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parfaits</span> </div> </a> <ul id="toc-Loi_des_gaz_parfaits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Autonomie_d'une_bouteille_de_gaz" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Autonomie_d'une_bouteille_de_gaz"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Autonomie d'une bouteille de gaz</span> </div> </a> <ul id="toc-Autonomie_d'une_bouteille_de_gaz-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Voir aussi</span> </div> </a> <button aria-controls="toc-Voir_aussi-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Voir aussi</span> </button> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> <li id="toc-Références" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Références"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Références</span> </div> </a> <ul id="toc-Références-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliographie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliographie"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Bibliographie</span> </div> </a> <ul id="toc-Bibliographie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liens_externes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liens_externes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Liens externes</span> </div> </a> <ul id="toc-Liens_externes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-sublist" class="vector-toc-list"> </ul> </li> </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="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <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">Basculer la table des matières</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">Loi de Boyle-Mariotte</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="Aller à un article dans une autre langue. Disponible en 75 langues." > <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-75" 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">75 langues</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%A8%D9%88%D9%8A%D9%84" title="قانون بويل – arabe" lang="ar" hreflang="ar" data-title="قانون بويل" data-language-autonym="العربية" data-language-local-name="arabe" 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/Llei_de_Boyle-Mariotte" title="Llei de Boyle-Mariotte – asturien" lang="ast" hreflang="ast" data-title="Llei de Boyle-Mariotte" data-language-autonym="Asturianu" data-language-local-name="asturien" 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/Boyl-Mariott_qanunu" title="Boyl-Mariott qanunu – azerbaïdjanais" lang="az" hreflang="az" data-title="Boyl-Mariott qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</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%91%D0%BE%D0%B9%D0%BB%D1%8F-%D0%9C%D0%B0%D1%80%D1%8B%D1%91%D1%82%D0%B0" title="Закон Бойля-Марыёта – biélorusse" lang="be" hreflang="be" data-title="Закон Бойля-Марыёта" data-language-autonym="Беларуская" data-language-local-name="biélorusse" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BD%D0%B0_%D0%91%D0%BE%D0%B9%D0%BB_%E2%80%93_%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82" title="Закон на Бойл – Мариот – bulgare" lang="bg" hreflang="bg" data-title="Закон на Бойл – Мариот" data-language-autonym="Български" data-language-local-name="bulgare" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%AF%E0%A6%BC%E0%A7%87%E0%A6%B2%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="বয়েলের সূত্র – bengali" lang="bn" hreflang="bn" data-title="বয়েলের সূত্র" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Boyle-Mariotteov_zakon" title="Boyle-Mariotteov zakon – bosniaque" lang="bs" hreflang="bs" data-title="Boyle-Mariotteov zakon" data-language-autonym="Bosanski" data-language-local-name="bosniaque" 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_Boyle" title="Llei de Boyle – catalan" lang="ca" hreflang="ca" data-title="Llei de Boyle" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DB%8C%D8%A7%D8%B3%D8%A7%DB%8C_%D8%A8%DB%86%DB%8C%DA%B5" title="یاسای بۆیڵ – sorani" lang="ckb" hreflang="ckb" data-title="یاسای بۆیڵ" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Boyle%C5%AFv%E2%80%93Mariott%C5%AFv_z%C3%A1kon" title="Boyleův–Mariottův zákon – tchèque" lang="cs" hreflang="cs" data-title="Boyleův–Mariottův zákon" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%91%D0%BE%D0%B9%D0%BB%D1%8C_%E2%80%94_%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D1%82_%D1%81%D0%B0%D0%BA%D0%BA%D1%83%D0%BD%C4%95" title="Бойль — Мариотт саккунĕ – tchouvache" lang="cv" hreflang="cv" data-title="Бойль — Мариотт саккунĕ" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Deddf_Boyle" title="Deddf Boyle – gallois" lang="cy" hreflang="cy" data-title="Deddf Boyle" data-language-autonym="Cymraeg" data-language-local-name="gallois" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Boyles_lov" title="Boyles lov – danois" lang="da" hreflang="da" data-title="Boyles lov" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Gesetz_von_Boyle-Mariotte" title="Gesetz von Boyle-Mariotte – allemand" lang="de" hreflang="de" data-title="Gesetz von Boyle-Mariotte" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%9C%CF%80%CF%8C%CE%B9%CE%BB" title="Νόμος του Μπόιλ – grec" lang="el" hreflang="el" data-title="Νόμος του Μπόιλ" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Boyle%27s_law" title="Boyle's law – anglais" lang="en" hreflang="en" data-title="Boyle's law" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Le%C4%9Do_de_Boyle" title="Leĝo de Boyle – espéranto" lang="eo" hreflang="eo" data-title="Leĝo de Boyle" data-language-autonym="Esperanto" data-language-local-name="espéranto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ley_de_Boyle-Mariotte" title="Ley de Boyle-Mariotte – espagnol" lang="es" hreflang="es" data-title="Ley de Boyle-Mariotte" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Boyle%27i-Mariotte%27i_seadus" title="Boyle'i-Mariotte'i seadus – estonien" lang="et" hreflang="et" data-title="Boyle'i-Mariotte'i seadus" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Boyle-Mariotteren_legea" title="Boyle-Mariotteren legea – basque" lang="eu" hreflang="eu" data-title="Boyle-Mariotteren 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%A8%D9%88%DB%8C%D9%84" title="قانون بویل – persan" lang="fa" hreflang="fa" data-title="قانون بویل" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Boylen_laki" title="Boylen laki – finnois" lang="fi" hreflang="fi" data-title="Boylen laki" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Dl%C3%AD_Boyle" title="Dlí Boyle – irlandais" lang="ga" hreflang="ga" data-title="Dlí Boyle" data-language-autonym="Gaeilge" data-language-local-name="irlandais" 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_%C3%9Ai_Bhaoghail" title="Dlighe Úi Bhaoghail – gaélique écossais" lang="gd" hreflang="gd" data-title="Dlighe Úi Bhaoghail" data-language-autonym="Gàidhlig" data-language-local-name="gaélique écossais" 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/Lei_de_Boyle" title="Lei de Boyle – galicien" lang="gl" hreflang="gl" data-title="Lei de Boyle" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</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%91%D7%95%D7%99%D7%9C-%D7%9E%D7%A8%D7%99%D7%95%D7%98" title="חוק בויל-מריוט – hébreu" lang="he" hreflang="he" data-title="חוק בויל-מריוט" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%89%E0%A4%AF%E0%A4%B2_%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="बॉयल का नियम – hindi" lang="hi" hreflang="hi" data-title="बॉयल 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/Boyle-Mariotteov_zakon" title="Boyle-Mariotteov zakon – croate" lang="hr" hreflang="hr" data-title="Boyle-Mariotteov zakon" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Boyle%E2%80%93Mariotte-t%C3%B6rv%C3%A9ny" title="Boyle–Mariotte-törvény – hongrois" lang="hu" hreflang="hu" data-title="Boyle–Mariotte-törvény" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%B8%D5%B5%D5%AC-%D5%84%D5%A1%D6%80%D5%AB%D5%B8%D5%BF%D5%AB_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Բոյլ-Մարիոտի օրենք – arménien" lang="hy" hreflang="hy" data-title="Բոյլ-Մարիոտի օրենք" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_Boyle" title="Hukum Boyle – indonésien" lang="id" hreflang="id" data-title="Hukum Boyle" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/L%C3%B6gm%C3%A1l_Boyles" title="Lögmál Boyles – islandais" lang="is" hreflang="is" data-title="Lögmál Boyles" data-language-autonym="Íslenska" data-language-local-name="islandais" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Legge_di_Boyle-Mariotte" title="Legge di Boyle-Mariotte – italien" lang="it" hreflang="it" data-title="Legge di Boyle-Mariotte" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9C%E3%82%A4%E3%83%AB%E3%81%AE%E6%B3%95%E5%89%87" title="ボイルの法則 – japonais" lang="ja" hreflang="ja" data-title="ボイルの法則" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Hukum_Boyle" title="Hukum Boyle – javanais" lang="jv" hreflang="jv" data-title="Hukum Boyle" data-language-autonym="Jawa" data-language-local-name="javanais" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%BE%D0%B9%D0%BB%D1%8C%E2%80%93%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D1%82_%D0%B7%D0%B0%D2%A3%D1%8B" title="Бойль–Мариотт заңы – kazakh" lang="kk" hreflang="kk" data-title="Бойль–Мариотт заңы" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B4%EC%9D%BC%EC%9D%98_%EB%B2%95%EC%B9%99" title="보일의 법칙 – coréen" lang="ko" hreflang="ko" data-title="보일의 법칙" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D0%BE%D0%B9%D0%BB%D1%8C-%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D1%82_%D0%BC%D1%8B%D0%B9%D0%B7%D0%B0%D0%BC%D1%8B" title="Бойль-Мариотт мыйзамы – kirghize" lang="ky" hreflang="ky" data-title="Бойль-Мариотт мыйзамы" data-language-autonym="Кыргызча" data-language-local-name="kirghize" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Lezze_de_Boyle" title="Lezze de Boyle – ligure" lang="lij" hreflang="lij" data-title="Lezze de Boyle" data-language-autonym="Ligure" data-language-local-name="ligure" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Boilio_ir_Marioto_d%C4%97snis" title="Boilio ir Marioto dėsnis – lituanien" lang="lt" hreflang="lt" data-title="Boilio ir Marioto dėsnis" data-language-autonym="Lietuvių" data-language-local-name="lituanien" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Boila%E2%80%94Mariota_likums" title="Boila—Mariota likums – letton" lang="lv" hreflang="lv" data-title="Boila—Mariota likums" data-language-autonym="Latviešu" data-language-local-name="letton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%BE%D1%98%D0%BB-%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Бојл-Мариотов закон – macédonien" lang="mk" hreflang="mk" data-title="Бојл-Мариотов закон" data-language-autonym="Македонски" data-language-local-name="macédonien" 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%AC%E0%B5%8B%E0%B4%AF%E0%B4%BF%E0%B5%BD_%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="ബോയിൽ നിയമം – malayalam" lang="ml" hreflang="ml" data-title="ബോയിൽ 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_Boyle" title="Hukum Boyle – malais" lang="ms" hreflang="ms" data-title="Hukum Boyle" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" 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%98%E1%80%BD%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9C%E1%80%BA%E1%81%8F_%E1%80%94%E1%80%AD%E1%80%9A%E1%80%AC%E1%80%99" title="ဘွိုင်းလ်၏ နိယာမ – birman" lang="my" hreflang="my" data-title="ဘွိုင်းလ်၏ နိယာမ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_van_Boyle" title="Wet van Boyle – néerlandais" lang="nl" hreflang="nl" data-title="Wet van Boyle" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Boyle-Mariotte-lova" title="Boyle-Mariotte-lova – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Boyle-Mariotte-lova" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Boyle-Mariottes_lov" title="Boyle-Mariottes lov – norvégien bokmål" lang="nb" hreflang="nb" data-title="Boyle-Mariottes lov" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A9%8B%E0%A8%8F%E0%A8%B2_%E0%A8%A6%E0%A8%BE_%E0%A8%95%E0%A8%BE%E0%A8%A8%E0%A9%82%E0%A9%B0%E0%A8%A8" title="ਬੋਏਲ ਦਾ ਕਾਨੂੰਨ – pendjabi" lang="pa" hreflang="pa" data-title="ਬੋਏਲ ਦਾ ਕਾਨੂੰਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pendjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_Boyle%E2%80%99a-Mariotte%E2%80%99a" title="Prawo Boyle’a-Mariotte’a – polonais" lang="pl" hreflang="pl" data-title="Prawo Boyle’a-Mariotte’a" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Lej_%C3%ABd_Boyle-Mariotte" title="Lej ëd Boyle-Mariotte – piémontais" lang="pms" hreflang="pms" data-title="Lej ëd Boyle-Mariotte" data-language-autonym="Piemontèis" data-language-local-name="piémontais" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D9%88%D8%A7%D8%A6%D9%84_%D8%AF%D8%A7_%D9%82%D9%86%D9%88%D9%86" title="بوائل دا قنون – Western Punjabi" lang="pnb" hreflang="pnb" data-title="بوائل دا قنون" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Lei_de_Boyle-Mariotte" title="Lei de Boyle-Mariotte – portugais" lang="pt" hreflang="pt" data-title="Lei de Boyle-Mariotte" data-language-autonym="Português" data-language-local-name="portugais" 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_Boyle-Mariotte" title="Legea Boyle-Mariotte – roumain" lang="ro" hreflang="ro" data-title="Legea Boyle-Mariotte" data-language-autonym="Română" data-language-local-name="roumain" 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%91%D0%BE%D0%B9%D0%BB%D1%8F_%E2%80%94_%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D1%82%D0%B0" title="Закон Бойля — Мариотта – russe" lang="ru" hreflang="ru" data-title="Закон Бойля — Мариотта" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A8%D9%88%D8%A7%D8%A6%D9%84_%D8%AC%D9%88_%DA%AF%D9%8A%D8%B3_%D8%AC%D9%88_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="بوائل جو گيس جو قانون – sindhi" lang="sd" hreflang="sd" data-title="بوائل جو گيس جو قانون" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Boyle-Mariotteov_zakon" title="Boyle-Mariotteov zakon – serbo-croate" lang="sh" hreflang="sh" data-title="Boyle-Mariotteov zakon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B6%E0%B7%9C%E0%B6%BA%E0%B7%92%E0%B6%BD%E0%B7%8A_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="බොයිල් නියමය – cingalais" lang="si" hreflang="si" data-title="බොයිල් නියමය" data-language-autonym="සිංහල" data-language-local-name="cingalais" 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/Boyle%27s_law" title="Boyle's law – Simple English" lang="en-simple" hreflang="en-simple" data-title="Boyle'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/Boylov-Mariottov_z%C3%A1kon" title="Boylov-Mariottov zákon – slovaque" lang="sk" hreflang="sk" data-title="Boylov-Mariottov zákon" data-language-autonym="Slovenčina" data-language-local-name="slovaque" 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/Boylov_zakon" title="Boylov zakon – slovène" lang="sl" hreflang="sl" data-title="Boylov zakon" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ligji_i_Bojl-Mariotit" title="Ligji i Bojl-Mariotit – albanais" lang="sq" hreflang="sq" data-title="Ligji i Bojl-Mariotit" data-language-autonym="Shqip" data-language-local-name="albanais" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%BE%D1%98%D0%BB%E2%80%94%D0%9C%D0%B0%D1%80%D0%B8%D0%BE%D1%82%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Бојл—Мариотов закон – serbe" lang="sr" hreflang="sr" data-title="Бојл—Мариотов закон" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Boyles_lag" title="Boyles lag – suédois" lang="sv" hreflang="sv" data-title="Boyles lag" data-language-autonym="Svenska" data-language-local-name="suédois" 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%AA%E0%AE%BE%E0%AE%AF%E0%AE%BF%E0%AE%B2%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="பாயிலின் விதி – tamoul" lang="ta" hreflang="ta" data-title="பாயிலின் விதி" data-language-autonym="தமிழ்" data-language-local-name="tamoul" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Batas_ni_Boyle" title="Batas ni Boyle – tagalog" lang="tl" hreflang="tl" data-title="Batas ni Boyle" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Boyle_yasas%C4%B1" title="Boyle yasası – turc" lang="tr" hreflang="tr" data-title="Boyle yasası" data-language-autonym="Türkçe" data-language-local-name="turc" 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%91%D0%BE%D0%B9%D0%BB%D1%8F_%E2%80%94_%D0%9C%D0%B0%D1%80%D1%96%D0%BE%D1%82%D1%82%D0%B0" title="Закон Бойля — Маріотта – ukrainien" lang="uk" hreflang="uk" data-title="Закон Бойля — Маріотта" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%A8%D9%88%D8%A7%D8%A6%D9%84" title="قانون بوائل – ourdou" lang="ur" hreflang="ur" data-title="قانون بوائل" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Boyl-Mariott_qonuni" title="Boyl-Mariott qonuni – ouzbek" lang="uz" hreflang="uz" data-title="Boyl-Mariott qonuni" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ouzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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_Boyle-Mariotte" title="Định luật Boyle-Mariotte – vietnamien" lang="vi" hreflang="vi" data-title="Định luật Boyle-Mariotte" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%8E%BB%E6%84%8F%E8%80%B3-%E9%A9%AC%E7%95%A5%E7%89%B9%E5%AE%9A%E5%BE%8B" title="玻意耳-马略特定律 – wu" lang="wuu" hreflang="wuu" data-title="玻意耳-马略特定律" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%8E%BB%E6%84%8F%E8%80%B3-%E9%A9%AC%E7%95%A5%E7%89%B9%E5%AE%9A%E5%BE%8B" title="玻意耳-马略特定律 – chinois" lang="zh" hreflang="zh" data-title="玻意耳-马略特定律" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Boyle_hoat-chek" title="Boyle hoat-chek – minnan" lang="nan" hreflang="nan" data-title="Boyle hoat-chek" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B3%A2%E7%88%BE%E5%AE%9A%E5%BE%8B" title="波爾定律 – cantonais" lang="yue" hreflang="yue" data-title="波爾定律" data-language-autonym="粵語" data-language-local-name="cantonais" 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class="noprint">Un article de Wikipédia, l'encyclopédie libre.</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="fr" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg/250px-Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg/375px-Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg/500px-Apparecchio_di_Kr%C3%B6ncke_per_la_dimostrazione_della_Legge_di_Boyle-Mariotte_-_Museo_scienza_tecnologia_Milano_04039.jpg 2x" data-file-width="1280" data-file-height="853" /></a><figcaption>Dispositif de Kröncke pour la démonstration de la loi Boyle-Mariotte.<br /><a href="/wiki/Mus%C3%A9e_des_sciences_et_des_techniques_L%C3%A9onard_de_Vinci" title="Musée des sciences et des techniques Léonard de Vinci">Musée des sciences de Milan</a>, (<abbr class="abbr indicateur-langue" title="Langue : italien">(it)</abbr> <a rel="nofollow" class="external text" href="http://www.museoscienza.org/dipartimenti/catalogo_collezioni/scheda_oggetto.asp?idk_in=ST110-00227&arg=Fisica">voir sur le site du musée</a>).</figcaption></figure> <p>La <b>loi de Boyle-Mariotte</b> ou <b>loi de Mariotte</b>, souvent appelée <b>loi de Boyle</b> dans le monde anglophone, du nom du <a href="/wiki/Physicien" title="Physicien">physicien</a> et <a href="/wiki/Chimiste" title="Chimiste">chimiste</a> irlandais <a href="/wiki/Robert_Boyle" title="Robert Boyle">Robert Boyle</a> et de l'abbé physicien et <a href="/wiki/Botaniste" title="Botaniste">botaniste</a> français <a href="/wiki/Edme_Mariotte" title="Edme Mariotte">Edme Mariotte</a>, est l'une des lois de la <a href="/wiki/Thermodynamique" title="Thermodynamique">thermodynamique</a> constituant la <a href="/wiki/Loi_des_gaz_parfaits" title="Loi des gaz parfaits">loi des gaz parfaits</a>. Elle relie la <a href="/wiki/Pression" title="Pression">pression</a> et le <a href="/wiki/Volume" title="Volume">volume</a> d'un <a href="/wiki/Gaz_parfait" title="Gaz parfait">gaz parfait</a> à <a href="/wiki/Temp%C3%A9rature" title="Température">température</a> constante. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Énoncé"><span id=".C3.89nonc.C3.A9"></span>Énoncé</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=1" title="Modifier la section : Énoncé" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=1" title="Modifier le code source de la section : Énoncé"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:Boyles_Law_animated.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Boyles_Law_animated.gif/250px-Boyles_Law_animated.gif" decoding="async" width="250" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Boyles_Law_animated.gif/375px-Boyles_Law_animated.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Boyles_Law_animated.gif/500px-Boyles_Law_animated.gif 2x" data-file-width="532" data-file-height="403" /></a><figcaption>Animation montrant la relation entre pression et volume lorsque la température est maintenue constante.</figcaption></figure> <p>La loi de Boyle-Mariotte relie la pression et le volume d'un <a href="/wiki/Gaz_parfait" title="Gaz parfait">gaz parfait</a> à température constante. On trace ainsi une courbe isotherme du gaz. Boyle et Mariotte ont constaté que la courbe <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=f\!\left(V\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>f</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mi>V</mi> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=f\!\left(V\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39d1278f9157ebf49ee82a492ebacbc17c692129" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.719ex; height:2.843ex;" alt="{\displaystyle P=f\!\left(V\right)}"></span> était proche, à quelques pourcents près, d'une branche d'<a href="/wiki/Hyperbole_(math%C3%A9matiques)#Hyperbole_équilatère" title="Hyperbole (mathématiques)">hyperbole équilatère</a> en <a href="/wiki/Diagramme_de_Clapeyron" title="Diagramme de Clapeyron">coordonnées de Clapeyron</a> <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(P,V\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>P</mi> <mo>,</mo> <mi>V</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(P,V\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fedac43f2195dd12b4eebb62df8d6be219be9e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.376ex; height:2.843ex;" alt="{\displaystyle \left(P,V\right)}"></span>, soit <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={\text{constante}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>constante</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV={\text{constante}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf745610a2f67d300468f4aa8d06f1dbe0c0d0bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.331ex; height:2.176ex;" alt="{\displaystyle PV={\text{constante}}}"></span> pour une température donnée constante. </p><p>En d'autres termes, à une température donnée et maintenue constante, une diminution du volume d'un gaz entraîne une augmentation de sa pression. Inversement, la diminution de la pression du gaz se traduit par une augmentation de son volume. La valeur exacte de la constante n'a pas besoin d'être connue pour appliquer la loi entre deux volumes de gaz sous des pressions différentes, à la même température : </p> <center><b>Loi de Boyle-Mariotte :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1}\times V_{1}=P_{2}\times V_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>×</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1}\times V_{1}=P_{2}\times V_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc7d4ce56f3c51e525f325badf1512abab6f122" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.691ex; height:2.509ex;" alt="{\displaystyle P_{1}\times V_{1}=P_{2}\times V_{2}}"></span></center> <p>La loi a été découverte à quelques années d'intervalle par l'Irlandais <a href="/wiki/Robert_Boyle" title="Robert Boyle">Robert Boyle</a> (en 1662) et par le Français <a href="/wiki/Edme_Mariotte" title="Edme Mariotte">Edme Mariotte</a> (en 1676). Le Français <a href="/wiki/Guillaume_Amontons" title="Guillaume Amontons">Guillaume Amontons</a> précisa en 1702 que cette loi n'est valable qu'à température constante et est plus précise aux basses pressions. </p> <div class="mw-heading mw-heading2"><h2 id="Limites">Limites</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=2" title="Modifier la section : Limites" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=2" title="Modifier le code source de la section : Limites"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:Isothermes_de_van_der_Waals_-_Amagat.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Isothermes_de_van_der_Waals_-_Amagat.jpg/350px-Isothermes_de_van_der_Waals_-_Amagat.jpg" decoding="async" width="350" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Isothermes_de_van_der_Waals_-_Amagat.jpg/525px-Isothermes_de_van_der_Waals_-_Amagat.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Isothermes_de_van_der_Waals_-_Amagat.jpg/700px-Isothermes_de_van_der_Waals_-_Amagat.jpg 2x" data-file-width="976" data-file-height="637" /></a><figcaption>Isothermes de l'<a href="/wiki/%C3%89quation_d%27%C3%A9tat_de_van_der_Waals" title="Équation d'état de van der Waals">équation d'état de van der Waals</a> dans un <a href="/wiki/Diagramme_d%27Amagat" title="Diagramme d'Amagat">diagramme d'Amagat</a>.<br />En marron : courbe de Boyle-Mariotte ; en violet : isotherme de Boyle-Mariotte ; en rouge : isotherme critique.<br />Dans ce type de diagramme, les courbes isothermes d'un <a href="/wiki/Gaz_parfait" title="Gaz parfait">gaz parfait</a> sont des droites horizontales en vertu de la loi de Boyle-Mariotte.</figcaption></figure> <p>Lorsque l'on trace dans un <a href="/wiki/Diagramme_d%27Amagat" title="Diagramme d'Amagat">diagramme d'Amagat</a>, à température <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> et <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité de matière</a> <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> constantes, le produit <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6ee9fce2e1b90f60d71f454bbfcee9ea3bf0d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.533ex; height:2.176ex;" alt="{\displaystyle PV}"></span> en fonction de la pression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> pour un gaz parfait, on obtient, en vertu de la loi de Boyle-Mariotte, une droite horizontale. En faisant varier la température, on obtient un faisceau de droites parallèles appelées <i>isothermes</i>. Plus la température est élevée, plus l'isotherme est haute dans le diagramme. </p><p>Il n'en va pas de même pour les gaz réels, pour lesquels le produit <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6ee9fce2e1b90f60d71f454bbfcee9ea3bf0d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.533ex; height:2.176ex;" alt="{\displaystyle PV}"></span>, à température <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> et quantité de matière <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> constantes, varie en fonction de la pression. La figure ci-contre représente le diagramme d'Amagat d'un gaz répondant à l'<a href="/wiki/%C3%89quation_d%27%C3%A9tat_de_van_der_Waals" title="Équation d'état de van der Waals">équation d'état de van der Waals</a> : cette <a href="/wiki/%C3%89quation_d%27%C3%A9tat" title="Équation d'état">équation d'état</a> représente qualitativement le <a href="/wiki/Ph%C3%A9nom%C3%A8ne_physique" title="Phénomène physique">phénomène physique</a> réel. </p><p>Les isothermes d'un <a href="/wiki/Gaz_r%C3%A9el" title="Gaz réel">gaz réel</a> dans un diagramme d'Amagat décroissent avec une pression croissante aux basses pressions, puis croissent avec la pression aux hautes pressions. Le point auquel la tangente à l'isotherme est horizontale, soit <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({\partial PV \over \partial P}\right)_{T,n}=0}"> <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>P</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\partial PV \over \partial P}\right)_{T,n}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41af90afc6b9cc7fdb70cc6655410ac70ef1760d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.202ex; height:6.509ex;" alt="{\displaystyle \left({\partial PV \over \partial P}\right)_{T,n}=0}"></span>, et auquel la pente de l'isotherme s'inverse, est appelé <i>point de Boyle-Mariotte</i> de l'isotherme. Le <a href="/wiki/Lieu_g%C3%A9om%C3%A9trique" title="Lieu géométrique">lieu géométrique</a> des points de Boyle-Mariotte, qui sont les minimums des isothermes, est appelé <i>courbe de Boyle-Mariotte</i><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. Il existe une température appelée <i>température de Boyle-Mariotte</i> au-delà de laquelle les isothermes sont <a href="/wiki/Fonction_monotone" title="Fonction monotone">croissantes monotones</a>, l'isotherme correspondante est appelée <i>isotherme de Boyle-Mariotte</i>. </p><p>Par contre, lorsque la pression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> tend vers zéro, quelle que soit la température <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>, le comportement d'un gaz réel, quel qu'il soit, tend vers celui du gaz parfait et la valeur de <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6ee9fce2e1b90f60d71f454bbfcee9ea3bf0d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.533ex; height:2.176ex;" alt="{\displaystyle PV}"></span> du gaz réel tend vers <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 nRT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle nRT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7fef316f4f27f4ebbf06069a8cf22bc713e1eb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.795ex; height:2.176ex;" alt="{\displaystyle nRT}"></span> (avec <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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> la <a href="/wiki/Constante_universelle_des_gaz_parfaits" title="Constante universelle des gaz parfaits">constante universelle des gaz parfaits</a>). La loi de Boyle-Mariotte n'est donc applicable qu'aux basses pressions, généralement moins de <span title="1 000 000 Pa ou 9,869 233 atm" style="cursor:help">10</span> bar ou <span title="1 013 250 Pa ou 10,132 5 bar" style="cursor:help">10</span> <abbr class="abbr" title="atmosphère normale">atm</abbr>. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=3" title="Modifier la section : Applications" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=3" title="Modifier le code source de la section : Applications"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Loi_des_gaz_parfaits">Loi des gaz parfaits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=4" title="Modifier la section : Loi des gaz parfaits" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=4" title="Modifier le code source de la section : Loi des gaz parfaits"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Loi_des_gaz_parfaits" title="Loi des gaz parfaits">Loi des gaz parfaits</a>.</div></div> <p>La loi de Boyle-Mariotte est l'une des composantes de la <a href="/wiki/Loi_des_gaz_parfaits" title="Loi des gaz parfaits">loi des gaz parfaits</a> : </p> <center><b>Loi des gaz parfaits :</b> <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=nRT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV=nRT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/934032db2ac1f12624f85a90eeba651dcf4af377" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.426ex; height:2.176ex;" alt="{\displaystyle PV=nRT}"></span></center> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> la <a href="/wiki/Pression" title="Pression">pression</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> le <a href="/wiki/Volume" title="Volume">volume</a> ;</li> <li><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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> la <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité de matière</a> (nombre de <a href="/wiki/Mole_(unit%C3%A9)" title="Mole (unité)">moles</a>) ;</li> <li><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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> la <a href="/wiki/Constante_universelle_des_gaz_parfaits" title="Constante universelle des gaz parfaits">constante universelle des gaz parfaits</a> (<span title="" style="cursor:help">8,314</span> <abbr class="abbr" title="joule par mole kelvin">J mol<sup>−1</sup> K<sup>−1</sup></abbr>) ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> la <a href="/wiki/Temp%C3%A9rature_absolue" title="Température absolue">température absolue</a>.</li></ul> <p>Ainsi pour une quantité de matière <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> donnée, à une température <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> donnée, quel que soit le gaz <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={\text{constante universelle}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>constante universelle</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PV={\text{constante universelle}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c0409ed4f81d90d8238c75335962a8b2f359399" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:27.59ex; height:2.176ex;" alt="{\displaystyle PV={\text{constante universelle}}}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Autonomie_d'une_bouteille_de_gaz"><span id="Autonomie_d.27une_bouteille_de_gaz"></span>Autonomie d'une bouteille de gaz</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=5" title="Modifier la section : Autonomie d'une bouteille de gaz" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=5" title="Modifier le code source de la section : Autonomie d'une bouteille de gaz"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:Pression-volume_ARI.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Pression-volume_ARI.png/250px-Pression-volume_ARI.png" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Pression-volume_ARI.png/375px-Pression-volume_ARI.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Pression-volume_ARI.png/500px-Pression-volume_ARI.png 2x" data-file-width="960" data-file-height="720" /></a><figcaption>Détente du contenu d'une bouteille respiratoire.</figcaption></figure> <p>La loi de Boyle-Mariotte permet de déterminer l'autonomie d'une source de gaz en fonction du débit de consommation : </p> <center><b>Autonomie d'une bouteille :</b> <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={PV \over Q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mi>V</mi> </mrow> <mi>Q</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={PV \over Q}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff387229bb9b04926dab8bb3129822230e7f4fef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.307ex; height:5.676ex;" alt="{\displaystyle t={PV \over Q}}"></span></center> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> l'autonomie de la bouteille (en <a href="/wiki/Minute_(temps)" title="Minute (temps)">minutes</a>) ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> la <a href="/wiki/Pression" title="Pression">pression</a> relative du gaz contenu dans la bouteille (en <a href="/wiki/Bar_(unit%C3%A9)" title="Bar (unité)">bars</a> relatifs) ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> le <a href="/wiki/Volume" title="Volume">volume</a> de la bouteille (en <a href="/wiki/Litre" title="Litre">litres</a>) ;</li> <li><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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> la consommation moyenne, soit le débit volumique de gaz après détente (en litres par minute, l/min).</li></ul> <p>Pour démontrer cette relation, on considère une bouteille de gaz ayant les caractéristiques suivantes : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1}=P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1}=P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf2d53166dd6883c042f16275f0b9a3f1849189d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.39ex; height:2.509ex;" alt="{\displaystyle P_{1}=P}"></span> la pression dans la bouteille ;</li> <li><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_{1}=V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{1}=V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af78fe8c011dd7b9f3cd760927657378e79a374c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.295ex; height:2.509ex;" alt="{\displaystyle V_{1}=V}"></span> le volume de la bouteille.</li></ul> <p>On considère également : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{2}=P_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{2}=P_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ee14610cf0670c0de38a21856e0e98e7c8a4d11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.2ex; height:2.509ex;" alt="{\displaystyle P_{2}=P_{\text{atm}}}"></span> la <a href="/wiki/Pression_atmosph%C3%A9rique" title="Pression atmosphérique">pression atmosphérique</a> (environ <span title="1,013 25 bar ou 1 atm" style="cursor:help">101 325</span> <abbr class="abbr" title="pascal">Pa</abbr>) ;</li> <li><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_{2}=V_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{2}=V_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e83c06f0bbaa1dc5303784c6721e80a27943ca6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.926ex; height:2.509ex;" alt="{\displaystyle V_{2}=V_{\text{atm}}}"></span> le volume produit par la détente du contenu de la bouteille à pression atmosphérique (en considérant la détente à température constante).</li></ul> <p>L'autonomie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> permise par la bouteille est donnée par : </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={V_{\text{atm}} \over Q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> <mi>Q</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={V_{\text{atm}} \over Q}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8679c4c7e712deb197ac7c636a4ea0952984409c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.192ex; height:5.676ex;" alt="{\displaystyle t={V_{\text{atm}} \over Q}}"></span></dd></dl> <p>La loi de Boyle-Mariotte donne : </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 P\times V=P_{\text{atm}}\times V_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>×</mo> <mi>V</mi> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> <mo>×</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\times V=P_{\text{atm}}\times V_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa768da547bf8b6c59e72553173600c8eb953d22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.285ex; height:2.509ex;" alt="{\displaystyle P\times V=P_{\text{atm}}\times V_{\text{atm}}}"></span></dd></dl> <p>on a : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t={P \over P_{\text{atm}}}{V \over Q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>Q</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={P \over P_{\text{atm}}}{V \over Q}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6508dc0daef76bff0b2436dfa7ea0ffa8c4ae962" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.004ex; height:5.676ex;" alt="{\displaystyle t={P \over P_{\text{atm}}}{V \over Q}}"></span></dd></dl> <p>En considérant les deux pressions en <a href="/wiki/Bar_(unit%C3%A9)" title="Bar (unité)">bars</a>, puisque <span class="nowrap"><span title="100 000 Pa ou 0,986 923 atm" style="cursor:help">1</span> bar = <span title="1 bar ou 0,986 923 atm" style="cursor:help">100 000</span> <abbr class="abbr" title="pascal">Pa</abbr></span>, <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e1cdf4584372f57c6be0867bf3dc2e93130bd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.555ex; height:2.509ex;" alt="{\displaystyle P_{\text{atm}}}"></span> ≈ <span title="100 000 Pa ou 0,986 923 atm" style="cursor:help">1</span> bar</span>, on retrouve la relation donnée plus haut. </p> <dl><dt>Remarque</dt></dl> <dl><dd>La pression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> dans la bouteille est la pression <i>relative</i> et non la pression <i>absolue</i> du gaz, qui est égale à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{\prime }=P+P_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>P</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{\prime }=P+P_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4876c9dc786d28122d348b061204a2c9943a09e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.746ex; height:2.843ex;" alt="{\displaystyle P^{\prime }=P+P_{\text{atm}}}"></span>. En effet, lorsque la pression dans la bouteille atteint la pression atmosphérique la bouteille cesse de se vider et le reliquat de gaz dans la bouteille, égal au volume <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{atm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>atm</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{atm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e1cdf4584372f57c6be0867bf3dc2e93130bd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.555ex; height:2.509ex;" alt="{\displaystyle P_{\text{atm}}}"></span>, n'est pas utilisable. Considérer la pression absolue dans le calcul précédent fausse donc le calcul de l'autonomie de la bouteille en produisant une valeur surestimée.</dd></dl> <dl><dt>Exemple</dt></dl> <dl><dd>La loi de Boyle-Mariotte permet par exemple d'estimer l'autonomie permise par les bouteilles de plongée, les <a href="/wiki/Appareil_respiratoire_isolant" title="Appareil respiratoire isolant">ARI</a> utilisés par les <a href="/wiki/Pompier" title="Pompier">pompiers</a>, les mono-bouteilles utilisées en <a href="/wiki/Oxyg%C3%A9noth%C3%A9rapie_normobare" title="Oxygénothérapie normobare">oxygénothérapie</a>.</dd></dl> <dl><dd>Pour une bouteille d'<a href="/wiki/Appareil_respiratoire_isolant" title="Appareil respiratoire isolant">ARI</a> portée par un <a href="/wiki/Pompier" title="Pompier">sapeur-pompier</a> ayant un matériel normé et une condition physique normale : <ul><li>la pression minimale nécessaire pour l'engagement d'une mono-bouteille d'un ARI est de <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> = <span title="28 000 000 Pa ou 276,338 524 atm" style="cursor:help">280</span> bar</span> (pression relative) ;</li> <li>le volume d'une mono-bouteille <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> = <span title="0,006 8 m³ ou 229,935 2 fl.oz." style="cursor:help">6,8</span> litres</span> ;</li> <li>la consommation moyenne d'air d'un individu normal lors d'un entrainement <span class="nowrap"><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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> = 90 <abbr class="abbr" title="litre par minute">l/min</abbr>.</span></li></ul></dd></dl> <dl><dd>On a :</dd></dl> <dl><dd><dl><dd><span class="nowrap"><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={P\times V \over Q}={280\times 6{,}8 \over 90}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo>×</mo> <mi>V</mi> </mrow> <mi>Q</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>280</mn> <mo>×</mo> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>8</mn> </mrow> <mn>90</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={P\times V \over Q}={280\times 6{,}8 \over 90}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34e2dbf22be90c510dc7896e7d04257570605933" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.381ex; height:5.843ex;" alt="{\displaystyle t={P\times V \over Q}={280\times 6{,}8 \over 90}}"></span> ≈ 21,155 minutes.</span></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=6" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=6" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Références"><span id="R.C3.A9f.C3.A9rences"></span>Références</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=7" title="Modifier la section : Références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=7" title="Modifier le code source de la section : Références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text"><span class="ouvrage" id="BorelFavrat2005"><span class="ouvrage" id="Lucien_BorelDaniel_Favrat2005">Lucien Borel et Daniel Favrat, <cite class="italique">Thermodynamique et énergétique</cite>, <abbr class="abbr" title="volume">vol.</abbr> 1, <a href="/wiki/Presses_polytechniques_et_universitaires_romandes" title="Presses polytechniques et universitaires romandes">Presses polytechniques et universitaires romandes</a> (PPUR), <time>2005</time>, 814 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9782880745455" title="Spécial:Ouvrages de référence/9782880745455"><span class="nowrap">9782880745455</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=ApHgAgC8lG0C&pg=PA264">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 264<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamique+et+%C3%A9nerg%C3%A9tique&rft.pub=Presses+polytechniques+et+universitaires+romandes&rft.aulast=Borel&rft.aufirst=Lucien&rft.au=Daniel+Favrat&rft.date=2005&rft.volume=1&rft.pages=264&rft.tpages=814&rft.isbn=9782880745455&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ALoi+de+Boyle-Mariotte"></span></span></span>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Taillet">Richard Taillet, Loïc Villain et Pascal Febvre, <cite class="italique">Dictionnaire de physique</cite>, Louvain-la-Neuve, <a href="/wiki/De_Boeck_Sup%C3%A9rieur" class="mw-redirect" title="De Boeck Supérieur">De Boeck Supérieur</a>, <time>2018</time>, 956 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-8073-0744-5" title="Spécial:Ouvrages de référence/978-2-8073-0744-5"><span class="nowrap">978-2-8073-0744-5</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=pjlFDwAAQBAJ&pg=PA538">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 538<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dictionnaire+de+physique&rft.place=Louvain-la-Neuve&rft.pub=De+Boeck+Sup%C3%A9rieur&rft.au=Richard+Taillet&rft.au=Lo%C3%AFc+Villain&rft.au=Pascal+Febvre&rft.date=2018&rft.pages=538&rft.tpages=956&rft.isbn=978-2-8073-0744-5&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ALoi+de+Boyle-Mariotte"></span></span>.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliographie">Bibliographie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=8" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=8" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="Baeyens-VolantLaurentWarzée2019"><span class="ouvrage" id="Danielle_Baeyens-VolantPascal_LaurentNathalie_Warzée2019">Danielle Baeyens-Volant, Pascal Laurent et Nathalie Warzée, <cite class="italique">Chimie générale : Exercices et méthodes</cite>, <a href="/wiki/%C3%89ditions_Dunod" title="Éditions Dunod">Dunod</a>, <time>2019</time>, 384 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-10-080272-2" title="Spécial:Ouvrages de référence/978-2-10-080272-2"><span class="nowrap">978-2-10-080272-2</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=otuuDwAAQBAJ&pg=PA188">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 188<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chimie+g%C3%A9n%C3%A9rale&rft.pub=Dunod&rft.stitle=Exercices+et+m%C3%A9thodes&rft.aulast=Baeyens-Volant&rft.aufirst=Danielle&rft.au=Pascal+Laurent&rft.au=Nathalie+Warz%C3%A9e&rft.date=2019&rft.pages=188&rft.tpages=384&rft.isbn=978-2-10-080272-2&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ALoi+de+Boyle-Mariotte"></span></span></span>.</li> <li><span class="ouvrage" id="Lagière1996"><span class="ouvrage" id="Michel_Lagière1996">Michel Lagière, <cite class="italique">Physique industrielle des fluides : Notions fondamentales et applications numériques</cite>, Paris, Éditions Technip, <time>1996</time>, 394 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2-7108-0701-7" title="Spécial:Ouvrages de référence/2-7108-0701-7"><span class="nowrap">2-7108-0701-7</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=786lZTxFoo4C&pg=PA122">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 122<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physique+industrielle+des+fluides&rft.place=Paris&rft.pub=%C3%89ditions+Technip&rft.stitle=Notions+fondamentales+et+applications+num%C3%A9riques&rft.aulast=Lagi%C3%A8re&rft.aufirst=Michel&rft.date=1996&rft.pages=122&rft.tpages=394&rft.isbn=2-7108-0701-7&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ALoi+de+Boyle-Mariotte"></span></span></span>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Liens_externes">Liens externes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=9" title="Modifier la section : Liens externes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=9" title="Modifier le code source de la section : Liens externes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.alloprof.qc.ca/bv/pages/c1007.aspx">Loi de Boyle-Mariotte</a> sur le site Bibliothèque virtuelle Allô Prof.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Articles_connexes">Articles connexes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&veaction=edit&section=10" title="Modifier la section : Articles connexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Loi_de_Boyle-Mariotte&action=edit&section=10" title="Modifier le code source de la section : Articles connexes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Diagramme_d%27Amagat" title="Diagramme d'Amagat">Diagramme d'Amagat</a></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Lois_des_gaz" title="Modèle:Palette Lois des gaz"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Lois_des_gaz&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%">Lois des <a href="/wiki/Gaz" title="Gaz">gaz</a></div></th> </tr> <tr> <th class="navbox-group" style="width:70px"><span class="page_h"><a href="/wiki/Variable" class="mw-disambig" title="Variable">Variables</a></span> et <a href="/wiki/Constante_fondamentale" title="Constante fondamentale">constantes</a></th> <td class="navbox-list" style="background:#ECECFF; text-align:left;"><table class="navbox-subgroup" style=""> <tbody><tr> <th class="navbox-group" style="width:200px">Variables <a href="/wiki/Extensivit%C3%A9_et_intensivit%C3%A9_(physique)#Intensivité" title="Extensivité et intensivité (physique)">intensives</a></th> <td class="navbox-list" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Pression" title="Pression">pression</a></li> <li><a href="/wiki/Volume_molaire" title="Volume molaire">volume molaire</a></li> <li><a href="/wiki/Temp%C3%A9rature_thermodynamique" title="Température thermodynamique">température thermodynamique</a></li> <li><a href="/wiki/Facteur_de_compressibilit%C3%A9" title="Facteur de compressibilité">facteur de compressibilité</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:200px">Variables <a href="/wiki/Extensivit%C3%A9_et_intensivit%C3%A9_(physique)#Extensivité" title="Extensivité et intensivité (physique)">extensives</a></th> <td class="navbox-list navbox-even" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Volume" title="Volume">volume</a></li> <li><a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité de matière</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:200px">Constantes</th> <td class="navbox-list" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Constante_universelle_des_gaz_parfaits" title="Constante universelle des gaz parfaits">constante universelle des gaz parfaits</a></li> <li><a href="/wiki/Constante_de_Boltzmann" title="Constante de Boltzmann">constante de Boltzmann</a></li> <li><a href="/wiki/Nombre_d%27Avogadro" title="Nombre d'Avogadro">nombre d'Avogadro</a></li> <li><a href="/wiki/Constante_sp%C3%A9cifique_d%27un_gaz_parfait" title="Constante spécifique d'un gaz parfait">constante spécifique d'un gaz parfait</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:200px">Caractéristiques des <a href="/wiki/Corps_pur" title="Corps pur">corps purs</a></th> <td class="navbox-list navbox-even" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Point_critique_(thermodynamique)" title="Point critique (thermodynamique)">pression, température, volume molaire critiques</a></li> <li><a href="/wiki/Masse_molaire" title="Masse molaire">masse molaire</a></li> <li><a href="/wiki/Facteur_acentrique" title="Facteur acentrique">facteur acentrique</a></li></ul> </div></td> </tr> </tbody></table></td> </tr> <tr> <th class="navbox-group" style="width:70px"><a href="/wiki/Gaz_parfait" title="Gaz parfait">Gaz parfait</a></th> <td class="navbox-list navbox-even" style="background:#ECECFF; text-align:left;"><table class="navbox-subgroup" style=""> <tbody><tr> <th class="navbox-group" style="width:200px"><a href="/wiki/Loi_des_gaz_parfaits" title="Loi des gaz parfaits">Loi des gaz parfaits</a></th> <td class="navbox-list" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Loi_d%27Avogadro" title="Loi d'Avogadro">loi d'Avogadro</a></li> <li><a class="mw-selflink selflink">loi de Boyle-Mariotte</a></li> <li><a href="/wiki/Loi_de_Charles" title="Loi de Charles">loi de Charles</a></li> <li><a href="/wiki/Loi_de_Gay-Lussac" title="Loi de Gay-Lussac">loi de Gay-Lussac</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:200px"><a href="/wiki/M%C3%A9lange_de_gaz_parfaits" title="Mélange de gaz parfaits">Mélange de gaz parfaits</a></th> <td class="navbox-list navbox-even" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Loi_d%27Amagat" title="Loi d'Amagat">loi d'Amagat</a></li> <li><a href="/wiki/Loi_de_Dalton" title="Loi de Dalton">loi de Dalton</a></li> <li><a href="/wiki/Th%C3%A9or%C3%A8me_de_Gibbs" title="Théorème de Gibbs">théorème de Gibbs</a></li></ul> </div></td> </tr> </tbody></table></td> </tr> <tr> <th class="navbox-group" style="width:70px"><a href="/wiki/Gaz_r%C3%A9el" title="Gaz réel">Gaz réel</a></th> <td class="navbox-list" style="background:#ECECFF; text-align:left;"><table class="navbox-subgroup" style=""> <tbody><tr> <th class="navbox-group" style="width:200px"><a href="/wiki/%C3%89quation_d%27%C3%A9tat" title="Équation d'état">Équations d'état</a></th> <td class="navbox-list" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/%C3%89quation_d%27%C3%A9tat_de_Dieterici" title="Équation d'état de Dieterici">Dieterici</a></li> <li><a href="/wiki/%C3%89quation_d%27%C3%A9tat_cubique" title="Équation d'état cubique">cubiques</a></li> <li><a href="/wiki/%C3%89quation_d%27%C3%A9tat_de_van_der_Waals" title="Équation d'état de van der Waals">van der Waals</a></li> <li><a href="/wiki/%C3%89quation_d%27%C3%A9tat_de_Redlich-Kwong" title="Équation d'état de Redlich-Kwong">Redlich-Kwong</a></li> <li><a href="/wiki/%C3%89quation_du_viriel" title="Équation du viriel">viriel</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:200px"><a href="/wiki/%C3%89quilibre_liquide-vapeur" title="Équilibre liquide-vapeur">Équilibre liquide-vapeur</a></th> <td class="navbox-list navbox-even" style=";background:#ECECFF; text-align:left;"><div class="liste-horizontale"> <ul><li><a href="/wiki/Diagramme_de_phase" title="Diagramme de phase">diagramme de phase</a></li> <li><a href="/wiki/Pression_de_vapeur_saturante" title="Pression de vapeur saturante">pression de vapeur saturante</a></li> <li><a href="/wiki/R%C3%A8gle_du_palier_de_Maxwell" title="Règle du palier de Maxwell">règle du palier de Maxwell</a></li> <li><a href="/wiki/Fugacit%C3%A9" title="Fugacité">fugacité</a></li> <li><a href="/wiki/Loi_de_Raoult" title="Loi de Raoult">loi de Raoult</a></li> <li><a href="/wiki/Loi_de_Henry" title="Loi de Henry">loi de Henry</a></li></ul> </div></td> </tr> </tbody></table></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Physique" title="Portail de la physique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/24px-Circle-icons-physics-logo.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/36px-Circle-icons-physics-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/48px-Circle-icons-physics-logo.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Physique" title="Portail:Physique">Portail de la physique</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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