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La théorie de la chaleur qui avait alors cours – celle du « fluide calorique » qu'avait développée Antoine Laurent de Lavoisier (1743-1794) – était fondée sur une hypothèse de conservation de la chaleur. Cette « loi » supposée..." /> <meta property="og:url" content="https://www.universalis.fr/encyclopedie/entropie/" /> <meta property="og:locale" content="fr_FR" /> <meta property="og:site_name" content="Encyclopædia Universalis" /> <meta property="og:type" content="website" /> <meta property="og:image" content="https://www.universalis.fr/_web/static/icons/favicon.png" /> <meta property="og:image:width" content="256" /> <meta property="og:image:height" content="252" /> <meta name="twitter:title" content="ENTROPIE" /> <meta name="twitter:description" content="La notion d'entropie est née au plein milieu du xix e siècle. La théorie de la chaleur qui avait alors cours – celle du « fluide calorique » qu'avait développée Antoine Laurent de Lavoisier (1743-1794) – était fondée sur une hypothèse de conservation de la chaleur. 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La th\u00e9orie de la chaleur qui avait alors cours \u2013\u00a0celle du \u00ab\u00a0fluide calorique\u00a0\u00bb qu'avait d\u00e9velopp\u00e9e Antoine Laurent de Lavoisier (1743-1794)\u00a0\u2013 \u00e9tait fond\u00e9e sur une hypoth\u00e8se de conservation de la chaleur. Cette \u00ab\u00a0loi\u00a0\u00bb suppos\u00e9e impliquait, entre autres cons\u00e9quences, que la chaleur contenue dans un corps isol\u00e9 (dont tout \u00e9change avec l'ext\u00e9rieur est interdit) \u00e9tait invariable. Benjamin Thompson (1753-1814) montra pourtant, exp\u00e9rimentalement, que la chaleur ne se conserve pas. Devant le vide th\u00e9orique ainsi cr\u00e9\u00e9, Rudolf Clausius (1822-1888), William Rankine (1820-1872) et William Thomson, lord Kelvin (1824-1907), cherch\u00e8rent, ind\u00e9pendammen...","url":"https:\/\/www.universalis.fr\/encyclopedie\/entropie\/","wordCount":"1350","image":{"@type":"ImageObject","url":"https:\/\/www.universalis.fr\/_web\/static\/icons\/favicon.png"},"isPartOf":{"@type":"WebPage","url":"https:\/\/www.universalis.fr\/encyclopedie\/entropie\/","name":"ENTROPIE"},"author":[{"@context":"https:\/\/schema.org","@type":"Person","name":"Bernard DIU","familyName":"DIU","givenName":"Bernard","description":"Professeur \u00e9m\u00e9rite \u00e0 l'universit\u00e9 de Paris-VII-Denis-Diderot.","url":"https:\/\/www.universalis.fr\/auteurs\/bernard-diu\/"}],"publisher":{"@type":"Organization","name":"Encyclop\u00e6dia 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href="/encyclopedie/entropie/"> 1. La variation d'entropie </a> </li> <li class="list-group-item "> <a class="d-block" title="ENTROPIE, L'entropie de Boltzmann" href="/encyclopedie/entropie/2-l-entropie-de-boltzmann/"> 2. L'entropie de Boltzmann </a> </li> <li class="list-group-item "> <a class="d-block" title="ENTROPIE, L'entropie statistique" href="/encyclopedie/entropie/3-l-entropie-statistique/"> 3. L'entropie statistique </a> </li> </ul> <button class="btn btn-sm btn-universalis" data-bs-toggle="collapse" data-bs-target="#free-toc" aria-expanded="false" title="Afficher / masquer le sommaire"> <i aria-hidden="true" class="fa fa-fw fa-eye"></i> Sommaire </button> </div> <h1 class="mb-1"> <strong>ENTROPIE</strong> </h1> <ul class="pagination justify-content-center public-links "><li class="page-item active"><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 1" class="page-link" title="Abonnez-vous" data-loaded="true">1</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 2" class="page-link" title="Abonnez-vous" data-loaded="true">2</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 3" class="page-link" title="Abonnez-vous" data-loaded="true">3</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 4" class="page-link" title="Abonnez-vous" data-loaded="true">4</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 5" class="page-link" title="Abonnez-vous" data-loaded="true">5</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 6" class="page-link" title="Abonnez-vous" data-loaded="true">6</a></li></ul><div class="content paged type-article" ><div class="block_1" data-ucode="yC099024_0"><i class="anchor" id="yC099024_0"></i><div class="clearfix"></div><div class="media-container float-md-start me-2 col-md-3 text-center"><figure class="figure text-center w-100 mb-0 p-1" style="position: relative"><a data-ucode="PH995141" data-showMediaPlayer="1" class="protected media-reference-copy " title="Média : Lord Kelvin" href="/media/lord-kelvin-ph995141/"><img id="PH995141" loading="lazy" src="/typo3temp/assets/_processed_/d/d/csm_ph995141_c08469870b.webp" class="figure-img rounded mx-auto media_resized" alt="Lord Kelvin - crédits : Herbert Barraud/ Getty Images" data-description="William Thomson, plus connu sous son titre de lord Kelvin (1824-1907), est l'un des plus célèbres physiciens britanniques du XIXe siècle." data-copyright="Herbert Barraud/ Getty Images" width="825" height="1024" /></a><figcaption class="figure-caption"><p class="m-0 mt-1 fw-bold text-gray-700 text-truncate"> Lord Kelvin </p><p class="m-0 copyright text-sm text-gray-700 text-truncate"> Herbert Barraud/ Getty Images </p></figcaption></figure></div><p>La notion d'entropie est née au plein milieu du <span class="pc">xix</span><sup>e</sup> siècle. La théorie de la <a data-bs-toggle="popover" data-bs-content="La première tentative d'interprétation physique assimilait la chaleur à un fluide dit subtil et indestructible dénommé le calorique , répandu partout au sein de la matière. Son passage d'un corps à un autre était notamment responsable du refroidissement du premier et de l'échauffement du second. L'adoption vers le milieu du xix e siècle du principe de l'équivalence de la chaleur..." title="Article : CHALEUR" href="/encyclopedie/chaleur/">chaleur</a> qui avait alors cours – celle du « fluide calorique » qu'avait développée Antoine Laurent de Lavoisier (1743-1794) – était fondée sur une hypothèse de conservation de la chaleur. Cette « loi » supposée impliquait, entre autres conséquences, que la chaleur contenue dans un corps isolé (dont tout échange avec l'extérieur est interdit) était invariable. <a data-bs-toggle="popover" data-bs-content="Biographie de THOMPSON sir BENJAMIN comte de Rumford. Physicien britannique, né le 26 mars 1753 à Woburn (Massachusetts), mort le 21 août 1814 à Auteuil (France).. Sujet britannique né dans l’une des treize colonies américaines, Benjamin Thompson épouse en 1772 une veuve fortunée, Sarah Walker, et s’installe à Rumford (auj. Concord), dans le New Hampshire. Fidèle à la Couronne b..." title="Article : THOMPSON sir BENJAMIN comte de Rumford" href="/encyclopedie/thompson-sir-benjamin-comte-de-rumford/">Benjamin Thompson</a> (1753-1814) montra pourtant, expérimentalement, que la chaleur ne se conserve pas. Devant le vide théorique ainsi créé, <a data-bs-toggle="popover" data-bs-content="Biographie de RUDOLF CLAUSIUS (1822-1888). Rudolf Julius Emanuel Clausius, l'un des plus grands physiciens du xix e siècle, est connu principalement pour sa contribution à l'étude de la thermodynamique. Le premier, ce savant allemand formula ce qu'on a coutume d'appeler le deuxième principe et proposa une définition claire de l' entropie . Il est aussi l'un des principaux créateurs de l..." title="Article : RUDOLF CLAUSIUS (1822-1888)" href="/encyclopedie/rudolf-clausius/">Rudolf Clausius</a> (1822-1888), William Rankine (1820-1872) et William Thomson, lord Kelvin (1824-1907), cherchèrent, indépendamment les uns des autres, s'il pouvait exister une autre grandeur, apparentée à la chaleur, qui se conserverait. Ils étaient guidés en cela par les idées que <a data-bs-toggle="popover" data-bs-content="Biographie de SADI CARNOT (1796-1832). Fils aîné de Lazare Carnot, « l'Organisateur de la Victoire », Nicolas Léonard Sadi Carnot est un des pionniers de la thermodynamique. Son unique publication, les Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance , ignorée de son temps , mais redécouverte trente ans plus tard par Clapeyron, per..." title="Article : SADI CARNOT (1796-1832)" href="/encyclopedie/sadi-carnot/">Sadi Carnot</a> (1796-1832) avait exposées dans un mémoire prémonitoire,<em> La Puissance motrice du feu</em> (1824). Le résultat de ces recherches fut l'invention de l'entropie (1854). Ce nom vient d'un mot grec, <em>entropê</em>, qui signifie « retour ».</p><div class="clearfix"></div></div><div class="block_1" data-ucode="yC099024_1"><i class="anchor" id="yC099024_1"></i><h2>La variation d'entropie</h2><p> La variation d'entropie entre deux états d'un système thermodynamique se calcule à partir d'une transformation réversible (Carnot disait « idéale ») qui joint ces deux états. Supposons que, au cours de cette transformation, le système soit mis en contact avec plusieurs sources de chaleur, de températures absolues T<sub>1</sub>, T<sub>2</sub>,..., qui lui fournissent les quantités de chaleur (algébriques) Q<sub>1</sub>, Q<sub>2</sub>,... respectivement. La variation d'entropie ΔS entre les deux états considérés est la somme des quotients Q<sub>1</sub>/T<sub>1</sub>, Q<sub>2</sub>/T<sub>2</sub>,... associés aux diverses sources : ΔS = Q<sub>1</sub>/T<sub>1 </sub>+ Q<sub>2</sub>/T<sub>2 </sub>+... (transformation réversible).</p><p>Mais Clausius eut une intuition qui allait s'avérer primordiale. Partant du fait, qu'il avait élevé au rang de principe, que la chaleur ne s'écoule jamais d'un corps plus <a data-bs-toggle="popover" data-bs-content="L'idée commune de froid est attachée à des conditions climatiques polaires ou hivernales et, dans ce sens, elle prend un caractère absolu : « il fait froid ». Mais, pour l'industriel ou le physicien, le froid est relatif, et de l'eau bouillante est beaucoup plus froide qu'un morceau de fer porté au rouge. On ne crée pas du froid, on crée seulement du « plus froid que quelque chose �..." title="Article : FROID, physique" href="/encyclopedie/froid-physique/">froid</a> vers un corps plus chaud, il proposa que l'égalité précédente devînt, pour les transformations réelles, une inégalité, qui porte depuis le nom de Clausius : ΔS ≥ Q<sub>1</sub>/T<sub>1</sub>+ Q<sub>2</sub>/T<sub>2 </sub>+... ΔS est toujours la différence entre l'entropie du système dans son état final et celle de son état initial ; Q<sub>1</sub> est la quantité de chaleur (comptée algébriquement) que le système a reçue de la source de température absolue T<sub>1</sub>,... ; l'inégalité de Clausius se transforme en égalité pour les transformations réversibles, et pour elles seulement.</p><p>L'inégalité de Clausius exprime de façon compacte le deuxième principe de la thermodynamique, dont les applications sont multiples et variées.</p><div class="clearfix"></div></div><div class="clearfix"></div></div><ul class="pagination justify-content-center public-links "><li class="page-item active"><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 1" class="page-link" title="Abonnez-vous" data-loaded="true">1</a></li><li class="page-item "><a href="/abonnement" data-matomo-category="Article" data-matomo-name="Folio" data-matomo-value="page 2" class="page-link" 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à l'université de Paris-VII-Denis-Diderot </li></ul></section><section class="mb-5"><div class="text-center mb-3 d-print-none"><a class="d-inline-flex flex-row justify-content-center align-items-center btn btn-light btn-large text-start" title="Carte mentale : ENTROPIE" href="/carte-mentale/entropie/"><i class="fa fa-sitemap fa-rotate-270 me-1 fs-1 text-universalis"></i><p class="m-0"><strong class="fs-4">Carte mentale</strong><br /> Élargissez votre recherche dans Universalis </p></a></div></section> <section class="mb-5 article-classification" data-print-label="la classification" data-print-target=".article-classification"> <i class="anchor" id="yC099024_ROOT_LINES"></i> <p class="title-minor">Classification</p> <nav aria-label="Classification 1"> <ol class="breadcrumb"> <li class="breadcrumb-item"> <a title="Classification : Physique" href="/classification/physique/"> Physique </a> </li> <li class="breadcrumb-item"> <a title="Classification : Chaleur et thermodynamique" href="/classification/physique/chaleur-et-thermodynamique/"> Chaleur et thermodynamique </a> </li> <li class="breadcrumb-item"> <a title="Classification : Thermodynamique" href="/classification/physique/chaleur-et-thermodynamique/thermodynamique/"> Thermodynamique </a> </li> <li class="breadcrumb-item active" data-dc-subject="Principes et fondements de la thermodynamique"> <a title="Classification : Principes et fondements de la thermodynamique" href="/classification/physique/chaleur-et-thermodynamique/thermodynamique/principes-et-fondements-de-la-thermodynamique/"> Principes et fondements de la thermodynamique </a> </li> </ol> </nav> </section> <section class="mb-5 d-print-none"> <i class="anchor" id="yC099024_MEDIAS"></i> <p class="title-minor">Médias</p> <div class="row"> <div class="col-12 col-md-6 text-center p-1"> <figure class="figure text-center w-100 mb-0 p-1" style="position: relative"> <a data-ucode="PH995141" data-showMediaPlayer="1" class="protected media-reference-copy " title="Média : Lord Kelvin" href="/media/lord-kelvin-ph995141/"> <img id="PH995141" loading="lazy" src="/typo3temp/assets/_processed_/d/d/csm_ph995141_c08469870b.webp" class="figure-img rounded mx-auto media_resized" alt="Lord Kelvin - crédits : Herbert Barraud/ Getty Images" data-description="William Thomson, plus connu sous son titre de lord Kelvin (1824-1907), est l'un des plus célèbres physiciens britanniques du XIXe siècle." data-copyright="Herbert Barraud/ Getty Images" width="825" height="1024" /> </a> <figcaption class="figure-caption"> <p class="m-0 mt-1 fw-bold text-gray-700 text-truncate"> Lord Kelvin </p> <p class="m-0 copyright text-sm text-gray-700 text-truncate"> Herbert Barraud/ Getty Images </p> </figcaption> </figure> </div> <div class="col-12 col-md-6 text-center p-1"> <figure class="figure text-center w-100 mb-0 p-1" style="position: relative"> <a data-ucode="PH995113" data-showMediaPlayer="1" class="protected media-reference-copy " title="Média : Ludwig Boltzmann" href="/media/ludwig-boltzmann-ph995113/"> <img id="PH995113" loading="lazy" src="/typo3temp/assets/_processed_/5/4/csm_ph995113_1343f2fdfa.webp" class="figure-img rounded mx-auto media_resized" alt="Ludwig Boltzmann - crédits : ullstein bild/ Getty Images" data-description="Physicien et philosophe des sciences, Ludwig Boltzmann (1844-1906) a laissé de nombreux théorèmes, lois et équations qui portent son nom." data-copyright="ullstein bild/ Getty Images" width="769" height="1024" /> </a> <figcaption class="figure-caption"> <p class="m-0 mt-1 fw-bold text-gray-700 text-truncate"> Ludwig Boltzmann </p> <p class="m-0 copyright text-sm text-gray-700 text-truncate"> ullstein bild/ Getty Images </p> </figcaption> </figure> </div> </div> </section> <section class="mb-5 d-print-none learn-more"> <i class="anchor" id="yC099024_REFERENCES"></i> <p class="title-minor">Autres références</p> <ul class="list-group"> <li class="list-group-item"> <h3 class="fs-5 m-0 mt-1"> <a href="/encyclopedie/ludwig-boltzmann/#c20082"> <span class="rg">BOLTZMANN </span><span class="pc">LUDWIG </span><span class="rm">(1844-1906)</span> </a> </h3> <ul class="list-inline list-inline-bullet mb-1 text-muted"> <li class="list-inline-item text-sm">Écrit par <span rel="author">Pierre COSTABEL</span> </li> <li class="list-inline-item text-sm">1 634 mots</li> <li class="list-inline-item text-sm">1 média </li> </ul> <div class="d-none d-md-inline-block float-start me-3"> <a class="protected" title="Article : BOLTZMANN LUDWIG (1844-1906)" href="/encyclopedie/ludwig-boltzmann/"> <img class="rounded shadow" loading="lazy" alt="Ludwig Boltzmann - crédits : ullstein bild/ Getty Images" width="125" height="125" src="/typo3temp/assets/_processed_/5/4/csm_ph995113_d8501747c2.webp"/> </a> </div> <div class="snippet-content mt-3"> ...gaz par l'ensemble des nombres <em>n</em> et précisa la probabilité relative de cet état. Il montra que le logarithme de la probabilité coïncide avec l' entropie S, à un facteur et à une constante <em>k</em> près, dans l'état d'équilibre thermodynamique, et que cette probabilité conserve un sens pendant tout processus... </div> </li> <li class="list-group-item"> <h3 class="fs-5 m-0 mt-1"> <a href="/encyclopedie/rudolf-clausius/#c20082"> <span class="rg">CLAUSIUS </span><span class="pc">RUDOLF </span><span class="rm">(1822-1888)</span> </a> </h3> <ul class="list-inline list-inline-bullet mb-1 text-muted"> <li class="list-inline-item text-sm">Écrit par <span rel="author">Robert FOX</span> </li> <li class="list-inline-item text-sm">1 001 mots</li> </ul> <div class="snippet-content mt-3"> En 1854, Clausius, poussant plus avant les vues exprimées dès 1850, proposa le premier énoncé clair du concept de l'entropie. Il cherchait à mesurer l'aptitude de l'énergie calorifique de n'importe quel système réel non idéal à fournir du travail. Dans le cas de la conduction ... </div> </li> <li class="list-group-item"> <h3 class="fs-5 m-0 mt-1"> <a href="/encyclopedie/energie-la-notion/#c20082"> <span class="rg">ÉNERGIE - </span><span class="rm">La notion</span> </a> </h3> <ul class="list-inline list-inline-bullet mb-1 text-muted"> <li class="list-inline-item text-sm">Écrit par <span rel="author">Julien BOK</span> </li> <li class="list-inline-item text-sm">7 543 mots</li> <li class="list-inline-item text-sm">4 médias </li> </ul> <div class="d-none d-md-inline-block float-start me-3"> <a class="protected" title="Article : &Eacute;NERGIE - La notion" href="/encyclopedie/energie-la-notion/"> <img class="rounded shadow" loading="lazy" alt="Énergie de liaison - crédits : Encyclopædia Universalis France" width="125" height="125" src="/typo3temp/assets/_processed_/9/3/csm_v080295_91dc05f12b.webp"/> </a> </div> <div class="snippet-content mt-3"> ...configuration microscopique correspondant à un même état thermodynamique d'énergie donnée a la même probabilité d'être réalisée : principe microcanonique. L'état macroscopique qui est le plus probable est celui qui correspond au nombre maximal Ω de configurations microscopiques possibles. On définit l'entropie... </div> </li> <li class="list-group-item"> <h3 class="fs-5 m-0 mt-1"> <a href="/encyclopedie/hasard-et-necessite/#c20082"> <span class="rg">HASARD & NÉCESSITÉ</span> </a> </h3> <ul class="list-inline list-inline-bullet mb-1 text-muted"> <li class="list-inline-item text-sm">Écrit par <span rel="author"> Encyclopædia Universalis</span> , <span rel="author">Ilya PRIGOGINE</span> et <span rel="author">Isabelle STENGERS</span> </li> <li class="list-inline-item text-sm">9 614 mots</li> </ul> <div class="snippet-content mt-3"> ...vain de séparer déterminisme dynamique et réversibilité (I. Prigogine et I. Stengers, 1988), c'est-à-dire de montrer que l'évolution irréversible, à entropie croissante, vers l' équilibre thermodynamique si elle n'avait pas de sens en ce qui concerne une particule individuelle, pouvait prendre un sens... </div> </li> <li class="list-unstyled text-center mt-3"> <a class="btn btn-sm btn-primary" title="Afficher la liste complète des références" rel="related" href="/index/entropie/"> Afficher les 27 références <i aria-hidden="true" class="fa fa-fw fa-chevron-right"></i> </a> </li> </ul> </section> </div> <div class="col-lg-4 col-xl-3 px-0 d-none d-lg-block side-bar position-relative"> <div id="ad_rightslot" class="pub-container text-center"> <div class="pub-placeholder"></div> </div> <div id="ad_rightslot2" class="pub-container text-center"> <div class="pub-placeholder"></div> </div> <a class="wrapper cta" href="/abonnement" title="Abonnez-vous à Universalis pour 1 euro" data-matomo-category="CTA" data-matomo-name="Clic" data-matomo-value="Col right"> <img src="/typo3temp/assets/_processed_/b/6/csm_abo-3_f303c484f7.webp" class="full-height" loading="lazy" width="290" height="476" alt="Abonnez-vous à Universalis pour 1 euro"> </a> <div id="newsletter_subscription" class="wrapper p-3"> <p class="fs-3 fw-bold text-center text-light mb-1">Rejoignez-nous</p> <p class="text-center"> Inscrivez-vous à notre <strong>newsletter</strong></p> <div class="input-group mb-3"> <input type="text" class="form-control" placeholder="votre email"> <div class="input-group-append"> <button id="newsletter_subscription_button" class="btn btn-primary text-uppercase" type="button"> <strong>S'inscrire</strong></button> </div> </div> </div> </div> </div> </main> <div id="bandeau-footer"> <div class="container"> <p><a href="/abonnement" title="Abonnez-vous à Universalis pour 1 euro">Accédez à l'intégralité d'Universalis.fr <strong>sans publicité</strong></a></p> </div> </div> <footer class="container footer text-center d-print-none"> <ul class="list-inline list-inline-bullet mb-2"> <li class="list-inline-item"> <a href="http://www.encyclopaedia-universalis.fr/" title="Encyclopædia Universalis" rel="noopener" target="_blank">Encyclopædia Universalis </a> </li> <li class="list-inline-item"> <a href="https://www.encyclopaedia-universalis.fr/nous-contacter/infos/" title="Contactez-nous" rel="noopener nofollow" target="_blank">Contact</a></li> <li class="list-inline-item"> <a title="Mentions légales" rel="nofollow" href="/mentions-legales/">Mentions légales et politique de confidentialité</a> </li> <li class="list-inline-item"> <a href="https://abonnement.universalis.fr/typo3conf/ext/mailer/Resources/Public/Pdf/cgv.pdf" rel="noopener nofollow" target="_blank" title="Conditions générales de vente">CGV</a> </li> <li class="list-inline-item d-none d-md-inline-block"> <a href="javascript:" id="rgpd" rel="nofollow" title="Consentement RGPD">RGPD</a> </li> </ul> <p class="mb-2">Consulter le <a title="Dictionnaire de l'Encyclopædia Universalis" href="/dictionnaire/"> dictionnaire de l'Encyclopædia Universalis </a> </p> <p class="mb-3">© 2024 Encyclopædia Universalis France. 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