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class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Charles's law</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 51 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-51" 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">51 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%B4%D8%A7%D8%B1%D9%84" title="قانون شارل – Arabic" lang="ar" hreflang="ar" data-title="قانون شارل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C5%9Earl_qanunu" title="Şarl qanunu – Azerbaijani" lang="az" hreflang="az" data-title="Şarl qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%B2%E0%A6%B8%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="চার্লসের সূত্র – Bangla" lang="bn" hreflang="bn" data-title="চার্লসের সূত্র" 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%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%A8%D0%B0%D1%80%D0%BB%D1%8F" title="Закон Шарля – Belarusian" lang="be" hreflang="be" data-title="Закон Шарля" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%A8%D0%B0%D1%80%D0%BB%D1%8F" title="Закон Шарля – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Закон Шарля" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BD%D0%B0_%D0%A8%D0%B0%D1%80%D0%BB" title="Закон на Шарл – Bulgarian" lang="bg" hreflang="bg" data-title="Закон на Шарл" 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/Charlesov_zakon" title="Charlesov zakon – Bosnian" lang="bs" hreflang="bs" data-title="Charlesov zakon" 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/Llei_de_Charles_i_Gay-Lussac" title="Llei de Charles i Gay-Lussac – Catalan" lang="ca" hreflang="ca" data-title="Llei de Charles i Gay-Lussac" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D0%B0%D1%80%D0%BB%D1%8C_%D1%81%D0%B0%D0%BA%D0%BA%D1%83%D0%BD%C4%95" title="Шарль саккунĕ – Chuvash" lang="cv" hreflang="cv" data-title="Шарль саккунĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Charles%C5%AFv_z%C3%A1kon" title="Charlesův zákon – Czech" lang="cs" hreflang="cs" data-title="Charlesův zákon" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Thermische_Zustandsgleichung_idealer_Gase#Gesetz_von_Gay-Lussac" title="Thermische Zustandsgleichung idealer Gase – German" lang="de" hreflang="de" data-title="Thermische Zustandsgleichung idealer Gase" 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/Charles%27i_seadus" title="Charles'i seadus – Estonian" lang="et" hreflang="et" data-title="Charles'i seadus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%A3%CE%B1%CF%81%CE%BB" title="Νόμος του Σαρλ – Greek" lang="el" hreflang="el" data-title="Νόμος του Σαρλ" 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/Ley_de_Charles" title="Ley de Charles – Spanish" lang="es" hreflang="es" data-title="Ley de Charles" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Charlesen_legea" title="Charlesen legea – Basque" lang="eu" hreflang="eu" data-title="Charlesen legea" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%B4%D8%A7%D8%B1%D9%84" title="قانون شارل – Persian" lang="fa" hreflang="fa" data-title="قانون شارل" 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/Loi_de_Charles" title="Loi de Charles – French" lang="fr" hreflang="fr" data-title="Loi de Charles" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Dl%C3%AD_Charles" title="Dlí Charles – Irish" lang="ga" hreflang="ga" data-title="Dlí Charles" 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/Dlighe_Charles" title="Dlighe Charles – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Dlighe Charles" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%83%A4%EB%A5%BC%EC%9D%98_%EB%B2%95%EC%B9%99" title="샤를의 법칙 – Korean" lang="ko" hreflang="ko" data-title="샤를의 법칙" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi badge-Q70893996 mw-list-item" title=""><a href="https://hi.wikipedia.org/wiki/%E0%A4%9A%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%B2_%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="चार्ल का नियम – Hindi" lang="hi" hreflang="hi" data-title="चार्ल का नियम" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Charlesov_zakon" title="Charlesov zakon – Croatian" lang="hr" hreflang="hr" data-title="Charlesov zakon" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_Charles" title="Hukum Charles – Indonesian" lang="id" hreflang="id" data-title="Hukum Charles" 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/Prima_legge_di_Gay-Lussac" title="Prima legge di Gay-Lussac – Italian" lang="it" hreflang="it" data-title="Prima legge di Gay-Lussac" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%95%D7%A7_%D7%A9%D7%90%D7%A8%D7%9C" title="חוק שארל – Hebrew" lang="he" hreflang="he" data-title="חוק שארל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B0%D1%80%D0%BB%D1%8C_%D0%B7%D0%B0%D2%A3%D1%8B" title="Шарль заңы – Kazakh" lang="kk" hreflang="kk" data-title="Шарль заңы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%A0arla_likums" title="Šarla likums – Latvian" lang="lv" hreflang="lv" data-title="Šarla likums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Charles-t%C3%B6rv%C3%A9ny" title="Charles-törvény – Hungarian" lang="hu" hreflang="hu" data-title="Charles-törvény" 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%A8%D0%B0%D1%80%D0%BB%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Шарлов закон – Macedonian" lang="mk" hreflang="mk" data-title="Шарлов закон" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9A%E0%B4%BE%E0%B5%BE%E0%B4%B8%E0%B5%8D_%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="ചാൾസ് നിയമം – Malayalam" lang="ml" hreflang="ml" data-title="ചാൾസ് നിയമം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_Charles" title="Hukum Charles – Malay" lang="ms" hreflang="ms" data-title="Hukum Charles" 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%81%E1%80%BB%E1%80%AC%E1%80%B8%E1%80%9C%E1%80%BA%E1%80%85%E1%80%BA%E1%81%8F_%E1%80%94%E1%80%AD%E1%80%9A%E1%80%AC%E1%80%99" title="ချားလ်စ်၏ နိယာမ – Burmese" lang="my" hreflang="my" data-title="ချားလ်စ်၏ နိယာမ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%AB%E3%81%AE%E6%B3%95%E5%89%87" title="シャルルの法則 – Japanese" lang="ja" hreflang="ja" data-title="シャルルの法則" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Lej_%C3%ABd_Charles" title="Lej ëd Charles – Piedmontese" lang="pms" hreflang="pms" data-title="Lej ëd Charles" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_Charles%E2%80%99a" title="Prawo Charles’a – Polish" lang="pl" hreflang="pl" data-title="Prawo Charles’a" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Lei_de_Charles" title="Lei de Charles – Portuguese" lang="pt" hreflang="pt" data-title="Lei de Charles" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Legea_lui_Charles" title="Legea lui Charles – Romanian" lang="ro" hreflang="ro" data-title="Legea lui Charles" 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%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%A8%D0%B0%D1%80%D0%BB%D1%8F" title="Закон Шарля – Russian" lang="ru" hreflang="ru" data-title="Закон Шарля" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%A0%E0%B7%8F%E0%B6%BD%E0%B7%8A%E0%B7%83%E0%B7%8A_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="චාල්ස් නියමය – Sinhala" lang="si" hreflang="si" data-title="චාල්ස් නියමය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Charles%27s_law" title="Charles's law – Simple English" lang="en-simple" hreflang="en-simple" data-title="Charles's law" 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/Charlesov_z%C3%A1kon" title="Charlesov zákon – Slovak" lang="sk" hreflang="sk" data-title="Charlesov zákon" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A8%D0%B0%D1%80%D0%BB%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Шарлов закон – Serbian" lang="sr" hreflang="sr" data-title="Шарлов закон" 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/Charlesov_zakon" title="Charlesov zakon – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Charlesov zakon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Charlesin_laki" title="Charlesin laki – Finnish" lang="fi" hreflang="fi" data-title="Charlesin laki" 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/Charles_lag" title="Charles lag – Swedish" lang="sv" hreflang="sv" data-title="Charles lag" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%B2%E0%AE%9A%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="சார்லசின் விதி – Tamil" lang="ta" hreflang="ta" data-title="சார்லசின் விதி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Charles_yasas%C4%B1" title="Charles yasası – Turkish" lang="tr" hreflang="tr" data-title="Charles yasası" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%A8%D0%B0%D1%80%D0%BB%D1%8F" title="Закон Шарля – Ukrainian" lang="uk" hreflang="uk" data-title="Закон Шарля" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%86%D8%A7%D8%B1%D9%84%D8%B3_%DA%A9%D8%A7_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="چارلس کا قانون – Urdu" lang="ur" hreflang="ur" data-title="چارلس کا قانون" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_lu%E1%BA%ADt_Charles" title="Định luật Charles – Vietnamese" lang="vi" hreflang="vi" data-title="Định luật Charles" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none"> Relationship between volume and temperature of a gas at constant pressure </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Charles_and_Gay-Lussac%27s_Law_animated.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Charles_and_Gay-Lussac%27s_Law_animated.gif/290px-Charles_and_Gay-Lussac%27s_Law_animated.gif" decoding="async" width="290" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Charles_and_Gay-Lussac%27s_Law_animated.gif/435px-Charles_and_Gay-Lussac%27s_Law_animated.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e4/Charles_and_Gay-Lussac%27s_Law_animated.gif 2x" data-file-width="533" data-file-height="403" /></a><figcaption>An animation demonstrating the relationship between volume and temperature</figcaption></figure> <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 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nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=-D{\frac {d\varphi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.874ex; height:5.509ex;" alt="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"></span><div class="sidebar-caption"><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Laws</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Conservations</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Mass</a></li> <li><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">Momentum</a></li> <li><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Energy</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Inequalities</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem (entropy)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Deformation_(physics)" title="Deformation (physics)">Deformation</a></li> <li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a></li> <li><a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">Strain</a> <ul><li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Finite strain</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain</a></li></ul></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li> <li><a href="/wiki/Bending" title="Bending">Bending</a></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">frictional</a></li></ul></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Fluid" title="Fluid">Fluids</a></th></tr><tr><td class="sidebar-content"> <div class="wraplinks"> <ul><li><a href="/wiki/Hydrostatics" title="Hydrostatics">Statics</a> <b>·</b> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Dynamics</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <b>·</b> <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Hagen%E2%80%93Poiseuille_equation" title="Hagen–Poiseuille equation">Poiseuille equation</a> <b>·</b> <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li>(<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> <b>·</b> <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>)</li></ul></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a> <b>·</b> <a href="/wiki/Mixing_(process_engineering)" title="Mixing (process engineering)">Mixing</a> <b>·</b> <a href="/wiki/Pressure" title="Pressure">Pressure</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Liquid" title="Liquid">Liquids</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Adhesion" title="Adhesion">Adhesion</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a></li> <li><a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">Cohesion (chemistry)</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Gas" title="Gas">Gases</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a class="mw-selflink selflink">Charles's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Fick%27s_law" class="mw-redirect" title="Fick's law">Fick's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></th></tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Rheology" title="Rheology">Rheology</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Adolf_Eugen_Fick" title="Adolf Eugen Fick">Fick</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Graham</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Walter_Noll" title="Walter Noll">Noll</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li> <li><a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">Truesdell</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" 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mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Continuum_mechanics" title="Special:EditPage/Template:Continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Ideal_gas_law_relationships.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ideal_gas_law_relationships.svg/200px-Ideal_gas_law_relationships.svg.png" decoding="async" width="200" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ideal_gas_law_relationships.svg/300px-Ideal_gas_law_relationships.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ideal_gas_law_relationships.svg/400px-Ideal_gas_law_relationships.svg.png 2x" data-file-width="512" data-file-height="341" /></a><figcaption>Relationships between <a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's</a>, <a class="mw-selflink selflink">Charles's</a>, <a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's</a>, <a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's</a>, <a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">combined</a> and <span class="nowrap"><a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas laws</a></span>, with the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> <span class="texhtml"><var style="padding-right: 1px;">k</var><sub><var style="padding-right: 1px;"></var></sub> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><var style="padding-right: 1px;">R</var></span><span class="sr-only">/</span><span class="den"><var style="padding-right: 1px;">N</var><sub><var style="padding-right: 1px;">A</var></sub></span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><var style="padding-right: 1px;">n</var> <var style="padding-right: 1px;">R</var></span><span class="sr-only">/</span><span class="den"><var style="padding-right: 1px;">N</var></span></span>⁠</span></span> (in each law, <a href="/wiki/Physical_property" title="Physical property">properties</a> circled are variable and properties not circled are held constant)</figcaption></figure> <p><b>Charles's law</b> (also known as the <b>law of volumes</b>) is an experimental <a href="/wiki/Gas_laws" title="Gas laws">gas law</a> that describes how <a href="/wiki/Gas" title="Gas">gases</a> <a href="/wiki/Thermal_expansion" title="Thermal expansion">tend to expand when heated</a>. A modern statement of Charles's law is: </p> <blockquote> <p>When the <a href="/wiki/Pressure" title="Pressure">pressure</a> on a sample of a dry gas is held constant, the Kelvin <a href="/wiki/Temperature" title="Temperature">temperature</a> and the <a href="/wiki/Volume" title="Volume">volume</a> will be in direct proportion.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <p>This relationship of <a href="/wiki/Proportionality_(mathematics)#Direct_proportionality" title="Proportionality (mathematics)">direct proportion</a> can be written as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V\propto T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>∝</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\propto T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdd10ef227c1e2f9bb313f1c9eeaefc6886c6376" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.522ex; height:2.176ex;" alt="{\displaystyle V\propto T}"></span></dd></dl> <p>So this means: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mi>k</mi> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>or</mtext> </mrow> <mspace width="1em" /> <mi>V</mi> <mo>=</mo> <mi>k</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3289038640d01a1c1cd2ae552ef6b75b3908607d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.419ex; height:5.176ex;" alt="{\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}"></span></dd></dl> <p>where: </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">V</span> is the <a href="/wiki/Volume" title="Volume">volume</a> of the <a href="/wiki/Gas" title="Gas">gas</a>,</li> <li><span class="texhtml mvar" style="font-style:italic;">T</span> is the <a href="/wiki/Temperature" title="Temperature">temperature</a> of the gas (measured in <a href="/wiki/Kelvin" title="Kelvin">kelvins</a>), and</li> <li><span class="texhtml mvar" style="font-style:italic;">k</span> is a <a href="/wiki/Constant_(mathematics)" title="Constant (mathematics)">constant</a> for a particular <a href="/wiki/Pressure" title="Pressure">pressure</a> and <a href="/wiki/Amount_of_substance" title="Amount of substance">amount</a> of gas.</li></ul> <p>This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dac6c4cc0111f3adcee36af38f87a7de1634f9a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:9.594ex; height:5.509ex;" alt="{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}}"></span> </p><p>The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Charles%27s_law&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The law was named after scientist <a href="/wiki/Jacques_Charles" title="Jacques Charles">Jacques Charles</a>, who formulated the original law in his unpublished work from the 1780s. </p><p>In two of a series of four essays presented between 2 and 30 October 1801,<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> <a href="/wiki/John_Dalton" title="John Dalton">John Dalton</a> demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature. The <a href="/wiki/France" title="France">French</a> <a href="/wiki/Natural_philosopher" class="mw-redirect" title="Natural philosopher">natural philosopher</a> <a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Joseph Louis Gay-Lussac</a> confirmed the discovery in a presentation to the French National Institute on 31 Jan 1802,<sup id="cite_ref-GL02_3-0" class="reference"><a href="#cite_note-GL02-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> although he credited the discovery to unpublished work from the 1780s by <a href="/wiki/Jacques_Charles" title="Jacques Charles">Jacques Charles</a>. The basic principles had already been described by <a href="/wiki/Guillaume_Amontons" title="Guillaume Amontons">Guillaume Amontons</a><sup id="cite_ref-Amontons_4-0" class="reference"><a href="#cite_note-Amontons-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Francis_Hauksbee" title="Francis Hauksbee">Francis Hauksbee</a><sup id="cite_ref-Hauksbee_5-0" class="reference"><a href="#cite_note-Hauksbee-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> a century earlier. </p><p>Dalton was the first to demonstrate that the law applied generally to all gases, and to the <a href="/wiki/Vapour" class="mw-redirect" title="Vapour">vapours</a> of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred.<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> With measurements only at the two thermometric fixed points of water (0°C and 100°C), Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function. On mathematical grounds alone, Gay-Lussac's paper does not permit the assignment of any law stating the linear relation. Both Dalton's and Gay-Lussac's main conclusions can be expressed mathematically as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{100}-V_{0}=kV_{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>100</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mi>k</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{100}-V_{0}=kV_{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/407445d708ea90f282ae0b49e97d40d7f719075e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.41ex; height:2.509ex;" alt="{\displaystyle V_{100}-V_{0}=kV_{0}\,}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">V</span><sub>100</sub> is the volume occupied by a given sample of gas at 100 °C; <span class="texhtml mvar" style="font-style:italic;">V</span><sub>0</sub> is the volume occupied by the same sample of gas at 0 °C; and <span class="texhtml mvar" style="font-style:italic;">k</span> is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so is not what became known as Charles's Law. Gay-Lussac's value for <span class="texhtml mvar" style="font-style:italic;">k</span> (<style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2.6666</span></span>), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2.7315</span></span>. Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787. In the absence of a firm record, the gas law relating volume to temperature cannot be attributed to Charles. Dalton's measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the fixed points of water but also at two intermediate points. Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, “any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”, was unable to confirm it for gases. </p> <div class="mw-heading mw-heading2"><h2 id="Relation_to_absolute_zero">Relation to absolute zero</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Charles%27s_law&action=edit&section=2" title="Edit section: Relation to absolute zero"><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/Kelvin" title="Kelvin">Kelvin</a></div> <p>Charles's law appears to imply that the volume of a gas will descend to <a href="/wiki/Absolute_zero" title="Absolute zero">zero</a> at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or −273.15 °C. Gay-Lussac was clear in his description that the law was not applicable at low temperatures: </p> <blockquote> <p>but I may mention that this last conclusion cannot be true except so long as the compressed vapours remain entirely in the elastic state; and this requires that their temperature shall be sufficiently elevated to enable them to resist the pressure which tends to make them assume the liquid state.<sup id="cite_ref-GL02_3-1" class="reference"><a href="#cite_note-GL02-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <p>At <a href="/wiki/Absolute_zero" title="Absolute zero">absolute zero</a> temperature, the gas possesses zero energy and hence the molecules restrict motion. Gay-Lussac had no experience of <a href="/wiki/Liquid_air" title="Liquid air">liquid air</a> (first prepared in 1877), although he appears to have believed (as did Dalton) that the "permanent gases" such as air and hydrogen could be liquified. Gay-Lussac had also worked with the vapours of volatile liquids in demonstrating Charles's law, and was aware that the law does not apply just above the boiling point of the liquid: </p> <blockquote> <p>I may, however, remark that when the temperature of the ether is only a little above its boiling point, its condensation is a little more rapid than that of atmospheric air. This fact is related to a phenomenon which is exhibited by a great many bodies when passing from the liquid to the solid-state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.<sup id="cite_ref-GL02_3-2" class="reference"><a href="#cite_note-GL02-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <p>The first mention of a temperature at which the volume of a gas might descend to zero was by <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">William Thomson</a> (later known as Lord Kelvin) in 1848:<sup id="cite_ref-Kelvin48_7-0" class="reference"><a href="#cite_note-Kelvin48-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <blockquote> <p>This is what we might anticipate when we reflect that infinite cold must correspond to a finite number of degrees of the air-thermometer below zero; since if we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low. </p> </blockquote> <p>However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, which Thomson himself described in 1852.<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> Thomson did not assume that this was equal to the "zero-volume point" of Charles's law, merely said that Charles's law provided the minimum temperature which could be attained. The two can be shown to be equivalent by <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann's</a> <a href="/wiki/Entropy_(statistical_thermodynamics)" title="Entropy (statistical thermodynamics)">statistical view of entropy</a> (1870). </p><p>However, Charles also stated: </p> <dl><dd>The volume of a fixed mass of dry gas increases or decreases by <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">273</span></span> times the volume at 0 °C for every 1 °C rise or fall in temperature. Thus:</dd></dl> <dl><dd><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 V_{T}=V_{0}+({\tfrac {1}{273}}\times V_{0})\times T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>273</mn> </mfrac> </mstyle> </mrow> <mo>×</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>×</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{T}=V_{0}+({\tfrac {1}{273}}\times V_{0})\times T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e473f267fa7c6f5468f65042549afd19fc15887d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:25.931ex; height:3.676ex;" alt="{\displaystyle V_{T}=V_{0}+({\tfrac {1}{273}}\times V_{0})\times T}"></span></dd></dl></dd></dl> <dl><dd><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 V_{T}=V_{0}(1+{\tfrac {T}{273}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>T</mi> <mn>273</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{T}=V_{0}(1+{\tfrac {T}{273}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb05f1c73b0b811e9010fe244908f824c887df92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:17.367ex; height:3.676ex;" alt="{\displaystyle V_{T}=V_{0}(1+{\tfrac {T}{273}})}"></span></dd></dl></dd></dl> <dl><dd>where <span class="texhtml mvar" style="font-style:italic;">V<sub>T</sub></span> is the volume of gas at temperature <span class="texhtml mvar" style="font-style:italic;">T</span> (in degrees <a href="/wiki/Celsius" title="Celsius">Celsius</a>), <span class="texhtml mvar" style="font-style:italic;">V<sub>0</sub></span> is the volume at 0 °C.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Relation_to_kinetic_theory">Relation to kinetic theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Charles%27s_law&action=edit&section=3" title="Edit section: Relation to kinetic theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Kinetic_theory_of_gases" title="Kinetic theory of gases">kinetic theory of gases</a> relates the <a href="/wiki/Macroscopic" class="mw-redirect" title="Macroscopic">macroscopic</a> properties of gases, such as pressure and volume, to the <a href="/wiki/Microscopic" class="mw-redirect" title="Microscopic">microscopic</a> properties of the molecules which make up the gas, particularly the mass and speed of the molecules. To derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> of the gas molecules, <span style="text-decoration:overline;"><i>E</i></span><sub>k</sub>: </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 T\propto {\bar {E_{\rm {k}}}}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>∝</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> </mrow> </msub> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\propto {\bar {E_{\rm {k}}}}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd7afc225bf33127bea4367a1d8b2e9a06d75a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.584ex; height:2.843ex;" alt="{\displaystyle T\propto {\bar {E_{\rm {k}}}}.\,}"></span></dd></dl> <p>Under this definition, the demonstration of Charles's law is almost trivial. The kinetic theory equivalent of the ideal gas law relates <span class="texhtml mvar" style="font-style:italic;">PV</span> to the average kinetic energy: </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 PV={\frac {2}{3}}N{\bar {E_{\rm {k}}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> </mrow> </msub> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV={\frac {2}{3}}N{\bar {E_{\rm {k}}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed7c4252302b4fac8aa8191e6cd52098adf64a7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.896ex; height:5.176ex;" alt="{\displaystyle PV={\frac {2}{3}}N{\bar {E_{\rm {k}}}}\,}"></span></dd></dl> <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=Charles%27s_law&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a> – Relation between gas pressure and volume</li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a> – Combination of Charles', Boyle's and Gay-Lussac's gas laws</li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a> – Relationship between pressure and temperature of a gas at constant volume</li> <li><a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's law</a> – Relationship between volume and amount of a gas at constant temperature and pressure</li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a> – Equation of the state of a hypothetical ideal gas</li> <li><a href="/wiki/Hand_boiler" title="Hand boiler">Hand boiler</a> – glass sculpture sometimes used as a collector's item to measure love<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Thermal_expansion" title="Thermal expansion">Thermal expansion</a> – Tendency of matter to change volume in response to a change in temperature</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Charles%27s_law&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFFullick1994" class="citation cs2">Fullick, P. (1994), <i>Physics</i>, Heinemann, pp. 141–42, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-435-57078-1" title="Special:BookSources/978-0-435-57078-1"><bdi>978-0-435-57078-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics&rft.pages=141-42&rft.pub=Heinemann&rft.date=1994&rft.isbn=978-0-435-57078-1&rft.aulast=Fullick&rft.aufirst=P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" 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">J. Dalton (1802), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595">"Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," </a> <i>Memoirs of the Literary and Philosophical Society of Manchester</i>, vol. 8, pt. 2, pp. 550–74, 595–602.</span> </li> <li id="cite_note-GL02-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-GL02_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-GL02_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-GL02_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGay-Lussac,_J._L.1802" class="citation cs2"><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac, J. L.</a> (1802), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA137">"Recherches sur la dilatation des gaz et des vapeurs"</a> [Researches on the expansion of gases and vapors], <i>Annales de Chimie</i>, <b>43</b>: 137–75</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annales+de+Chimie&rft.atitle=Recherches+sur+la+dilatation+des+gaz+et+des+vapeurs&rft.volume=43&rft.pages=137-75&rft.date=1802&rft.au=Gay-Lussac%2C+J.+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZ6ctSn3TIeYC%26pg%3DPA137&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span>. <a rel="nofollow" class="external text" href="http://web.lemoyne.edu/~giunta/gaygas.html">English translation (extract).</a><br /> On page 157, Gay-Lussac mentions the unpublished findings of Charles: "<i>Avant d'aller plus loin, je dois prévenir que quoique j'eusse reconnu un grand nombre de fois que les gaz oxigène, azote, hydrogène et acide carbonique, et l'air atmosphérique se dilatent également depuis 0° jusqu'a 80°, le cit. Charles avait remarqué depuis 15 ans la même propriété dans ces gaz; mais n'avant jamais publié ses résultats, c'est par le plus grand hasard que je les ai connus</i>." (Before going further, I should inform [you] that although I had recognized many times that the gases oxygen, nitrogen, hydrogen, and carbonic acid [i.e., carbon dioxide], and atmospheric air also expand from 0° to 80°, citizen Charles had noticed 15 years ago the same property in these gases; but having never published his results, it is by the merest chance that I knew of them.)</span> </li> <li id="cite_note-Amontons-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Amontons_4-0">^</a></b></span> <span class="reference-text">See: <ul><li>Amontons, G. (presented 1699, published 1732) <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_czOAAAAMAAJ&pg=RA1-PA114">"Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines"</a> (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), <i>Mémoires de l’Académie des sciences de Paris</i> (presented 1699, published 1732), 112–26; see especially pp. 113–17.</li> <li>Amontons, G. (presented 1702, published 1743) <a rel="nofollow" class="external text" href="https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA155">"Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre"</a> (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), <i>Mémoires de l’Académie des sciences de Paris</i>, 155–74.</li> <li>Review of Amontons' findings: <a rel="nofollow" class="external text" href="https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA1">"Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre"</a> (On a new property of the air and a new construction of thermometer), <i>Histoire de l'Académie Royale des Sciences</i>, 1–8 (submitted: 1702; published: 1743).</li></ul> </span></li> <li id="cite_note-Hauksbee-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hauksbee_5-0">^</a></b></span> <span class="reference-text">* Englishman <a href="/wiki/Francis_Hauksbee" title="Francis Hauksbee">Francis Hauksbee</a> (1660–1713) independently also discovered Charles's law: Francis Hauksbee (1708) <a rel="nofollow" class="external text" href="http://rstl.royalsocietypublishing.org/content/26/313-324/93.full.pdf+html">"An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate,"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151214093602/http://rstl.royalsocietypublishing.org/content/26/313-324/93.full.pdf+html#">Archived</a> 2015-12-14 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <i>Philosophical Transactions of the Royal Society of London</i> <b>26</b>(315): 93–96.</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">Gay-Lussac (1802), from <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA166">p. 166</a>:<br /> "<i>Si l'on divise l'augmentation totale de volume par le nombre de degrés qui l'ont produite ou par 80, on trouvera, en faisant le volume à la température 0 égal à l'unité, que l'augmentation de volume pour chaque degré est de 1 / 223.33 ou bien de 1 / 266.66 pour chaque degré du thermomètre centrigrade.</i>"<br /> If one divides the total increase in volume by the number of degrees that produce it or by 80, one will find, by making the volume at the temperature 0 equal to unity (1), that the increase in volume for each degree is 1 / 223.33 or 1 / 266.66 for each degree of the centigrade thermometer.<br /> From <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA174">p. 174</a>:<br /> "<i> … elle nous porte, par conséquent, à conclure que tous les gaz et toutes les vapeurs se dilatent également par les mêmes degrés de chaleur.</i>"<br /> … it leads us, consequently, to conclude that all gases and all vapors expand equally [when subjected to] the same degrees of heat.</span> </li> <li id="cite_note-Kelvin48-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kelvin48_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomson,_William1848" class="citation cs2"><a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">Thomson, William</a> (1848), <a rel="nofollow" class="external text" href="http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html">"On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations"</a>, <i>Philosophical Magazine</i>: 100–06</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=On+an+Absolute+Thermometric+Scale+founded+on+Carnot%27s+Theory+of+the+Motive+Power+of+Heat%2C+and+calculated+from+Regnault%27s+Observations&rft.pages=100-06&rft.date=1848&rft.au=Thomson%2C+William&rft_id=http%3A%2F%2Fzapatopi.net%2Fkelvin%2Fpapers%2Fon_an_absolute_thermometric_scale.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomson,_William1852" class="citation cs2"><a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">Thomson, William</a> (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", <i>Philosophical Magazine</i>, <b>4</b></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=On+the+Dynamical+Theory+of+Heat%2C+with+numerical+results+deduced+from+Mr+Joule%27s+equivalent+of+a+Thermal+Unit%2C+and+M.+Regnault%27s+Observations+on+Steam&rft.volume=4&rft.date=1852&rft.au=Thomson%2C+William&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span>. <a rel="nofollow" class="external text" href="http://web.lemoyne.edu/~giunta/KELVIN1.html">Extract.</a></span> </li> </ol></div></div> <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=Charles%27s_law&action=edit&section=6" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrönig,_A.1856" class="citation cs2"><a href="/wiki/August_Kr%C3%B6nig" title="August Krönig">Krönig, A.</a> (1856), <a rel="nofollow" class="external text" href="https://zenodo.org/record/1423642">"Grundzüge einer Theorie der Gase"</a>, <i>Annalen der Physik</i>, <b>001</b> (10): 315–22, <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/1856AnP...175..315K">1856AnP...175..315K</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18561751008">10.1002/andp.18561751008</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Grundz%C3%BCge+einer+Theorie+der+Gase&rft.volume=001&rft.issue=10&rft.pages=315-22&rft.date=1856&rft_id=info%3Adoi%2F10.1002%2Fandp.18561751008&rft_id=info%3Abibcode%2F1856AnP...175..315K&rft.au=Kr%C3%B6nig%2C+A.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1423642&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span>. <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15184h/f327.table">Facsimile at the Bibliothèque nationale de France (pp. 315–22).</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClausius,_R.1857" class="citation cs2"><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius, R.</a> (1857), <a rel="nofollow" class="external text" href="https://zenodo.org/record/1423644">"Ueber die Art der Bewegung, welche wir Wärme nennen"</a>, <i>Annalen der Physik und Chemie</i>, <b>176</b> (3): 353–79, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1857AnP...176..353C">1857AnP...176..353C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18571760302">10.1002/andp.18571760302</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik+und+Chemie&rft.atitle=Ueber+die+Art+der+Bewegung%2C+welche+wir+W%C3%A4rme+nennen&rft.volume=176&rft.issue=3&rft.pages=353-79&rft.date=1857&rft_id=info%3Adoi%2F10.1002%2Fandp.18571760302&rft_id=info%3Abibcode%2F1857AnP...176..353C&rft.au=Clausius%2C+R.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1423644&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span>. <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k15185v/f371.table">Facsimile at the Bibliothèque nationale de France (pp. 353–79).</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051023112122/http://www.polytechnique.fr/bcx/associations/gaylussac/pages/CommunicationsGL.html"><i>Joseph Louis Gay-Lussac – Liste de ses communications</i></a>, archived from <a rel="nofollow" class="external text" href="http://www.polytechnique.fr/bcx/associations/gaylussac/pages/CommunicationsGL.html">the original</a> on October 23, 2005</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Joseph+Louis+Gay-Lussac+%E2%80%93+Liste+de+ses+communications&rft_id=http%3A%2F%2Fwww.polytechnique.fr%2Fbcx%2Fassociations%2Fgaylussac%2Fpages%2FCommunicationsGL.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACharles%27s+law" class="Z3988"></span> . <span class="languageicon">(in French)</span></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=Charles%27s_law&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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demonstration</a> by Prof. Robert Burk, <a href="/wiki/Carleton_University" title="Carleton University">Carleton University</a>, Ottawa, Canada</li> <li><a rel="nofollow" class="external text" href="http://video.google.com/videoplay?docid=-4506461547173401204">Charles's law animation</a> from the Leonardo Project (GTEP/<a href="/wiki/Cramlington_Learning_Village" title="Cramlington Learning Village">CCHS</a>, UK)</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Charles's law</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's law</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" 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