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id="toc-Life_and_work-sublist" class="vector-toc-list"> <li id="toc-Kirchhoff's_circuit_laws" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kirchhoff's_circuit_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Kirchhoff's circuit laws</span> </div> </a> <ul id="toc-Kirchhoff's_circuit_laws-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kirchhoff's_three_laws_of_spectroscopy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kirchhoff's_three_laws_of_spectroscopy"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Kirchhoff's three laws of spectroscopy</span> </div> </a> <ul id="toc-Kirchhoff's_three_laws_of_spectroscopy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kirchhoff's_law_of_thermal_radiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kirchhoff's_law_of_thermal_radiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Kirchhoff's law of thermal radiation</span> </div> </a> <ul id="toc-Kirchhoff's_law_of_thermal_radiation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kirchhoff's_law_of_thermochemistry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kirchhoff's_law_of_thermochemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Kirchhoff's law of thermochemistry</span> </div> </a> <ul id="toc-Kirchhoff's_law_of_thermochemistry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kirchhoff's_theorem_in_graph_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kirchhoff's_theorem_in_graph_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Kirchhoff's theorem in graph theory</span> </div> </a> <ul id="toc-Kirchhoff's_theorem_in_graph_theory-sublist" class="vector-toc-list"> </ul> </li> </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">2</span> <span>Works</span> </div> </a> <ul id="toc-Works-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">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">5</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">6</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-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">7</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">8</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">Gustav Kirchhoff</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 84 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-84" 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">84 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/%D8%BA%D9%88%D8%B3%D8%AA%D8%A7%D9%81_%D8%B1%D9%88%D8%A8%D8%B1%D8%AA_%D9%83%D9%8A%D8%B1%D8%B4%D9%87%D9%88%D9%81" title="غوستاف روبرت كيرشهوف – Arabic" lang="ar" hreflang="ar" data-title="غوستاف روبرت كيرشهوف" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Asturian" lang="ast" hreflang="ast" data-title="Gustav Kirchhoff" 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/Qustav_Kirxhof" title="Qustav Kirxhof – Azerbaijani" lang="az" hreflang="az" data-title="Qustav Kirxhof" 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/%D9%82%D9%88%D8%B3%D8%AA%D8%A7%D9%88_%DA%A9%DB%8C%D8%B1%D8%B4%D9%87%D9%81" title="قوستاو کیرشهف – South Azerbaijani" lang="azb" hreflang="azb" data-title="قوستاو کیرشهف" 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%97%E0%A7%81%E0%A6%B8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%AB_%E0%A6%95%E0%A6%BF%E0%A6%B0%E0%A6%B6%E0%A6%AB" title="গুস্টাফ কিরশফ – Bangla" lang="bn" hreflang="bn" data-title="গুস্টাফ কিরশফ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D1%83%D1%81%D1%82%D0%B0%D1%9E_%D0%9A%D1%96%D1%80%D1%85%D0%B3%D0%BE%D1%84" title="Густаў Кірхгоф – Belarusian" lang="be" hreflang="be" data-title="Густаў Кірхгоф" 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%93%D1%83%D1%81%D1%82%D0%B0%D1%9E_%D0%9A%D1%96%D1%80%D1%85%D0%B3%D0%BE%D1%84" title="Густаў Кірхгоф – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Густаў Кірхгоф" 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%93%D1%83%D1%81%D1%82%D0%B0%D0%B2_%D0%9A%D0%B8%D1%80%D1%85%D0%BE%D1%84" title="Густав Кирхоф – Bulgarian" lang="bg" hreflang="bg" data-title="Густав Кирхоф" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Bosnian" lang="bs" hreflang="bs" data-title="Gustav Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Catalan" lang="ca" hreflang="ca" data-title="Gustav Robert Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Czech" lang="cs" hreflang="cs" data-title="Gustav Kirchhoff" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Danish" lang="da" hreflang="da" data-title="Gustav Robert Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – German" lang="de" hreflang="de" data-title="Gustav Robert Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Estonian" lang="et" hreflang="et" data-title="Gustav Kirchhoff" 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%93%CE%BA%CE%BF%CF%8D%CF%83%CF%84%CE%B1%CE%B2_%CE%9A%CE%AF%CF%81%CF%87%CE%BF%CF%86" title="Γκούσταβ Κίρχοφ – Greek" lang="el" hreflang="el" data-title="Γκούσταβ Κίρχοφ" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Spanish" lang="es" hreflang="es" data-title="Gustav Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Esperanto" lang="eo" hreflang="eo" data-title="Gustav Robert Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Basque" lang="eu" hreflang="eu" data-title="Gustav Robert Kirchhoff" 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/%DA%AF%D9%88%D8%B3%D8%AA%D8%A7%D9%88_%DA%A9%DB%8C%D8%B1%D8%B4%D9%87%D9%81" title="گوستاو کیرشهف – Persian" lang="fa" hreflang="fa" data-title="گوستاو کیرشهف" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – French" lang="fr" hreflang="fr" data-title="Gustav Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Irish" lang="ga" hreflang="ga" data-title="Gustav Kirchhoff" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Gustav Kirchhoff" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Galician" lang="gl" hreflang="gl" data-title="Gustav Kirchhoff" 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/%EA%B5%AC%EC%8A%A4%ED%83%80%ED%94%84_%ED%82%A4%EB%A5%B4%ED%9E%88%ED%98%B8%ED%94%84" title="구스타프 키르히호프 – Korean" lang="ko" hreflang="ko" data-title="구스타프 키르히호프" 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%B3%D5%B8%D6%82%D5%BD%D5%BF%D5%A1%D5%BE_%D4%BF%D5%AB%D6%80%D5%AD%D5%B0%D5%B8%D6%86" title="Գուստավ Կիրխհոֆ – Armenian" lang="hy" hreflang="hy" data-title="Գուստավ Կիրխհոֆ" 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%97%E0%A5%81%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B5_%E0%A4%95%E0%A4%BF%E0%A4%B0%E0%A4%9A%E0%A5%89%E0%A4%AB" title="गुस्ताव किरचॉफ – Hindi" lang="hi" hreflang="hi" data-title="गुस्ताव किरचॉफ" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Croatian" lang="hr" hreflang="hr" data-title="Gustav Robert Kirchhoff" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Ido" lang="io" hreflang="io" data-title="Gustav Kirchhoff" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Indonesian" lang="id" hreflang="id" data-title="Gustav Robert Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Italian" lang="it" hreflang="it" data-title="Gustav Robert Kirchhoff" 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%92%D7%95%D7%A1%D7%98%D7%91_%D7%A7%D7%99%D7%A8%D7%9B%D7%94%D7%95%D7%A3" title="גוסטב קירכהוף – Hebrew" lang="he" hreflang="he" data-title="גוסטב קירכהוף" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Gustav_Kirchoff" title="Gustav Kirchoff – Javanese" lang="jv" hreflang="jv" data-title="Gustav Kirchoff" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B2%B8%E0%B3%8D%E0%B2%9F%E0%B2%BE%E0%B2%B5%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%95%E0%B2%BF%E0%B2%B0%E0%B3%8D%E0%B2%96%E0%B2%AB%E0%B3%8D" title="ಗಸ್ಟಾವ್ ರಾಬರ್ಟ್ ಕಿರ್ಖಫ್ – Kannada" lang="kn" hreflang="kn" data-title="ಗಸ್ಟಾವ್ ರಾಬರ್ಟ್ ಕಿರ್ಖಫ್" 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%92%E1%83%A3%E1%83%A1%E1%83%A2%E1%83%90%E1%83%95_%E1%83%99%E1%83%98%E1%83%A0%E1%83%AE%E1%83%B0%E1%83%9D%E1%83%A4%E1%83%98" title="გუსტავ კირხჰოფი – Georgian" lang="ka" hreflang="ka" data-title="გუსტავ კირხჰოფი" 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%93%D1%83%D1%81%D1%82%D0%B0%D0%B2_%D0%9A%D0%B8%D1%80%D1%85%D0%B3%D0%BE%D1%84" title="Густав Кирхгоф – Kazakh" lang="kk" hreflang="kk" data-title="Густав Кирхгоф" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Swahili" lang="sw" hreflang="sw" data-title="Gustav Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Haitian Creole" lang="ht" hreflang="ht" data-title="Gustav Robert Kirchhoff" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Gustavus_Robertus_Kirchhoff" title="Gustavus Robertus Kirchhoff – Latin" lang="la" hreflang="la" data-title="Gustavus Robertus Kirchhoff" 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/Gustavs_Roberts_Kirhofs" title="Gustavs Roberts Kirhofs – Latvian" lang="lv" hreflang="lv" data-title="Gustavs Roberts Kirhofs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Luxembourgish" lang="lb" hreflang="lb" data-title="Gustav Robert Kirchhoff" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Lithuanian" lang="lt" hreflang="lt" data-title="Gustav Kirchhoff" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Hungarian" lang="hu" hreflang="hu" data-title="Gustav Robert Kirchhoff" 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%93%D1%83%D1%81%D1%82%D0%B0%D0%B2_%D0%A0%D0%BE%D0%B1%D0%B5%D1%80%D1%82_%D0%9A%D0%B8%D1%80%D1%85%D0%BE%D1%84" title="Густав Роберт Кирхоф – Macedonian" lang="mk" hreflang="mk" data-title="Густав Роберт Кирхоф" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Malagasy" lang="mg" hreflang="mg" data-title="Gustav Kirchhoff" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%81%E0%B4%B8%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B4%BE%E0%B4%B5%E0%B5%8D_%E0%B4%95%E0%B4%BF%E0%B5%BC%E0%B4%9A%E0%B5%8D%E2%80%8C%E0%B4%B9%E0%B5%8B%E0%B4%AB%E0%B5%8D" title="ഗുസ്റ്റാവ് കിർച്‌ഹോഫ് – Malayalam" lang="ml" hreflang="ml" data-title="ഗുസ്റ്റാവ് കിർച്‌ഹോഫ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%97%E0%A5%81%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B5_%E0%A4%95%E0%A4%BF%E0%A4%B0%E0%A5%8D%E0%A4%B6%E0%A4%B9%E0%A5%8B%E0%A4%AB" title="गुस्ताव किर्शहोफ – Marathi" lang="mr" hreflang="mr" data-title="गुस्ताव किर्शहोफ" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%92%E1%83%A3%E1%83%A1%E1%83%A2%E1%83%90%E1%83%95_%E1%83%99%E1%83%98%E1%83%A0%E1%83%AE%E1%83%B0%E1%83%9D%E1%83%A4%E1%83%98" title="გუსტავ კირხჰოფი – Mingrelian" lang="xmf" hreflang="xmf" data-title="გუსტავ კირხჰოფი" 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%AC%D9%88%D8%B3%D8%AA%D8%A7%D9%81_%D9%83%D9%8A%D8%B1%D8%B4%D9%87%D9%88%D9%81" title="جوستاف كيرشهوف – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جوستاف كيرشهوف" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Malay" lang="ms" hreflang="ms" data-title="Gustav Kirchhoff" 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-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%82%E1%80%AF%E1%80%85%E1%80%90%E1%80%AC%E1%80%B7%E1%80%96%E1%80%BA_%E1%80%80%E1%80%85%E1%80%BA%E1%80%9B%E1%80%BA%E1%80%9B%E1%80%BE%E1%80%BA%E1%80%9F%E1%80%B1%E1%80%AC%E1%80%B7%E1%80%96%E1%80%BA" title="ဂုစတာ့ဖ် ကစ်ရ်ရှ်ဟော့ဖ် – Burmese" lang="my" hreflang="my" data-title="ဂုစတာ့ဖ် ကစ်ရ်ရှ်ဟော့ဖ်" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Dutch" lang="nl" hreflang="nl" data-title="Gustav Robert Kirchhoff" 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%B0%E3%82%B9%E3%82%BF%E3%83%95%E3%83%BB%E3%82%AD%E3%83%AB%E3%83%92%E3%83%9B%E3%83%95" title="グスタフ・キルヒホフ – Japanese" lang="ja" hreflang="ja" data-title="グスタフ・キルヒホフ" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Gustav Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Gustav Kirchhoff" 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-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%97%E0%AD%81%E0%AC%B8%E0%AD%8D%E0%AC%A4%E0%AC%AD%E0%AD%8D_%E0%AC%95%E0%AC%BF%E0%AC%B0%E0%AD%8D%E0%AC%9A%E0%AC%AB%E0%AD%8D%E2%80%8C" title="ଗୁସ୍ତଭ୍ କିର୍ଚଫ୍‌ – Odia" lang="or" hreflang="or" data-title="ଗୁସ୍ତଭ୍ କିର୍ଚଫ୍‌" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Uzbek" lang="uz" hreflang="uz" data-title="Gustav Kirchhoff" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%AF%D8%B3%D8%AA%D8%A7%D9%81_%DA%A9%D8%B1%D8%AE%DB%81%D9%88%D9%81" title="گستاف کرخہوف – Western Punjabi" lang="pnb" hreflang="pnb" data-title="گستاف کرخہوف" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Polish" lang="pl" hreflang="pl" data-title="Gustav Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Portuguese" lang="pt" hreflang="pt" data-title="Gustav Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Romanian" lang="ro" hreflang="ro" data-title="Gustav Robert Kirchhoff" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B8%D1%80%D1%85%D0%B3%D0%BE%D1%84,_%D0%93%D1%83%D1%81%D1%82%D0%B0%D0%B2" title="Кирхгоф, Густав – Russian" lang="ru" hreflang="ru" data-title="Кирхгоф, Густав" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Scots" lang="sco" hreflang="sco" data-title="Gustav Kirchhoff" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Albanian" lang="sq" hreflang="sq" data-title="Gustav Robert Kirchhoff" 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%B6%9C%E0%B7%94%E0%B7%83%E0%B7%8A%E0%B6%A7%E0%B7%86%E0%B7%8A_%E0%B6%9A%E0%B6%BB%E0%B7%8A%E0%B6%A0%E0%B7%9C%E0%B7%86%E0%B7%8A" title="ගුස්ටෆ් කර්චොෆ් – Sinhala" lang="si" hreflang="si" data-title="ගුස්ටෆ් කර්චොෆ්" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Simple English" lang="en-simple" hreflang="en-simple" data-title="Gustav Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Slovak" lang="sk" hreflang="sk" data-title="Gustav Robert Kirchhoff" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Slovenian" lang="sl" hreflang="sl" data-title="Gustav Robert Kirchhoff" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%93%D1%83%D1%81%D1%82%D0%B0%D1%84_%D0%9A%D0%B8%D1%80%D1%85%D0%BE%D1%84" title="Густаф Кирхоф – Serbian" lang="sr" hreflang="sr" data-title="Густаф Кирхоф" 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/Gustav_Robert_Kirchhoff" title="Gustav Robert Kirchhoff – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Gustav Robert Kirchhoff" 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-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Sundanese" lang="su" hreflang="su" data-title="Gustav Kirchhoff" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Finnish" lang="fi" hreflang="fi" data-title="Gustav Kirchhoff" 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/Gustav_Kirchhoff" title="Gustav Kirchhoff – Swedish" lang="sv" hreflang="sv" data-title="Gustav Kirchhoff" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff – Tagalog" lang="tl" hreflang="tl" data-title="Gustav Kirchhoff" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%9A%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BE%E0%AE%B5%E0%AF%8D_%E0%AE%95%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%BE%E0%AE%83%E0%AE%AA%E0%AF%8D" title="குசுத்தாவ் கிர்க்காஃப் – Tamil" lang="ta" hreflang="ta" data-title="குசுத்தாவ் கிர்க்காஃப்" 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%93%D1%83%D1%81%D1%82%D0%B0%D0%B2_%D0%9A%D0%B8%D1%80%D1%85%D2%BB%D0%BE%D1%84" title="Густав Кирхһоф – Tatar" lang="tt" hreflang="tt" data-title="Густав Кирхһоф" 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-th mw-list-item"><a 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.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">Gustav Kirchhoff</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Gustav_Robert_Kirchhoff.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Gustav_Robert_Kirchhoff.jpg/220px-Gustav_Robert_Kirchhoff.jpg" decoding="async" width="220" height="310" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Gustav_Robert_Kirchhoff.jpg/330px-Gustav_Robert_Kirchhoff.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Gustav_Robert_Kirchhoff.jpg/440px-Gustav_Robert_Kirchhoff.jpg 2x" data-file-width="2425" data-file-height="3417" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Gustav Robert Kirchhoff</div><br /><span style="display:none">(<span class="bday">1824-03-12</span>)</span>12 March 1824<br /><div style="display:inline" class="birthplace"><a href="/wiki/K%C3%B6nigsberg" title="Königsberg">Königsberg</a>, <a href="/wiki/East_Prussia" title="East Prussia">East Prussia</a>, <a href="/wiki/Kingdom_of_Prussia" title="Kingdom of Prussia">Kingdom of Prussia</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">17 October 1887<span style="display:none">(1887-10-17)</span> (aged 63)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Berlin" title="Berlin">Berlin</a>, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Resting place</th><td class="infobox-data label"><a href="/wiki/Alter_St.-Matth%C3%A4us-Kirchhof" title="Alter St.-Matthäus-Kirchhof">Alter St.-Matthäus-Kirchhof</a>, Berlin</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_K%C3%B6nigsberg" title="University of Königsberg">University of Königsberg</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li>Formulating <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's circuit laws</a> (1845)</li> <li>Discovering <a href="/wiki/Caesium" title="Caesium">caesium</a> (1860)</li> <li>Formulating <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law of thermal radiation</a> (1860)</li> <li>Discovering <a href="/wiki/Rubidium" title="Rubidium">rubidium</a> (1861)</li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Spouses</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1151524712">.mw-parser-output .marriage-line-margin2px{line-height:0;margin-bottom:-2px}.mw-parser-output .marriage-line-margin3px{line-height:0;margin-bottom:-3px}.mw-parser-output .marriage-display-ws{display:inline;white-space:nowrap}</style> <div class="marriage-display-ws"><div style="display:inline-block;line-height:normal;margin-top:1px;white-space:normal;">Clara Richelot</div> <div class="marriage-line-margin2px"></div> <div style="display:inline-block;margin-bottom:1px;"></div>(<abbr title="married">m.</abbr> 1857; died 1869)<wbr /></div><br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1151524712"> <div class="marriage-display-ws"><div style="display:inline-block;line-height:normal;">Luise brömmel</div> <div style="display:inline-block;"></div>(<abbr title="married">m.</abbr> 1872)<wbr /></div></td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data">5</td></tr><tr><th scope="row" class="infobox-label">Relatives</th><td class="infobox-data"><a href="/wiki/Friedrich_Julius_Richelot" title="Friedrich Julius Richelot">Friedrich Julius Richelot</a> (father-in-law)</td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Rumford_Medal" title="Rumford Medal">Rumford Medal</a> (1862)</li> <li><a href="/wiki/Cothenius_Medal" title="Cothenius Medal">Cothenius Medal</a> (1876)</li> <li><a href="/wiki/Matteucci_Medal" title="Matteucci Medal">Matteucci Medal</a> (1877)</li> <li><a href="/wiki/Davy_Medal" title="Davy Medal">Davy Medal</a> (1877)</li> <li><a href="/wiki/Janssen_Medal_(French_Academy_of_Sciences)" title="Janssen Medal (French Academy of Sciences)">Janssen Medal</a> (1887)</li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Honours</th><td class="infobox-data"><span typeof="mw:File"><a href="/wiki/File:D-PRU_Pour_le_Merite_1_BAR.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/D-PRU_Pour_le_Merite_1_BAR.svg/25px-D-PRU_Pour_le_Merite_1_BAR.svg.png" decoding="async" width="25" height="7" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/D-PRU_Pour_le_Merite_1_BAR.svg/38px-D-PRU_Pour_le_Merite_1_BAR.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/D-PRU_Pour_le_Merite_1_BAR.svg/50px-D-PRU_Pour_le_Merite_1_BAR.svg.png 2x" data-file-width="218" data-file-height="60" /></a></span> <i><a href="/wiki/Pour_le_M%C3%A9rite#Civil_class" title="Pour le Mérite">Pour le Mérite</a></i> (1874)</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"><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><div class="hlist"><ul><li><a href="/wiki/Chemistry" title="Chemistry">Chemistry</a></li><li><a href="/wiki/Mathematics" title="Mathematics">mathematics</a></li><li><a href="/wiki/Physics" title="Physics">physics</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a> (1847–1850, 1875–1887)</li> <li><a href="/wiki/University_of_Breslau" class="mw-redirect" title="University of Breslau">University of Breslau</a> (1850–1854)</li> <li><a href="/wiki/University_of_Heidelberg" class="mw-redirect" title="University of Heidelberg">University of Heidelberg</a> (1854–1875)</li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Academic advisors</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a></li><li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Franz Ernst Neumann</a></li><li>Friedrich Julius Richelot</li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a></li><li><a href="/wiki/Gabriel_Lippmann" title="Gabriel Lippmann">Gabriel Lippmann</a></li><li><a href="/wiki/Arthur_Schuster" title="Arthur Schuster">Arthur Schuster</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Lor%C3%A1nd_E%C3%B6tv%C3%B6s" title="Loránd Eötvös">Loránd Eötvös</a></li><li><a href="/wiki/Edward_Leamington_Nichols" title="Edward Leamington Nichols">Edward Leamington Nichols</a></li><li><a href="/wiki/Max_Noether" title="Max Noether">Max Noether</a></li><li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Heike Kamerlingh Onnes</a></li><li><a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a></li><li><a href="/wiki/Ernst_Schr%C3%B6der_(mathematician)" title="Ernst Schröder (mathematician)">Ernst Schröder</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><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><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File/Frameless"><a href="/wiki/File:VFPt_Solenoid_correct2.svg" class="mw-file-description" title="Solenoid"><img alt="Solenoid" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/190px-VFPt_Solenoid_correct2.svg.png" decoding="async" width="190" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/285px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/380px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electricity" title="Electricity">Electricity</a></li> <li><a href="/wiki/Magnetism" title="Magnetism">Magnetism</a></li> <li><a href="/wiki/Optics" title="Optics">Optics</a></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks</a></li> <li><a href="/wiki/List_of_electrical_phenomena" title="List of electrical phenomena">Phenomena</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <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/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a href="/wiki/Magnetic_scalar_potential" title="Magnetic scalar potential">Magnetic scalar potential</a></li> <li><a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">Magnetic vector potential</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">Permeability</a></li> <li><a href="/wiki/Right-hand_rule#Electromagnetism" title="Right-hand rule">Right-hand rule</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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/Classical_electromagnetism" title="Classical electromagnetism">Electrodynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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/Electrical_network" title="Electrical network">Electrical network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a></li> <li><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></li> <li><a href="/wiki/Current_density" title="Current density">Current density</a></li> <li><a href="/wiki/Direct_current" title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content 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title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <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)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a class="mw-selflink selflink">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></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:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Gustav Robert Kirchhoff</b> (<style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">German:</span> <span class="IPA nowrap" lang="de-Latn-fonipa"><a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[ˈgʊs.taːf<span class="wrap"> </span>ˈkɪʁç.hɔf]</a></span>; 12 March 1824 – 17 October 1887) was a German <a href="/wiki/Chemist" title="Chemist">chemist</a>, <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and <a href="/wiki/Physicist" title="Physicist">physicist</a> who contributed to the fundamental understanding of <a href="/wiki/Electrical_circuit" class="mw-redirect" title="Electrical circuit">electrical circuits</a>, <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopy</a> and the emission of <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a> by heated objects.<sup id="cite_ref-Marshall_1-0" class="reference"><a href="#cite_note-Marshall-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> He also coined the term <i><a href="/wiki/Black_body" title="Black body">black body</a></i> in 1860.<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>Several different sets of concepts are named "Kirchhoff's laws" after him, which include <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's circuit laws</a>, <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law of thermal radiation</a>, and Kirchhoff's law of thermochemistry. </p><p>The <a href="/wiki/Bunsen%E2%80%93Kirchhoff_Award" title="Bunsen–Kirchhoff Award">Bunsen–Kirchhoff Award</a> for spectroscopy is named after Kirchhoff and his colleague, <a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life_and_work">Life and work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=1" title="Edit section: Life and work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gustav Kirchhoff was born on 12 March 1824 in <a href="/wiki/K%C3%B6nigsberg" title="Königsberg">Königsberg</a>, <a href="/wiki/Prussia" title="Prussia">Prussia</a>, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke.<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> His family were <a href="/wiki/Lutheranism" title="Lutheranism">Lutherans</a> in the <a href="/wiki/Evangelical_Church_of_Prussia" class="mw-redirect" title="Evangelical Church of Prussia">Evangelical Church of Prussia</a>. He graduated from the Albertus <a href="/wiki/University_of_K%C3%B6nigsberg" title="University of Königsberg">University of Königsberg</a> in 1847 where he attended the mathematico-physical seminar directed by <a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a>,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Franz Ernst Neumann</a> and <a href="/wiki/Friedrich_Julius_Richelot" title="Friedrich Julius Richelot">Friedrich Julius Richelot</a>. In the same year, he moved to <a href="/wiki/Berlin" title="Berlin">Berlin</a>, where he stayed until he received a professorship at <a href="/wiki/Breslau" class="mw-redirect" title="Breslau">Breslau</a>. Later, in 1857, he married Clara Richelot, the daughter of his mathematics professor Richelot. The couple had five children. Clara died in 1869. He married Luise Brömmel in 1872.<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> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Bunsen-Kirchhoff.jpg" class="mw-file-description"><img alt="Black-and-white image of two middle-aged men, either one leaning with one elbow on a wooden column in the middle. Both wear long jackets, and the shorter man on the left has a beard." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Bunsen-Kirchhoff.jpg/170px-Bunsen-Kirchhoff.jpg" decoding="async" width="170" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Bunsen-Kirchhoff.jpg/255px-Bunsen-Kirchhoff.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/0/0e/Bunsen-Kirchhoff.jpg 2x" data-file-width="300" data-file-height="408" /></a><figcaption>Kirchhoff (left) and <a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a>, <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1850</span></figcaption></figure> <p>Kirchhoff formulated <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">his circuit laws</a>, which are now ubiquitous in <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, in 1845, while he was still a student. He completed this study as a seminar exercise; it later became his doctoral dissertation. He was called to the <a href="/wiki/University_of_Heidelberg" class="mw-redirect" title="University of Heidelberg">University of Heidelberg</a> in 1854, where he collaborated in spectroscopic work with <a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a>. In 1857, he calculated that an electric signal in a <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistanceless</a> wire travels along the wire at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><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> He proposed his <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">law of thermal radiation</a> in 1859, and gave a proof in 1861. Together Kirchhoff and Bunsen invented the <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscope</a>, which Kirchhoff used to pioneer the identification of the <a href="/wiki/Sun#Composition" title="Sun">elements in the Sun</a>, showing in 1859 that the Sun contains <a href="/wiki/Sodium" title="Sodium">sodium</a>. He and Bunsen discovered <a href="/wiki/Caesium" title="Caesium">caesium</a> and <a href="/wiki/Rubidium" title="Rubidium">rubidium</a> in 1861.<sup id="cite_ref-Weeks_9-0" class="reference"><a href="#cite_note-Weeks-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> At <a href="/wiki/Heidelberg" title="Heidelberg">Heidelberg</a> he ran a mathematico-physical seminar, modelled on Franz Ernst Neumann's, with the mathematician <a href="/wiki/Leo_Koenigsberger" class="mw-redirect" title="Leo Koenigsberger">Leo Koenigsberger</a>. Among those who attended this seminar were <a href="/wiki/Arthur_Schuster" title="Arthur Schuster">Arthur Schuster</a> and <a href="/wiki/Sofia_Kovalevskaya" class="mw-redirect" title="Sofia Kovalevskaya">Sofia Kovalevskaya</a>. </p><p>He contributed greatly to the field of <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopy</a> by formalizing three laws that describe the <a href="/wiki/Optical_spectrum" class="mw-redirect" title="Optical spectrum">spectral</a> composition of <a href="/wiki/Light" title="Light">light</a> emitted by incandescent objects, building substantially on the discoveries of <a href="/wiki/David_Alter" title="David Alter">David Alter</a> and <a href="/wiki/Anders_Jonas_%C3%85ngstr%C3%B6m" title="Anders Jonas Ångström">Anders Jonas Ångström</a>. In 1862, he was awarded the <a href="/wiki/Rumford_Medal" title="Rumford Medal">Rumford Medal</a> for his researches on the fixed lines of the solar spectrum, and on the inversion of the bright lines in the spectra of artificial light.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> In 1875 Kirchhoff accepted the first chair dedicated specifically to <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a> at Berlin. </p><p>He also contributed to <a href="/wiki/Optics" title="Optics">optics</a>, carefully solving the <a href="/wiki/Wave_equation" title="Wave equation">wave equation</a> to provide a solid foundation for <a href="/wiki/Huygens%27_principle" class="mw-redirect" title="Huygens' principle">Huygens' principle</a> (and correct it in the process).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-miller1991_13-0" class="reference"><a href="#cite_note-miller1991-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In 1864, he was elected as a member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In 1884, he became foreign member of the <a href="/wiki/Royal_Netherlands_Academy_of_Arts_and_Sciences" title="Royal Netherlands Academy of Arts and Sciences">Royal Netherlands Academy of Arts and Sciences</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Kirchhoff died in 1887, and was buried in the <a href="/wiki/Alter_St.-Matth%C3%A4us-Kirchhof" title="Alter St.-Matthäus-Kirchhof">St Matthäus Kirchhof Cemetery</a> in <a href="/wiki/Sch%C3%B6neberg" title="Schöneberg">Schöneberg</a>, Berlin (just a few meters from the graves of the <a href="/wiki/Brothers_Grimm" title="Brothers Grimm">Brothers Grimm</a>). <a href="/wiki/Leopold_Kronecker" title="Leopold Kronecker">Leopold Kronecker</a> is buried in the same cemetery. </p> <div class="mw-heading mw-heading3"><h3 id="Kirchhoff's_circuit_laws"><span id="Kirchhoff.27s_circuit_laws"></span>Kirchhoff's circuit laws</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=2" title="Edit section: Kirchhoff's circuit laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Main article: <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's circuit laws</a></div> <p>Kirchhoff's first law is that the algebraic sum of currents in a network of conductors meeting at a point (or node) is zero. The second law is that in a closed circuit, the directed sums of the voltages in the system is zero. </p> <div class="mw-heading mw-heading3"><h3 id="Kirchhoff's_three_laws_of_spectroscopy"><span id="Kirchhoff.27s_three_laws_of_spectroscopy"></span>Kirchhoff's three laws of spectroscopy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=3" title="Edit section: Kirchhoff's three laws of spectroscopy"><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">See also: <a href="/wiki/History_of_spectroscopy" title="History of spectroscopy">History of spectroscopy</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Kirchhof_laws.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Kirchhof_laws.svg/220px-Kirchhof_laws.svg.png" decoding="async" width="220" height="178" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Kirchhof_laws.svg/330px-Kirchhof_laws.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Kirchhof_laws.svg/440px-Kirchhof_laws.svg.png 2x" data-file-width="1375" data-file-height="1110" /></a><figcaption>Visual depiction of Kirchhoff's laws of spectroscopy</figcaption></figure> <ol><li>A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum.</li> <li>A low-density gas excited to emit light will do so at specific wavelengths, and this produces an <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission spectrum</a>.</li> <li>If light composing a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum.</li></ol><p> Kirchhoff did not know about the existence of <a href="/wiki/Energy_level" title="Energy level">energy levels</a> in atoms. The existence of discrete spectral lines was known since <a href="/wiki/Fraunhofer_lines" title="Fraunhofer lines">Fraunhofer</a> discovered them in 1814. And that the lines formed a discrete mathematical pattern was described by <a href="/wiki/Johann_Balmer" class="mw-redirect" title="Johann Balmer">Johann Balmer</a> in 1885. <a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Joseph Larmor</a> explained the splitting of the <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> in a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> known as the <a href="/wiki/Zeeman_Effect" class="mw-redirect" title="Zeeman Effect">Zeeman Effect</a> by the <a href="/wiki/Oscillation" title="Oscillation">oscillation</a> of electrons.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> But these discrete spectral lines were not explained as electron transitions until the <a href="/wiki/Bohr_model" title="Bohr model">Bohr model</a> of the atom in 1913, which helped lead to <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.</p><div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Kirchhoff's_law_of_thermal_radiation"><span id="Kirchhoff.27s_law_of_thermal_radiation"></span>Kirchhoff's law of thermal radiation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=4" title="Edit section: Kirchhoff's law of thermal radiation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It was <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law of thermal radiation</a> in which he proposed an unknown universal law for radiation that led <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> to the discovery of the quantum of action leading to <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Kirchhoff's_law_of_thermochemistry"><span id="Kirchhoff.27s_law_of_thermochemistry"></span>Kirchhoff's law of thermochemistry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=5" title="Edit section: Kirchhoff's law of thermochemistry"><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">See also: <a href="/wiki/Standard_enthalpy_of_reaction#Variation_with_temperature_or_pressure" title="Standard enthalpy of reaction">Standard enthalpy of reaction § Variation with temperature or pressure</a></div> <p>Kirchhoff showed in 1858 that, in <a href="/wiki/Thermochemistry" title="Thermochemistry">thermochemistry</a>, the variation of the <a href="/wiki/Standard_enthalpy_of_reaction" title="Standard enthalpy of reaction">heat of a chemical reaction</a> is given by the difference in <a href="/wiki/Heat_capacity" title="Heat capacity">heat capacity</a> between products and reactants: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Delta H}{\partial T}}\right)_{p}=\Delta C_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Δ</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Delta H}{\partial T}}\right)_{p}=\Delta C_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d06ed13b448cfda5772760db7d3868f4678ab082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:18.389ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Delta H}{\partial T}}\right)_{p}=\Delta C_{p}}"></span>.</dd></dl> <p>Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Kirchhoff's_theorem_in_graph_theory"><span id="Kirchhoff.27s_theorem_in_graph_theory"></span>Kirchhoff's theorem in graph theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=6" title="Edit section: Kirchhoff's theorem in graph theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kirchhoff also worked in the mathematical field of <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a>, in which he proved <a href="/wiki/Kirchhoff%27s_theorem" title="Kirchhoff's theorem">Kirchhoff's matrix tree theorem</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=7" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=11943571"><i>Gesammelte Abhandlungen</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1882.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gesammelte+Abhandlungen&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1882&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D11943571&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=11946679"><i>Vorlesungen über Electricität und Magnetismus</i></a> (in German). Leipzig: Benedictus Gotthelf Teubner. 1891.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+Electricit%C3%A4t+und+Magnetismus&rft.place=Leipzig&rft.pub=Benedictus+Gotthelf+Teubner&rft.date=1891&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D11946679&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><i>Vorlesungen über mathematische Physik</i>. 4 vols., B. G. Teubner, Leipzig 1876–1894. <ul><li>Vol. 1: <i>Mechanik</i>. 1. Auflage, B. G. Teubner, Leipzig 1876 (<a rel="nofollow" class="external text" href="http://archive.org/stream/vorlesungenberm02kircgoog#page/n7/mode/1up">online</a>).</li> <li>Vol. 2: <i>Mathematische Optik</i>. B. G. Teubner, Leipzig 1891 (Herausgegeben von Kurt Hensel, <a rel="nofollow" class="external text" href="http://archive.org/stream/vorlesungenberm01plangoog#page/n14/mode/1up">online</a>).</li> <li>Vol. 3: <i>Electricität und Magnetismus</i>. B. G. Teubner, Leipzig 1891 (Herausgegeben von Max Planck, <a rel="nofollow" class="external text" href="https://archive.thulb.uni-jena.de/hisbest/rsc/viewer/HisBest_derivate_00011231/KNT_63c_bild_Seite_002.tiff">online</a>).</li> <li>Vol. 4: <a rel="nofollow" class="external text" href="https://books.google.com/books?id=t0QMSU3Q8FQC"><i>Theorie der Wärme</i></a>. B. G. Teubner, Leipzig 1894, Herausgegeben von Max Planck<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Circuit_rank" title="Circuit rank">Circuit rank</a></li> <li><a href="/wiki/Computational_aeroacoustics" title="Computational aeroacoustics">Computational aeroacoustics</a></li> <li><a href="/wiki/Atomic_emission_spectroscopy" title="Atomic emission spectroscopy">Flame emission spectroscopy</a></li> <li><a href="/wiki/Spectroscope" class="mw-redirect" title="Spectroscope">Spectroscope</a></li> <li><a href="/wiki/Kirchhoff_Institute_of_Physics" class="mw-redirect" title="Kirchhoff Institute of Physics">Kirchhoff Institute of Physics</a></li> <li><a href="/wiki/List_of_German_inventors_and_discoverers" title="List of German inventors and discoverers">List of German inventors and discoverers</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=9" title="Edit section: Notes"><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-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Kirchhoff's banker, on hearing that Kirchhoff had identified the elements present in the Sun, remarked "of what use is gold in the Sun if it cannot be brought to Earth?" Kirchhoff deposited his prize money (gold sovereigns) with the banker, saying "here is gold from the Sun."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></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=Gustav_Kirchhoff&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Marshall-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Marshall_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarshallMarshall2008" class="citation journal cs1">Marshall, James L.; Marshall, Virginia R. (2008). <a rel="nofollow" class="external text" href="http://www.chem.unt.edu/~jimm/REDISCOVERY%207-09-2018/Hexagon%20Articles/bunsen%20and%20spectroscopy.pdf">"Rediscovery of the Elements: Mineral Waters and Spectroscopy"</a> <span class="cs1-format">(PDF)</span>. <i>The Hexagon</i>: <span class="nowrap">42–</span>48<span class="reference-accessdate">. Retrieved <span class="nowrap">31 December</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Hexagon&rft.atitle=Rediscovery+of+the+Elements%3A+Mineral+Waters+and+Spectroscopy&rft.pages=%3Cspan+class%3D%22nowrap%22%3E42-%3C%2Fspan%3E48&rft.date=2008&rft.aulast=Marshall&rft.aufirst=James+L.&rft.au=Marshall%2C+Virginia+R.&rft_id=http%3A%2F%2Fwww.chem.unt.edu%2F~jimm%2FREDISCOVERY%25207-09-2018%2FHexagon%2520Articles%2Fbunsen%2520and%2520spectroscopy.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWaygood2013" class="citation book cs1">Waygood, Adrian (19 June 2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8qHGRTC7h-MC&pg=PT79"><i>An Introduction to Electrical Science</i></a>. Routledge. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781135071134" title="Special:BookSources/9781135071134"><bdi>9781135071134</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Electrical+Science&rft.pub=Routledge&rft.date=2013-06-19&rft.isbn=9781135071134&rft.aulast=Waygood&rft.aufirst=Adrian&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D8qHGRTC7h-MC%26pg%3DPT79&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmitz2018" class="citation book cs1">Schmitz, Kenneth S. (2018). <i>Physical Chemistry</i>. Elsevier. p. 278. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780128005996" title="Special:BookSources/9780128005996"><bdi>9780128005996</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physical+Chemistry&rft.pages=278&rft.pub=Elsevier&rft.date=2018&rft.isbn=9780128005996&rft.aulast=Schmitz&rft.aufirst=Kenneth+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKondepudiPrigogine2014" class="citation book cs1">Kondepudi, Dilip; Prigogine, Ilya (5 November 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=SPU8BQAAQBAJ&pg=PA288"><i>Modern Thermodynamics: From Heat Engines to Dissipative Structures</i></a>. John Wiley & Sons. p. 288. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781118698709" title="Special:BookSources/9781118698709"><bdi>9781118698709</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Thermodynamics%3A+From+Heat+Engines+to+Dissipative+Structures&rft.pages=288&rft.pub=John+Wiley+%26+Sons&rft.date=2014-11-05&rft.isbn=9781118698709&rft.aulast=Kondepudi&rft.aufirst=Dilip&rft.au=Prigogine%2C+Ilya&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSPU8BQAAQBAJ%26pg%3DPA288&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" 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="CITEREFHockey2009" class="citation book cs1">Hockey, Thomas (2009). <a rel="nofollow" class="external text" href="http://www.springerreference.com/docs/html/chapterdbid/58778.html">"Kirchhoff, Gustav Robert"</a>. <a href="/wiki/The_Biographical_Encyclopedia_of_Astronomers" class="mw-redirect" title="The Biographical Encyclopedia of Astronomers"><i>The Biographical Encyclopedia of Astronomers</i></a>. <a href="/wiki/Springer_Nature" title="Springer Nature">Springer Nature</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-31022-0" title="Special:BookSources/978-0-387-31022-0"><bdi>978-0-387-31022-0</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 August</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=The+Biographical+Encyclopedia+of+Astronomers&rft.pub=Springer+Nature&rft.date=2009&rft.isbn=978-0-387-31022-0&rft.aulast=Hockey&rft.aufirst=Thomas&rft_id=http%3A%2F%2Fwww.springerreference.com%2Fdocs%2Fhtml%2Fchapterdbid%2F58778.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.kip.uni-heidelberg.de/oeffwiss/kirchhoff">"Gustav Robert Kirchhoff – Dauerausstellung"</a>. Kirchhoff-Institute for Physics<span class="reference-accessdate">. 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(1925). "Zur Erinnerung an Gustav Kirchhoff". <i><a href="/wiki/Die_Naturwissenschaften" class="mw-redirect" title="Die Naturwissenschaften">Die Naturwissenschaften</a></i>. <b>13</b> (11): 205. <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/1925NW.....13..205W">1925NW.....13..205W</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%2FBF01558883">10.1007/BF01558883</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:30039558">30039558</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Die+Naturwissenschaften&rft.atitle=Zur+Erinnerung+an+Gustav+Kirchhoff&rft.volume=13&rft.issue=11&rft.pages=205&rft.date=1925&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A30039558%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01558883&rft_id=info%3Abibcode%2F1925NW.....13..205W&rft.aulast=Warburg&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStepanov1977" class="citation journal cs1">Stepanov, B. 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"Gustav Robert Kirchhoff (on the ninetieth anniversary of his death)". <i>Journal of Applied Spectroscopy</i>. <b>27</b> (3): 1099. <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/1977JApSp..27.1099S">1977JApSp..27.1099S</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%2FBF00625887">10.1007/BF00625887</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:95181496">95181496</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+Applied+Spectroscopy&rft.atitle=Gustav+Robert+Kirchhoff+%28on+the+ninetieth+anniversary+of+his+death%29&rft.volume=27&rft.issue=3&rft.pages=1099&rft.date=1977&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A95181496%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF00625887&rft_id=info%3Abibcode%2F1977JApSp..27.1099S&rft.aulast=Stepanov&rft.aufirst=B.+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverest1969" class="citation journal cs1">Everest, A. S. (1969). "Kirchhoff-Gustav Robert 1824–1887". <i><a href="/wiki/Physics_Education" title="Physics Education">Physics Education</a></i>. <b>4</b> (6): 341. <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/1969PhyEd...4..341E">1969PhyEd...4..341E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0031-9120%2F4%2F6%2F304">10.1088/0031-9120/4/6/304</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:250765281">250765281</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Education&rft.atitle=Kirchhoff-Gustav+Robert+1824%E2%80%931887&rft.volume=4&rft.issue=6&rft.pages=341&rft.date=1969&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250765281%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0031-9120%2F4%2F6%2F304&rft_id=info%3Abibcode%2F1969PhyEd...4..341E&rft.aulast=Everest&rft.aufirst=A.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKirchhoff1860" class="citation journal cs1">Kirchhoff, Gustav (1860). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=XDIXZiXWIuEC&pg=PA3">"Ueber die Fraunhoferschen Linien"</a>. <i><a href="/wiki/Monatsberichte_der_K%C3%B6nigliche_Preussische_Akademie_der_Wissenschaften_zu_Berlin" class="mw-redirect" title="Monatsberichte der Königliche Preussische Akademie der Wissenschaften zu Berlin">Monatsberichte der Königliche Preussische Akademie der Wissenschaften zu Berlin</a></i>: <span class="nowrap">662–</span>665. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-113-39933-5" title="Special:BookSources/978-1-113-39933-5"><bdi>978-1-113-39933-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monatsberichte+der+K%C3%B6nigliche+Preussische+Akademie+der+Wissenschaften+zu+Berlin&rft.atitle=Ueber+die+Fraunhoferschen+Linien&rft.pages=%3Cspan+class%3D%22nowrap%22%3E662-%3C%2Fspan%3E665&rft.date=1860&rft.isbn=978-1-113-39933-5&rft.aulast=Kirchhoff&rft.aufirst=Gustav&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DXDIXZiXWIuEC%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://hdl.handle.net/2027/mdp.39015050939274">HathiTrust full text</a>. Partial English translation available in <a href="/wiki/Magie,_William_Francis" class="mw-redirect" title="Magie, William Francis">Magie, William Francis</a>, <i>A Source Book in Physics</i> (1963). Cambridge: <a href="/wiki/Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>. p. 354-360.</li> <li>Kirchhoff, Gustav (1860). “IV. Ueber das Verhältniß zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht,” Annalen der Physik 185(2), 275–301. (coinage of term “blackbody”) [On the relationship between the emissivity and the absorptivity of bodies for heat and light]</li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gustav_Kirchhoff&action=edit&section=12" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=46968">Gustav Kirchhoff</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Kirchhoff.html">"Gustav Kirchhoff"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Gustav+Kirchhoff&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FKirchhoff.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_Wolfgang_Weisstein" class="mw-redirect" title="Eric Wolfgang Weisstein">Weisstein, Eric Wolfgang</a> (ed.). <a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/biography/Kirchhoff.html">"Kirchhoff, Gustav (1824–1887)"</a>. <i><a href="/wiki/ScienceWorld" class="mw-redirect" title="ScienceWorld">ScienceWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ScienceWorld&rft.atitle=Kirchhoff%2C+Gustav+%281824%E2%80%931887%29&rft_id=http%3A%2F%2Fscienceworld.wolfram.com%2Fbiography%2FKirchhoff.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><a href="/wiki/Klaus_Hentschel" title="Klaus Hentschel">Klaus Hentschel</a>: Gustav Robert Kirchhoff und seine Zusammenarbeit mit Robert Wilhelm Bunsen, in: Karl von Meyenn (Hrsg.) <i>Die Grossen Physiker</i>, Munich: Beck, vol. 1 (1997), pp. 416–430, 475–477, 532–534.</li> <li><a href="/wiki/Klaus_Hentschel" title="Klaus Hentschel">Klaus Hentschel</a>: <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WceRw3sr-rQC"><i>Mapping the Spectrum. Techniques of Visual Representation in Research and Teaching</i></a>, Oxford: OUP, 2002.</li> <li><a rel="nofollow" class="external text" href="http://www.ifi.unicamp.br/%7Eassis/Apeiron-V19-p19-25(1994).pdf">Kirchhoff's 1857 paper on the speed of electrical signals in a wire</a></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/15px-Wikisource-logo.svg.png" decoding="async" width="15" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/23px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/30px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span> Texts on Wikisource: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1">"<a href="https://en.wikisource.org/wiki/The_Encyclopedia_Americana_(1920)/Kirchhoff,_Gustav_Robert" class="extiw" title="s:The Encyclopedia Americana (1920)/Kirchhoff, Gustav Robert">Kirchhoff, Gustav Robert</a>". <i><a href="/wiki/Encyclopedia_Americana" title="Encyclopedia Americana">Encyclopedia Americana</a></i>. 1920.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=Encyclopedia+Americana&rft.date=1920&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1">"<a href="https://en.wikisource.org/wiki/The_New_Student%27s_Reference_Work/Kirchhoff,_Gustav_Robert" class="extiw" title="s:The New Student's Reference Work/Kirchhoff, Gustav Robert">Kirchhoff, Gustav Robert</a>". <i><a href="https://en.wikisource.org/wiki/The_New_Student%27s_Reference_Work" class="extiw" title="s:The New Student's Reference Work">The New Student's Reference Work</a></i>. 1914.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=The+New+Student%27s+Reference+Work&rft.date=1914&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1">"<a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Kirchhoff,_Gustav_Robert" class="extiw" title="s:1911 Encyclopædia Britannica/Kirchhoff, Gustav Robert">Kirchhoff, Gustav Robert</a>". <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i> (11th ed.). 1911.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.edition=11th&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1">"<a href="https://en.wikisource.org/wiki/The_New_International_Encyclop%C3%A6dia/Kirchhoff,_Gustav_Robert" class="extiw" title="s:The New International Encyclopædia/Kirchhoff, Gustav Robert">Kirchhoff, Gustav Robert</a>". <i><a href="/wiki/New_International_Encyclopedia" class="mw-redirect" title="New International Encyclopedia">New International Encyclopedia</a></i>. 1905.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=New+International+Encyclopedia&rft.date=1905&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation magazine cs1">"<a href="https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_33/May_1888/Sketch_of_Gustav_Robert_Kirchhoff" class="extiw" title="s:Popular Science Monthly/Volume 33/May 1888/Sketch of Gustav Robert Kirchhoff">Sketch of Gustav Robert Kirchhoff</a>". <i><a href="/wiki/Popular_Science_Monthly" class="mw-redirect" title="Popular Science Monthly">Popular Science Monthly</a></i>. Vol. 33. May 1888.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Popular+Science+Monthly&rft.atitle=Sketch+of+Gustav+Robert+Kirchhoff&rft.volume=33&rft.date=1888-05&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1">"<a href="https://en.wikisource.org/wiki/The_American_Cyclop%C3%A6dia_(1879)/Kirchhoff,_Gustav_Robert" class="extiw" title="s:The American Cyclopædia (1879)/Kirchhoff, Gustav Robert">Kirchhoff, Gustav Robert</a>". <i><a href="/wiki/The_American_Cyclop%C3%A6dia" class="mw-redirect" title="The American Cyclopædia">The American Cyclopædia</a></i>. 1879.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kirchhoff%2C+Gustav+Robert&rft.btitle=The+American+Cyclop%C3%A6dia&rft.date=1879&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGustav+Kirchhoff" class="Z3988"></span></li></ul></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=Gustav_Kirchhoff&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/13px-Wikiquote-logo.svg.png" decoding="async" width="13" height="16" class="mw-file-element" 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