="/wiki/Oxidation" class="mw-redirect" title="Oxidation">oxidation</a> as the primary source of <a href="/wiki/Energy" title="Energy">energy</a> for any <a href="/wiki/Life" title="Life">living creature</a>. His achievements were overlooked and priority for the discovery of the <i><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">mechanical equivalent of heat</a></i> was attributed to <a href="/wiki/James_Joule" class="mw-redirect" title="James Joule">James Joule</a> in the following year. He also proposed that <a href="/wiki/Plants" class="mw-redirect" title="Plants">plants</a> convert light into chemical energy. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life">Early life</h2></div> <p>si tu le isso voçe é um cu crambulhoso Von Mayer was born on November 25, 1814 in <a href="/wiki/Heilbronn" title="Heilbronn">Heilbronn</a>, <a href="/wiki/W%C3%BCrttemberg" title="Württemberg">Württemberg</a> (<a href="/wiki/Baden-W%C3%BCrttemberg" title="Baden-Württemberg">Baden-Württemberg</a>, modern day Germany), the son of a <a href="/wiki/Pharmacist" title="Pharmacist">pharmacist</a>. He grew up in Heilbronn. After completing his <i><a href="/wiki/Abitur" title="Abitur">Abitur</a></i>, he studied medicine at the <a href="/wiki/University_of_T%C3%BCbingen" title="University of Tübingen">University of Tübingen</a>, where he was a member of the <i>Corps Guestphalia</i>, a <a href="/wiki/German_Student_Corps" title="German Student Corps">German Student Corps</a>. During 1838 he attained his doctorate as well as passing the <i><a href="/wiki/Education_in_Germany" title="Education in Germany">Staatsexamen</a></i>. After a stay in Paris (1839/40) he left as a ship's physician on a <a href="/wiki/Netherlands" title="Netherlands">Dutch</a> three-mast <a href="/wiki/Sailing_ship" title="Sailing ship">sailing ship</a> for a journey to <a href="/wiki/Jakarta" title="Jakarta">Jakarta</a>. </p><p>Although he had hardly been interested before this journey in <a href="/wiki/Physical_phenomenon" class="mw-redirect" title="Physical phenomenon">physical phenomena</a>, his observation that storm-whipped waves are warmer than the calm sea started him thinking about the <a href="/wiki/Physical_law" class="mw-redirect" title="Physical law">physical laws</a>, in particular about the physical phenomenon of warmth and the question <i>whether the directly developed heat alone (the heat of combustion), or the sum of the quantities of heat developed in direct and indirect ways are to be accounted for in the burning process</i>. After his return in February 1841 Mayer dedicated his efforts to solve this problem. </p><p>In 1841 he settled in <a href="/wiki/Heilbronn" title="Heilbronn">Heilbronn</a> and married. </p> <div class="mw-heading mw-heading2"><h2 id="Development_of_ideas">Development of ideas</h2></div> <p>Even as a young child, Mayer showed an intense interest with various mechanical mechanisms. He was a young man who performed various experiments of the physical and chemical variety. In fact, one of his favorite hobbies was creating various types of electrical devices and air pumps. It was obvious that he was intelligent. Hence, Mayer attended Eberhard-Karls University in May 1832. He studied medicine during his time there. </p><p>In 1837, he and some of his friends were arrested for wearing the <a href="/wiki/Couleur" title="Couleur">couleurs</a> of a forbidden organization. The consequences for this arrest included a one year expulsion from the college and a brief period of incarceration. This diversion sent Mayer traveling to Switzerland, France, and the <a href="/wiki/Dutch_East_Indies" title="Dutch East Indies">Dutch East Indies</a>. Mayer drew some additional interest in mathematics and engineering from his friend Carl Baur through private tutoring. In 1841, Mayer returned to Heilbronn to practice medicine, but physics became his new passion. </p><p>In June 1841, he completed his first scientific paper entitled "On the Quantitative and Qualitative Determination of Forces". It was largely ignored by other professionals in the area. Then, Mayer became interested in the area of heat and its motion. He presented a value in numerical terms for the mechanical equivalent of heat. He also was the first person to describe the vital chemical process now referred to as oxidation as the primary source of energy for any living creature. </p><p>In 1848 he calculated that in the absence of a source of energy the Sun would cool down in only 5000 years, and he suggested that the impact of meteorites kept it hot.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Since he was not taken seriously at the time, his achievements were overlooked and credit was given to <a href="/wiki/James_Joule" class="mw-redirect" title="James Joule">James Joule</a>. Mayer almost committed suicide after he discovered this fact. He spent some time in mental institutions to recover from this and the loss of some of his children. Several of his papers were published due to the advanced nature of the physics and chemistry. He was awarded an honorary doctorate in 1859 by the philosophical faculty at the <a href="/wiki/University_of_T%C3%BCbingen" title="University of Tübingen">University of Tübingen</a>. His overlooked work was revived in 1862 by fellow physicist <a href="/wiki/John_Tyndall" title="John Tyndall">John Tyndall</a> in a lecture at the London Royal Institution. In July 1867, Mayer published "Die Mechanik der Wärme." This publication dealt with the mechanics of heat and its motion. On November 5, 1867, Mayer was awarded personal nobility by the <a href="/wiki/Kingdom_of_W%C3%BCrttemberg" title="Kingdom of Württemberg">Kingdom of Württemberg</a> (von Mayer) which is the German equivalent of a British knighthood. Julius Robert von Mayer died from <a href="/wiki/Tuberculosis" title="Tuberculosis">tuberculosis</a> on March 20, 1878 in Germany. </p> <div class="mw-heading mw-heading2"><h2 id="Mayer's_place_in_the_history_of_physics"><span id="Mayer.27s_place_in_the_history_of_physics"></span>Mayer's place in the history of physics</h2></div> <p>After <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a> stating it for caloric, Mayer was the first person to state the law of the conservation of energy, one of the most fundamental tenets of modern day physics. The law of the conservation of energy states that the total mechanical energy of a system remains constant in any isolated system of objects that interact with each other only by way of forces that are <a href="/wiki/Conservative_force" title="Conservative force">conservative</a>. </p><p>Mayer's first attempt at stating the conservation of energy was a paper he sent to <a href="/wiki/Johann_Christian_Poggendorff" title="Johann Christian Poggendorff">Johann Christian Poggendorff</a>'s <i><a href="/wiki/Annalen_der_Physik" title="Annalen der Physik">Annalen der Physik</a></i>, in which he postulated a conservation of force (<i>Erhaltungssatz der Kraft</i>). However, owing to Mayer's lack of advanced training in <a href="/wiki/Physics" title="Physics">physics</a>, it contained some fundamental mistakes and was not published. Mayer continued to pursue the idea steadfastly and argued with the <a href="/wiki/T%C3%BCbingen" title="Tübingen">Tübingen</a> physics professor <a href="/wiki/Johann_Gottlieb_N%C3%B6rremberg" title="Johann Gottlieb Nörremberg">Johann Gottlieb Nörremberg</a>, who rejected his <a href="/wiki/Hypothesis" title="Hypothesis">hypothesis</a>. Nörremberg did, however, give Mayer a number of valuable suggestions on how the idea could be examined experimentally; for example, if <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> transforms into heat energy, water should be warmed by <a href="/wiki/Oscillation" title="Oscillation">vibration</a>. </p><p>Mayer not only performed this demonstration, but determined also the quantitative factor of the transformation, calculating the mechanical equivalent of heat. The result of his investigations was published 1842 in the May edition of <a href="/wiki/Justus_von_Liebig" title="Justus von Liebig">Justus von Liebig</a>'s <i><a href="/wiki/Annalen_der_Chemie_und_Pharmacie" class="mw-redirect" title="Annalen der Chemie und Pharmacie">Annalen der Chemie und Pharmacie</a></i>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><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> It was translated as <i>Remarks on the Forces of Inorganic Nature</i><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> In his booklet <i>Die organische Bewegung im Zusammenhang mit dem Stoffwechsel</i> (<i>The Organic Movement in Connection with the Metabolism</i>, 1845) he specified the numerical value of the mechanical equivalent of heat: at first as 365 <a href="/wiki/Kilogram-force" title="Kilogram-force">kgf</a>·m/kcal,<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> later as 425 kgf·m/kcal; the modern values are 4.184 <a href="/wiki/Kilojoule" class="mw-redirect" title="Kilojoule">kJ</a>/kcal (426.6 kgf·m/kcal) for the thermochemical calorie and 4.1868 kJ/kcal (426.9 kgf·m/kcal) for the international steam table calorie. </p><p>This relation implies that, although work and heat are different forms of energy, they can be transformed into one another. This law is called the first law of the <a href="/wiki/Caloric_theory" title="Caloric theory">caloric theory</a> and led to the formulation of the general principle of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>, definitively stated by <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> in 1847. </p> <div class="mw-heading mw-heading3"><h3 id="Mayer's_relation"><span id="Mayer.27s_relation"></span>Mayer's relation</h3></div> <p>Mayer derived a relation between specific heat at constant pressure and the specific heat at constant volume for an ideal gas. The relation is: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{P,m}-C_{V,m}=R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{P,m}-C_{V,m}=R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26add6f14036fdfed49f798bd27f11469f8ac34c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.789ex; height:2.843ex;" alt="{\displaystyle C_{P,m}-C_{V,m}=R}"></span>, </p><p>where <i>C<sub>P,m</sub></i> is the <a href="/wiki/Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> at constant <a href="/wiki/Pressure" title="Pressure">pressure</a>, <i>C<sub>V,m</sub></i> is the specific heat at constant <a href="/wiki/Volume" title="Volume">volume</a> and <i>R</i> is the <a href="/wiki/Gas_constant" title="Gas constant">gas constant</a>. </p><p>For more general homogeneous substances, not just ideal gases, the difference takes the form, #do={reset </p> <pre> type= erase argument} done{} {true:=if][ text:says= /beta_{T}}\,</math> </pre> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{P}-C_{V}=VT{\frac {\alpha ^{2}}{\beta _{T}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mi>V</mi> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{P}-C_{V}=VT{\frac {\alpha ^{2}}{\beta _{T}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c390cf97087a366531090b0dcbaf13d8fda545a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.577ex; height:6.176ex;" alt="{\displaystyle C_{P}-C_{V}=VT{\frac {\alpha ^{2}}{\beta _{T}}}\,}"></span></dd></dl> <p>(see <a href="/wiki/Relations_between_heat_capacities" title="Relations between heat capacities">relations between heat capacities</a>), 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 C_{P}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{P}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/483b2a7b48dc2ca6e233a59b3f44049563b94302" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.128ex; height:2.509ex;" alt="{\displaystyle C_{P}}"></span> is the heat capacity of a body at constant pressure, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c18988639f2937d3fe4dc00dfa0b0bd7e0bec1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.158ex; height:2.509ex;" alt="{\displaystyle C_{V}}"></span> is the heat capacity at constant volume, <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/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> is the volume, <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 temperature, <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 \alpha _{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bae4c2d7a1f5097997a285df47dd01fb03ac1dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.877ex; height:2.009ex;" alt="{\displaystyle \alpha _{T}}"></span> is the <a href="/wiki/Coefficient_of_thermal_expansion" class="mw-redirect" title="Coefficient of thermal expansion">thermal expansion coefficient</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 \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> is the isothermal <a href="/wiki/Compressibility" title="Compressibility">compressibility</a>. </p><p>From this relation, several inferences can be made:<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> <ul><li>Since isothermal compressibility <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 \beta _{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta _{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f2855fc59047bc00f5bdedbcad68550a7ac6d13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.705ex; height:2.509ex;" alt="{\displaystyle \beta _{T}}"></span> is positive for all phases and the square of thermal expansion coefficient <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 {\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6289622b3b197c568f6e73e678814e9cb4c8a81b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle {\alpha }}"></span> is a positive quantity or zero, the specific heat at constant-pressure is always greater than or equal to specific heat at constant-volume.</li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{P,m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{P,m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66ce93a42885dc1ee6673533cf42357aac9ce953" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.028ex; height:2.843ex;" alt="{\displaystyle C_{P,m}}"></span> ≥ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{V,m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{V,m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/582a605ab6348b7d7caba07b63c2647fc53c0a50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.058ex; height:2.843ex;" alt="{\displaystyle C_{V,m}}"></span></dd></dl> <ul><li>As the <a href="/wiki/Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a> of the system approaches zero, the difference between C<sub>P,m</sub> and C<sub>V,m</sub> also approaches zero.</li> <li>For <a href="/wiki/Incompressible" class="mw-redirect" title="Incompressible">incompressible</a> substances, C<sub>P,m</sub> and C<sub>V,m</sub> are identical. Also for substances that are nearly incompressible, such as solids and liquids, the difference between the two specific heats is negligible.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Later_life">Later life</h2></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">For dispute over priority with Joule, see main article <a href="/wiki/Mechanical_equivalent_of_heat#Priority" title="Mechanical equivalent of heat">Mechanical equivalent of heat: Priority</a>.</div> <p>Mayer was aware of the importance of his discovery, but his inability to express himself scientifically led to degrading<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (March 2015)">clarification needed</span></a></i>]</sup> speculation and resistance from the scientific establishment. Contemporary physicists rejected his principle of conservation of energy, and even acclaimed physicists <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> and <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> viewed his ideas with hostility. The former doubted Mayer's qualifications in physical questions, and a bitter dispute over priority developed with the latter. </p><p>In 1848 two of his children died rapidly in succession, and Mayer's <a href="/wiki/Mental_health" title="Mental health">mental health</a> deteriorated. He attempted suicide on May 18, 1850 and was committed to a mental institution.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2014)">citation needed</span></a></i>]</sup> After he was released, he was a broken man and only timidly re-entered public life in 1860. However, in the meantime, his scientific fame had grown and he received a late appreciation of his achievement, although perhaps at a stage where he was no longer able to enjoy it. </p><p>He continued to work vigorously as a physician until his death. </p> <div class="mw-heading mw-heading2"><h2 id="Honors">Honors</h2></div> <ul><li>1840 Julius von Mayer received the Knight Cross of the <a href="/wiki/Order_of_the_Crown_(W%C3%BCrttemberg)" title="Order of the Crown (Württemberg)">Order of the Crown (Württemberg)</a>.</li> <li>1869 Mayer received the <a href="/wiki/Poncelet_Prize" title="Poncelet Prize"><i>prix Poncelet</i></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></li> <li>The <i>Robert-Mayer-Gymnasium</i> and the <i>Robert-Mayer-Volks- und Schulsternwarte</i> in <a href="/wiki/Heilbronn" title="Heilbronn">Heilbronn</a> bear his name.</li></ul> <p>In Chemistry, he invented the <a href="/wiki/Mayer%27s_reagent" title="Mayer's reagent">Mayer's reagent</a> which is used in detecting alkaloids. </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2></div> <ul><li><i>Ueber das Santonin : eine Inaugural-Dissertation, welche zur Erlangung der Doctorwürde in der Medicin & Chirurgie unter dem Praesidium von Wilhelm Rapp im July 1838 der öffentlichen Prüfung vorlegt Julius Robert Mayer</i> . M. Müller, Heilbronn 1838 <a rel="nofollow" class="external text" href="http://nbn-resolving.de/urn:nbn:de:hbz:061:2-19678">Digital edition</a> by the <a href="/wiki/University_and_State_Library_D%C3%BCsseldorf" title="University and State Library Düsseldorf">University and State Library Düsseldorf</a></li></ul> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Mayer, Robert (1841). Paper: 'Remarks on the Forces of Nature"; as quoted in: Lehninger, A. (1971). Biogenergetics – the Molecular Basis of Biological Energy Transformations, 2nd. Ed. London: The Benjamin/Cummings Publishing Company. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZGadhLuFIRcC&focus=searchwithinvolume&q=Robert+Mayer">First Law</a></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"><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 class="citation web cs1">"30+ Variations of the 1st Law of Thermodynamics". IoHT Publications.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=30%2B+Variations+of+the+1st+Law+of+Thermodynamics&rft.pub=IoHT+Publications&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Missing or empty <code class="cs1-code">|url=</code> (<a href="/wiki/Help:CS1_errors#cite_web_url" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHellemansBryan_Bunch1988" class="citation book cs1">Hellemans, Alexander; Bryan Bunch (1988). <i>The Timetables of Science</i>. New York, New York: Simon and Schuster. p. 316. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-671-62130-8" title="Special:BookSources/978-0-671-62130-8"><bdi>978-0-671-62130-8</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+Timetables+of+Science&rft.place=New+York%2C+New+York&rft.pages=316&rft.pub=Simon+and+Schuster&rft.date=1988&rft.isbn=978-0-671-62130-8&rft.aulast=Hellemans&rft.aufirst=Alexander&rft.au=Bryan+Bunch&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">J. R. von Mayer, <i>Annalen der Chemie und Pharmacie</i> <b>43</b>, 233 (1842).</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="CITEREFMayer1842" class="citation journal cs1">Mayer, J. R. (1842). "Bemerkungen über die Kräfte der unbelebten Natur". <i>Annalen der Chemie und Pharmacie</i>. <b>42</b> (2): 233–240. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fjlac.18420420212">10.1002/jlac.18420420212</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fumn.319510020751527">2027/umn.319510020751527</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Chemie+und+Pharmacie&rft.atitle=Bemerkungen+%C3%BCber+die+Kr%C3%A4fte+der+unbelebten+Natur&rft.volume=42&rft.issue=2&rft.pages=233-240&rft.date=1842&rft_id=info%3Ahdl%2F2027%2Fumn.319510020751527&rft_id=info%3Adoi%2F10.1002%2Fjlac.18420420212&rft.aulast=Mayer&rft.aufirst=J.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" 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="CITEREFMayer1862" class="citation journal cs1">Mayer, J R (1862). <a rel="nofollow" class="external text" href="https://www.biodiversitylibrary.org/item/121900#page/385/mode/1up">"Remarks on the Forces of Inorganic Nature"</a>. <i>Philosophical Magazine</i>. 4. <b>24</b> (162): 371–377. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786446208643372">10.1080/14786446208643372</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=Remarks+on+the+Forces+of+Inorganic+Nature&rft.volume=24&rft.issue=162&rft.pages=371-377&rft.date=1862&rft_id=info%3Adoi%2F10.1080%2F14786446208643372&rft.aulast=Mayer&rft.aufirst=J+R&rft_id=https%3A%2F%2Fwww.biodiversitylibrary.org%2Fitem%2F121900%23page%2F385%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span></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">The <a href="/wiki/Physical_unit" class="mw-redirect" title="Physical unit">physical unit</a> kgf·m/kcal measures mechanical energy, in <a href="/wiki/Kilogram-force" title="Kilogram-force">kgf</a>·m, against heat energy, in <a href="/wiki/Calorie" title="Calorie">kcal</a>. The mechanical energy is measured on the basis of raising a <a href="/wiki/Mass" title="Mass">mass</a> of <i>m</i> kg to a height of <i>h</i> m against Earth's gravity. This is equivalent to an energy of <i>mgh</i> <a href="/wiki/Joule" title="Joule">joules</a>, where <i>g</i> is the <a href="/wiki/Standard_gravity" title="Standard gravity">standard gravity</a>. Thus, 1 kgf·m/kcal = 9.80665 J/kcal.</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="CITEREFBoles2010" class="citation book cs1">Boles, Yunus A. Çengel, Michael A. (2010-01-25). <i>Thermodynamics : an engineering approach</i> (7th ed.). New York: McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-736674-2" title="Special:BookSources/978-0-07-736674-2"><bdi>978-0-07-736674-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+%3A+an+engineering+approach&rft.place=New+York&rft.edition=7th&rft.pub=McGraw-Hill&rft.date=2010-01-25&rft.isbn=978-0-07-736674-2&rft.aulast=Boles&rft.aufirst=Yunus+A.+%C3%87engel%2C+Michael+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</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 class="citation book cs1 cs1-prop-long-vol">"Prix". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ep5DAQAAIAAJ&pg=PA974"><i>Comptes rendus hebdomadaires des séances de l'Académie des sciences</i></a>. Vol. Tome 71, Juillet à Décembre 1870. Paris: Gauthier-Villars. 1870. p. 974.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Prix&rft.btitle=Comptes+rendus+hebdomadaires+des+s%C3%A9ances+de+l%27Acad%C3%A9mie+des+sciences&rft.place=Paris&rft.pages=974&rft.pub=Gauthier-Villars&rft.date=1870&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DEp5DAQAAIAAJ%26pg%3DPA974&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Julius_von_Mayer" class="extiw" title="q:Special:Search/Julius von Mayer">Julius von Mayer</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has the text of the <a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">1911 <i>Encyclopædia Britannica</i></a> article "<span style="font-weight:bold;"><a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Mayer,_Julius_Robert" class="extiw" title="wikisource:1911 Encyclopædia Britannica/Mayer, Julius Robert">Mayer, Julius Robert</a></span>".</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCaneva1993" class="citation book cs1">Caneva, Kenneth L. (1993). <i>Robert Mayer and the Conservation of Energy</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08758-0" title="Special:BookSources/978-0-691-08758-0"><bdi>978-0-691-08758-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Robert+Mayer+and+the+Conservation+of+Energy&rft.pub=Princeton+University+Press&rft.date=1993&rft.isbn=978-0-691-08758-0&rft.aulast=Caneva&rft.aufirst=Kenneth+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJulius+von+Mayer" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" 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title="Copley Medal">Copley Medallists</a> (1851–1900)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Richard_Owen" title="Richard Owen">Richard Owen</a> (1851)</span></li> <li><span class="nowrap"><a href="/wiki/Alexander_von_Humboldt" title="Alexander von Humboldt">Alexander von Humboldt</a> (1852)</span></li> <li><span class="nowrap"><a href="/wiki/Heinrich_Wilhelm_Dove" title="Heinrich Wilhelm Dove">Heinrich Wilhelm Dove</a> (1853)</span></li> <li><span class="nowrap"><a href="/wiki/Johannes_Peter_M%C3%BCller" title="Johannes Peter Müller">Johannes Peter Müller</a> (1854)</span></li> <li><span class="nowrap"><a href="/wiki/L%C3%A9on_Foucault" title="Léon Foucault">Léon Foucault</a> (1855)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Milne-Edwards" title="Henri Milne-Edwards">Henri Milne-Edwards</a> (1856)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Eug%C3%A8ne_Chevreul" title="Michel Eugène Chevreul">Michel Eugène Chevreul</a> (1857)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Lyell" title="Charles Lyell">Charles Lyell</a> (1858)</span></li> <li><span class="nowrap"><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Wilhelm Eduard Weber</a> (1859)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a> (1860)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Agassiz" title="Louis Agassiz">Louis Agassiz</a> (1861)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Thomas Graham</a> (1862)</span></li> <li><span class="nowrap"><a href="/wiki/Adam_Sedgwick" title="Adam Sedgwick">Adam Sedgwick</a> (1863)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Darwin" title="Charles Darwin">Charles Darwin</a> (1864)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Chasles" title="Michel Chasles">Michel Chasles</a> (1865)</span></li> <li><span class="nowrap"><a href="/wiki/Julius_Pl%C3%BCcker" title="Julius Plücker">Julius Plücker</a> (1866)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Ernst_von_Baer" title="Karl Ernst von Baer">Karl Ernst von Baer</a> (1867)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Wheatstone" title="Charles Wheatstone">Charles Wheatstone</a> (1868)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Victor_Regnault" title="Henri Victor Regnault">Henri Victor Regnault</a> (1869)</span></li> <li><span class="nowrap"><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> (1870)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">Julius Robert von Mayer</a> (1871)</span></li> <li><span class="nowrap"><a href="/wiki/Friedrich_W%C3%B6hler" title="Friedrich Wöhler">Friedrich Wöhler</a> (1872)</span></li> <li><span class="nowrap"><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> (1873)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Pasteur" title="Louis Pasteur">Louis Pasteur</a> (1874)</span></li> <li><span class="nowrap"><a href="/wiki/August_Wilhelm_von_Hofmann" title="August Wilhelm von Hofmann">August Wilhelm von Hofmann</a> (1875)</span></li> <li><span class="nowrap"><a href="/wiki/Claude_Bernard" title="Claude Bernard">Claude Bernard</a> (1876)</span></li> <li><span class="nowrap"><a href="/wiki/James_Dwight_Dana" title="James Dwight Dana">James Dwight Dana</a> (1877)</span></li> <li><span class="nowrap"><a href="/wiki/Jean-Baptiste_Boussingault" title="Jean-Baptiste Boussingault">Jean-Baptiste Boussingault</a> (1878)</span></li> <li><span class="nowrap"><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> (1879)</span></li> <li><span class="nowrap"><a href="/wiki/James_Joseph_Sylvester" title="James Joseph Sylvester">James Joseph Sylvester</a> (1880)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Adolphe_Wurtz" title="Charles Adolphe Wurtz">Charles Adolphe Wurtz</a> (1881)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Cayley" title="Arthur Cayley">Arthur Cayley</a> (1882)</span></li> <li><span class="nowrap"><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">William Thomson</a> (1883)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Ludwig" title="Carl Ludwig">Carl Ludwig</a> (1884)</span></li> <li><span class="nowrap"><a href="/wiki/August_Kekul%C3%A9" title="August Kekulé">Friedrich August Kekulé von Stradonitz</a> (1885)</span></li> <li><span class="nowrap"><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Franz Ernst Neumann</a> (1886)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_Dalton_Hooker" title="Joseph Dalton Hooker">Joseph Dalton Hooker</a> (1887)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Henry_Huxley" title="Thomas Henry Huxley">Thomas Henry Huxley</a> (1888)</span></li> <li><span class="nowrap"><a href="/wiki/George_Salmon" title="George Salmon">George Salmon</a> (1889)</span></li> <li><span class="nowrap"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a> (1890)</span></li> <li><span class="nowrap"><a href="/wiki/Stanislao_Cannizzaro" title="Stanislao Cannizzaro">Stanislao Cannizzaro</a> (1891)</span></li> <li><span class="nowrap"><a href="/wiki/Rudolf_Virchow" title="Rudolf Virchow">Rudolf Virchow</a> (1892)</span></li> <li><span class="nowrap"><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">George Gabriel Stokes</a> (1893)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Frankland" title="Edward Frankland">Edward Frankland</a> (1894)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> (1895)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Gegenbaur" title="Carl Gegenbaur">Carl Gegenbaur</a> (1896)</span></li> <li><span class="nowrap"><a href="/wiki/Albert_von_K%C3%B6lliker" title="Albert von Kölliker">Albert von Kölliker</a> (1897)</span></li> <li><span class="nowrap"><a href="/wiki/William_Huggins" title="William Huggins">William Huggins</a> (1898)</span></li> <li><span class="nowrap"><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">John William Strutt</a> (1899)</span></li> <li><span class="nowrap"><a href="/wiki/Marcellin_Berthelot" title="Marcellin Berthelot">Marcellin Berthelot</a> (1900)</span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q57171#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q57171#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q57171#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000081431283">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/64050667">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/139151/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJmXKcb3B6GVFkWxdrgVG3">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118579584">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n84806346">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12185921x">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12185921x">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35336660">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=nlk20010098505&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/1773864">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p070749116">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90600409">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=233529">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/gdsw0pr0218j379">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810566503305606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007265135505171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:mayer.robert">zbMATH</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/916437">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118579584.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118579584">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/083853790">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" 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