Calore specifico - Wikipedia

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<span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Attiva/disattiva la sottosezione Definizione generalizzata</span> </button> <ul id="toc-Definizione_generalizzata-sublist" class="vector-toc-list"> <li id="toc-Calore_specifico_isobaro_e_isocoro" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Calore_specifico_isobaro_e_isocoro"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Calore specifico isobaro e isocoro</span> </div> </a> <ul id="toc-Calore_specifico_isobaro_e_isocoro-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dipendenza_dalla_temperatura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dipendenza_dalla_temperatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Dipendenza dalla temperatura</span> </div> </a> <ul id="toc-Dipendenza_dalla_temperatura-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Relazioni_di_Mayer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relazioni_di_Mayer"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Relazioni di Mayer</span> </div> </a> <button aria-controls="toc-Relazioni_di_Mayer-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>Attiva/disattiva la sottosezione Relazioni di Mayer</span> </button> <ul id="toc-Relazioni_di_Mayer-sublist" class="vector-toc-list"> <li id="toc-Gas_perfetto" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gas_perfetto"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Gas perfetto</span> </div> </a> <ul id="toc-Gas_perfetto-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Determinazione_sperimentale" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Determinazione_sperimentale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Determinazione sperimentale</span> </div> </a> <ul id="toc-Determinazione_sperimentale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Calore_specifico_isobaro_di_alcune_sostanze" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Calore_specifico_isobaro_di_alcune_sostanze"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Calore specifico isobaro di alcune sostanze</span> </div> </a> <ul id="toc-Calore_specifico_isobaro_di_alcune_sostanze-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Calore_specifico_negativo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Calore_specifico_negativo"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Calore specifico negativo</span> </div> </a> <ul id="toc-Calore_specifico_negativo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Calore specifico</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="Vai a una voce in un'altra lingua. Disponibile in 58 lingue" > <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-58" 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">58 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Calor_especifica" title="Calor especifica - aragonese" lang="an" hreflang="an" data-title="Calor especifica" data-language-autonym="Aragonés" data-language-local-name="aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B1%D8%A7%D8%B1%D8%A9_%D9%86%D9%88%D8%B9%D9%8A%D8%A9" title="حرارة نوعية - arabo" lang="ar" hreflang="ar" data-title="حرارة نوعية" data-language-autonym="العربية" data-language-local-name="arabo" 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/Calor_espec%C3%ADfico" title="Calor específico - asturiano" lang="ast" hreflang="ast" data-title="Calor específico" data-language-autonym="Asturianu" data-language-local-name="asturiano" 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/X%C3%BCsusi_istilik_tutumu" title="Xüsusi istilik tutumu - azerbaigiano" lang="az" hreflang="az" data-title="Xüsusi istilik tutumu" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Spezifische_W%C3%A4rmekapazit%C3%A4t" title="Spezifische Wärmekapazität - bavarese" lang="bar" hreflang="bar" data-title="Spezifische Wärmekapazität" data-language-autonym="Boarisch" data-language-local-name="bavarese" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A3%D0%B4%D0%B7%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%86%D0%B5%D0%BF%D0%BB%D0%B0%D1%91%D0%BC%D1%96%D1%81%D1%82%D0%B0%D1%81%D1%86%D1%8C" title="Удзельная цеплаёмістасць - bielorusso" lang="be" hreflang="be" data-title="Удзельная цеплаёмістасць" data-language-autonym="Беларуская" data-language-local-name="bielorusso" 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%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%84%D0%B8%D1%87%D0%B5%D0%BD_%D1%82%D0%BE%D0%BF%D0%BB%D0%B8%D0%BD%D0%B5%D0%BD_%D0%BA%D0%B0%D0%BF%D0%B0%D1%86%D0%B8%D1%82%D0%B5%D1%82" title="Специфичен топлинен капацитет - bulgaro" lang="bg" hreflang="bg" data-title="Специфичен топлинен капацитет" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Specifi%C4%8Dna_toplota" title="Specifična toplota - bosniaco" lang="bs" hreflang="bs" data-title="Specifična toplota" data-language-autonym="Bosanski" data-language-local-name="bosniaco" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%95%D8%B1%D9%85%DB%8C%DB%8C_%D8%AC%DB%86%D8%B1%DB%8C" title="گەرمیی جۆری - curdo centrale" lang="ckb" hreflang="ckb" data-title="گەرمیی جۆری" data-language-autonym="کوردی" data-language-local-name="curdo centrale" 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/M%C4%9Brn%C3%A1_tepeln%C3%A1_kapacita" title="Měrná tepelná kapacita - ceco" lang="cs" hreflang="cs" data-title="Měrná tepelná kapacita" data-language-autonym="Čeština" data-language-local-name="ceco" 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%9F%D0%B0%D0%B9%D0%BB%D0%B0%D0%B2%D0%BB%D0%B0_%C4%83%D1%88%C4%83%D1%88%C4%83%D0%BD%C4%83%C3%A7%D1%82%D0%B0%D1%80%C4%83%D1%88" title="Пайлавла ăшăшăнăçтарăш - ciuvascio" lang="cv" hreflang="cv" data-title="Пайлавла ăшăшăнăçтарăш" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da badge-Q70893996 mw-list-item" title=""><a href="https://da.wikipedia.org/wiki/Varmefylde" title="Varmefylde - danese" lang="da" hreflang="da" data-title="Varmefylde" data-language-autonym="Dansk" data-language-local-name="danese" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Spezifische_W%C3%A4rmekapazit%C3%A4t" title="Spezifische Wärmekapazität - tedesco" lang="de" hreflang="de" data-title="Spezifische Wärmekapazität" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Specific_heat_capacity" title="Specific heat capacity - inglese" lang="en" hreflang="en" data-title="Specific heat capacity" data-language-autonym="English" data-language-local-name="inglese" 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/Masa_varmokapacito" title="Masa varmokapacito - esperanto" lang="eo" hreflang="eo" data-title="Masa varmokapacito" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es badge-Q17437798 badge-goodarticle mw-list-item" title="voce di qualità"><a href="https://es.wikipedia.org/wiki/Calor_espec%C3%ADfico" title="Calor específico - spagnolo" lang="es" hreflang="es" data-title="Calor específico" data-language-autonym="Español" data-language-local-name="spagnolo" 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/Erisoojus" title="Erisoojus - estone" lang="et" hreflang="et" data-title="Erisoojus" data-language-autonym="Eesti" data-language-local-name="estone" 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/Bero_espezifiko" title="Bero espezifiko - basco" lang="eu" hreflang="eu" data-title="Bero espezifiko" data-language-autonym="Euskara" data-language-local-name="basco" 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/%D8%B8%D8%B1%D9%81%DB%8C%D8%AA_%DA%AF%D8%B1%D9%85%D8%A7%DB%8C%DB%8C_%D9%88%DB%8C%DA%98%D9%87" title="ظرفیت گرمایی ویژه - persiano" lang="fa" hreflang="fa" data-title="ظرفیت گرمایی ویژه" data-language-autonym="فارسی" data-language-local-name="persiano" 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/Ominaisl%C3%A4mp%C3%B6kapasiteetti" title="Ominaislämpökapasiteetti - finlandese" lang="fi" hreflang="fi" data-title="Ominaislämpökapasiteetti" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Capacit%C3%A9_thermique_massique" title="Capacité thermique massique - francese" lang="fr" hreflang="fr" data-title="Capacité thermique massique" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Calor_espec%C3%ADfica" title="Calor específica - galiziano" lang="gl" hreflang="gl" data-title="Calor específica" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A4%BF%E0%A4%B7%E0%A5%8D%E0%A4%9F_%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE_%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A4%BF%E0%A4%A4%E0%A4%BE" title="विशिष्ट ऊष्मा धारिता - hindi" lang="hi" hreflang="hi" data-title="विशिष्ट ऊष्मा धारिता" 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/Specifi%C4%8Dna_toplina" title="Specifična toplina - croato" lang="hr" hreflang="hr" data-title="Specifična toplina" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A5%D5%BD%D5%A1%D5%AF%D5%A1%D6%80%D5%A1%D6%80_%D5%BB%D5%A5%D6%80%D5%B4%D5%B8%D6%82%D5%B6%D5%A1%D5%AF%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տեսակարար ջերմունակություն - armeno" lang="hy" hreflang="hy" data-title="Տեսակարար ջերմունակություն" data-language-autonym="Հայերեն" data-language-local-name="armeno" 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/Kalor_jenis" title="Kalor jenis - indonesiano" lang="id" hreflang="id" data-title="Kalor jenis" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" 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/E%C3%B0lisvarmi" title="Eðlisvarmi - islandese" lang="is" hreflang="is" data-title="Eðlisvarmi" data-language-autonym="Íslenska" data-language-local-name="islandese" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AF%94%E7%86%B1%E5%AE%B9%E9%87%8F" title="比熱容量 - giapponese" lang="ja" hreflang="ja" data-title="比熱容量" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/glanejni_sroka%27e" title="glanejni sroka'e - lojban" lang="jbo" hreflang="jbo" data-title="glanejni sroka'e" data-language-autonym="La .lojban." data-language-local-name="lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%97%E1%83%A0%E1%83%98_%E1%83%97%E1%83%91%E1%83%9D%E1%83%A2%E1%83%94%E1%83%95%E1%83%90%E1%83%93%E1%83%9D%E1%83%91%E1%83%90" title="კუთრი თბოტევადობა - georgiano" lang="ka" hreflang="ka" data-title="კუთრი თბოტევადობა" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B9%84%EC%97%B4%EC%9A%A9%EB%9F%89" title="비열용량 - coreano" lang="ko" hreflang="ko" data-title="비열용량" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Savitoji_%C5%A1ilumin%C4%97_talpa" title="Savitoji šiluminė talpa - lituano" lang="lt" hreflang="lt" data-title="Savitoji šiluminė talpa" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%84%D0%B8%D1%87%D0%B5%D0%BD_%D1%82%D0%BE%D0%BF%D0%BB%D0%B8%D0%BD%D1%81%D0%BA%D0%B8_%D0%BA%D0%B0%D0%BF%D0%B0%D1%86%D0%B8%D1%82%D0%B5%D1%82" title="Специфичен топлински капацитет - macedone" lang="mk" hreflang="mk" data-title="Специфичен топлински капацитет" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Muatan_haba_tentu" title="Muatan haba tentu - malese" lang="ms" hreflang="ms" data-title="Muatan haba tentu" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Soortelijke_warmte" title="Soortelijke warmte - olandese" lang="nl" hreflang="nl" data-title="Soortelijke warmte" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Spesifikk_varmekapasitet" title="Spesifikk varmekapasitet - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Spesifikk varmekapasitet" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Spesifikk_varmekapasitet" title="Spesifikk varmekapasitet - norvegese bokmål" lang="nb" hreflang="nb" data-title="Spesifikk varmekapasitet" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ciep%C5%82o_w%C5%82a%C5%9Bciwe" title="Ciepło właściwe - polacco" lang="pl" hreflang="pl" data-title="Ciepło właściwe" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Calor_espec%C3%ADfico" title="Calor específico - portoghese" lang="pt" hreflang="pt" data-title="Calor específico" data-language-autonym="Português" data-language-local-name="portoghese" 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/Capacitate_termic%C4%83_masic%C4%83" title="Capacitate termică masică - rumeno" lang="ro" hreflang="ro" data-title="Capacitate termică masică" data-language-autonym="Română" data-language-local-name="rumeno" 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%A3%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%B5%D0%BF%D0%BB%D0%BE%D1%91%D0%BC%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Удельная теплоёмкость - russo" lang="ru" hreflang="ru" data-title="Удельная теплоёмкость" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Caluri_spic%C3%ACficu" title="Caluri spicìficu - siciliano" lang="scn" hreflang="scn" data-title="Caluri spicìficu" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Specifi%C4%8Dna_toplota" title="Specifična toplota - serbo-croato" lang="sh" hreflang="sh" data-title="Specifična toplota" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Specific_heat" title="Specific heat - Simple English" lang="en-simple" hreflang="en-simple" data-title="Specific heat" 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/Hmotnostn%C3%A1_tepeln%C3%A1_kapacita" title="Hmotnostná tepelná kapacita - slovacco" lang="sk" hreflang="sk" data-title="Hmotnostná tepelná kapacita" data-language-autonym="Slovenčina" data-language-local-name="slovacco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl badge-Q17437796 badge-featuredarticle mw-list-item" title="voce in vetrina"><a href="https://sl.wikipedia.org/wiki/Specifi%C4%8Dna_toplota" title="Specifična toplota - sloveno" lang="sl" hreflang="sl" data-title="Specifična toplota" data-language-autonym="Slovenščina" data-language-local-name="sloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%84%D0%B8%D1%87%D0%BD%D0%B0_%D1%82%D0%BE%D0%BF%D0%BB%D0%BE%D1%82%D0%B0" title="Специфична топлота - serbo" lang="sr" hreflang="sr" data-title="Специфична топлота" data-language-autonym="Српски / srpski" data-language-local-name="serbo" 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/Specifik_v%C3%A4rmekapacitet" title="Specifik värmekapacitet - svedese" lang="sv" hreflang="sv" data-title="Specifik värmekapacitet" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%88%E0%B8%B8%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A3%E0%B9%89%E0%B8%AD%E0%B8%99%E0%B8%88%E0%B8%B3%E0%B9%80%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="ความจุความร้อนจำเพาะ - thailandese" lang="th" hreflang="th" data-title="ความจุความร้อนจำเพาะ" data-language-autonym="ไทย" data-language-local-name="thailandese" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96zg%C3%BCl_%C4%B1s%C4%B1" title="Özgül ısı - turco" lang="tr" hreflang="tr" data-title="Özgül ısı" data-language-autonym="Türkçe" data-language-local-name="turco" 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%9F%D0%B8%D1%82%D0%BE%D0%BC%D0%B0_%D1%82%D0%B5%D0%BF%D0%BB%D0%BE%D1%94%D0%BC%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Питома теплоємність - ucraino" lang="uk" hreflang="uk" data-title="Питома теплоємність" data-language-autonym="Українська" data-language-local-name="ucraino" 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/%D8%AD%D8%B1%D8%A7%D8%B1%D8%AA_%D8%A7%D8%B6%D8%A7%D9%81%DB%8C" title="حرارت اضافی - urdu" lang="ur" hreflang="ur" data-title="حرارت اضافی" data-language-autonym="اردو" data-language-local-name="urdu" 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/Solishtirma_issiqlik_sig%CA%BBimi" title="Solishtirma issiqlik sigʻimi - uzbeco" lang="uz" hreflang="uz" data-title="Solishtirma issiqlik sigʻimi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeco" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Ca%C5%82or_spesifego" title="Całor spesifego - veneto" lang="vec" hreflang="vec" data-title="Całor spesifego" data-language-autonym="Vèneto" data-language-local-name="veneto" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nhi%E1%BB%87t_dung_ri%C3%AAng" title="Nhiệt dung riêng - vietnamita" lang="vi" hreflang="vi" data-title="Nhiệt dung riêng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" 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/%E6%AF%94%E7%83%AD%E5%AE%B9" title="比热容 - wu" lang="wuu" hreflang="wuu" data-title="比热容" 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/%E6%AF%94%E7%86%B1%E5%AE%B9" title="比熱容 - cinese" lang="zh" hreflang="zh" data-title="比熱容" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AF%94%E7%86%B1%E5%AE%B9%E9%87%8F" title="比熱容量 - cantonese" lang="yue" hreflang="yue" data-title="比熱容量" data-language-autonym="粵語" data-language-local-name="cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q487756#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespace"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Calore_specifico" title="Vedi la voce [c]" accesskey="c"><span>Voce</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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href="/wiki/Speciale:PuntanoQui/Calore_specifico" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Calore_specifico" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Calore_specifico&oldid=141673924" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Calore_specifico&action=info" title="Ulteriori informazioni su questa pagina"><span>Informazioni pagina</span></a></li><li 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lang="it" dir="ltr"><p>Il <b>calore specifico</b> di una <a href="/wiki/Sostanza_pura" title="Sostanza pura">sostanza</a> è definito come la quantità di <a href="/wiki/Calore" title="Calore">calore</a> necessaria per innalzare, o diminuire, di un <a href="/wiki/Kelvin" title="Kelvin">Kelvin</a> la <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> di una unità di sostanza. </p><p>Esso può essere definito in termini di unità di <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>, pertanto viene detto <b>calore specifico massico</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 c_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5a92f980a7ccf6827b6925c6d6421984d9c5859" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.682ex; height:2.009ex;" alt="{\displaystyle c_{m}}"></span>, o semplicemente <b>calore specifico</b>, o in termini di unità di <a href="/wiki/Quantit%C3%A0_di_materia" class="mw-redirect" title="Quantità di materia">quantità di materia</a>, per cui prende il nome di <b>calore specifico molare</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 c_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b7e944bcb1be88e9a6a940638f2adce0ec4211a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.225ex; height:2.009ex;" alt="{\displaystyle c_{n}}"></span>, o semplicemente <b>calore molare</b>. </p><p>Nel <a href="/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura" title="Sistema internazionale di unità di misura">Sistema internazionale</a> l'<a href="/wiki/Unit%C3%A0_di_misura" title="Unità di misura">unità di misura</a> del calore specifico è il <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[\mathrm {J\cdot kg^{-1}\cdot K^{-1}} \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> <mo>⋅</mo> <mi mathvariant="normal">k</mi> <msup> <mi mathvariant="normal">g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi mathvariant="normal">K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\mathrm {J\cdot kg^{-1}\cdot K^{-1}} \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d44fc9523fb469df0eda6ee6f9dd2ae8d1fde5e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.356ex; height:3.343ex;" alt="{\displaystyle \left[\mathrm {J\cdot kg^{-1}\cdot K^{-1}} \right]}"></span>, anche se si usa molto la <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[\mathrm {kcal\cdot kg^{-1}\cdot {}^{\circ }C^{-1}} \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mo>⋅</mo> <mi mathvariant="normal">k</mi> <msup> <mi mathvariant="normal">g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <msup> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\mathrm {kcal\cdot kg^{-1}\cdot {}^{\circ }C^{-1}} \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beeb012374872596ce204651acd03d02f9e46bc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.155ex; height:3.343ex;" alt="{\displaystyle \left[\mathrm {kcal\cdot kg^{-1}\cdot {}^{\circ }C^{-1}} \right]}"></span>, mentre quella del calore molare è il <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[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> <mo>⋅</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <msup> <mi mathvariant="normal">l</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi mathvariant="normal">K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a239835e1d2eaf84216c8f57ed12a0092210a805" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.711ex; height:3.343ex;" alt="{\displaystyle \left[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}"></span>. </p><p>In maniera più astratta, si può definire come il coefficiente tra gli incrementi di temperatura e di calore: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=c\ \mathrm {d} T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> <mo>=</mo> <mi>c</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q=c\ \mathrm {d} T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb30dec5d9b2726e3200fc4183927110034d217b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.502ex; height:2.676ex;" alt="{\displaystyle \delta Q=c\ \mathrm {d} T}"></span> </p><p>che dipende dal tipo di trasformazione in corso </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definizione_generalizzata">Definizione generalizzata</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=1" title="Modifica la sezione Definizione generalizzata" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=1" title="Edit section's source code: Definizione generalizzata"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Esistono svariati modi per esprimere il calore specifico di una sostanza, a seconda dalla trasformazione, e in particolare (notazione) dalla <a href="/wiki/Grandezza_fisica" title="Grandezza fisica">grandezza fisica</a> <i>x</i> conservata nella trasformazione:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{x}=T\left({\frac {\partial s}{\partial T}}\right)_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{x}=T\left({\frac {\partial s}{\partial T}}\right)_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32aa74f04a1d862719c6242862be2df185fe802c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.298ex; height:6.176ex;" alt="{\displaystyle c_{x}=T\left({\frac {\partial s}{\partial T}}\right)_{x}}"></span></dd></dl> <p>Moltiplicando i calori specifici per la massa <i>m</i> otteniamo le <a href="/wiki/Capacit%C3%A0_termica" title="Capacità termica">capacità termiche</a> <i>C<sub>x</sub></i>. In generale si utilizzano due valori, riferiti a una trasformazione a <a href="/wiki/Coordinata_generalizzata" class="mw-redirect" title="Coordinata generalizzata">coordinata generalizzata</a> costante e a <a href="/wiki/Forza_generalizzata" class="mw-redirect" title="Forza generalizzata">forza generalizzata</a> costante: </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 {\begin{aligned}&c_{q}=T\left({\frac {\partial s}{\partial T}}\right)_{q}\\[4pt]&c_{F}=T\left({\frac {\partial s}{\partial T}}\right)_{F}\\[4pt]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.7em 0.7em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd /> <mtd> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&c_{q}=T\left({\frac {\partial s}{\partial T}}\right)_{q}\\[4pt]&c_{F}=T\left({\frac {\partial s}{\partial T}}\right)_{F}\\[4pt]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c66cff8a88bd4ceb6ed75d7177a75851f89c610" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.338ex; width:16.631ex; height:13.843ex;" alt="{\displaystyle {\begin{aligned}&c_{q}=T\left({\frac {\partial s}{\partial T}}\right)_{q}\\[4pt]&c_{F}=T\left({\frac {\partial s}{\partial T}}\right)_{F}\\[4pt]\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Calore_specifico_isobaro_e_isocoro">Calore specifico isobaro e isocoro</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=2" title="Modifica la sezione Calore specifico isobaro e isocoro" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=2" title="Edit section's source code: Calore specifico isobaro e isocoro"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I calori specifici più utilizzati sono riferiti al <a href="/wiki/Lavoro_di_volume" title="Lavoro di volume">lavoro di volume</a>: il calore specifico a <i>volume costante</i>, reso in simboli come <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1ed5361b532828e1bda88a5282706a31b5d082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.503ex; height:2.009ex;" alt="{\displaystyle c_{V}}"></span>, e il calore specifico a <i>pressione costante</i>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span> validi per la trasformazione <a href="/wiki/Isocora" title="Isocora">isocora</a> e quella <a href="/wiki/Isobara_(termodinamica)" title="Isobara (termodinamica)">isobara</a>. Se nel sistema i lavori generalizzati sono esclusivamente calore trasmesso e lavoro di volume, allora il <a href="/wiki/Primo_principio_della_termodinamica" title="Primo principio della termodinamica">primo principio della termodinamica</a> si può esprimere in <a href="/wiki/Energia_interna" title="Energia interna">energia interna</a> ed <a href="/wiki/Entalpia" title="Entalpia">entalpia</a> equivalenti per <a href="/wiki/Trasformata_di_Legendre" title="Trasformata di Legendre">trasformata di Legendre</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 {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S=0\\[4pt]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.7em 0.7em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>H</mi> <mo>−</mo> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S=0\\[4pt]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12db4c0c2164b312c84789c4ea4150dc7f53ae76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:22.727ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S=0\\[4pt]\end{aligned}}}"></span></dd></dl> <p>quindi: </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 c_{V}={\frac {\partial U}{\partial T}}\qquad c_{p}={\frac {\partial H}{\partial T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mspace width="2em" /> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}={\frac {\partial U}{\partial T}}\qquad c_{p}={\frac {\partial H}{\partial T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3672b98d0fd0e40543b7eab30c090691378d0455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.566ex; height:5.509ex;" alt="{\displaystyle c_{V}={\frac {\partial U}{\partial T}}\qquad c_{p}={\frac {\partial H}{\partial T}}}"></span></dd></dl> <p>altrimenti se ammettiamo altre forme di lavoro nel sistema, ovvero <i>altre</i> coordinate intesa ciascuna come <a href="/wiki/Funzione_di_stato" title="Funzione di stato">funzione di stato</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 {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S+F\ \delta q=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S+F\ \delta q=0\\[4pt]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.7em 0.7em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>+</mo> <mi>F</mi> <mtext> </mtext> <mi>δ</mi> <mi>q</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>H</mi> <mo>−</mo> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>p</mi> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>+</mo> <mi>F</mi> <mtext> </mtext> <mi>δ</mi> <mi>q</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S+F\ \delta q=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S+F\ \delta q=0\\[4pt]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ba57f3d3bbd47aa919e4ff2e2d8828c77900715" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:30.007ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}&\mathrm {d} U+p\mathrm {d} V-T\mathrm {d} S+F\ \delta q=0\\[4pt]&\mathrm {d} H-V\mathrm {d} p-T\mathrm {d} S+F\ \delta q=0\\[4pt]\end{aligned}}}"></span></dd></dl> <p>bisognerà considerare la loro influenza sui calori specifici: </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 c_{V}={\frac {\partial U}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{V}\qquad c_{p}={\frac {\partial H}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>F</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mspace width="2em" /> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>F</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}={\frac {\partial U}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{V}\qquad c_{p}={\frac {\partial H}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8620376815af3b8347a7cd061977dd07388cd1c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:49.706ex; height:6.509ex;" alt="{\displaystyle c_{V}={\frac {\partial U}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{V}\qquad c_{p}={\frac {\partial H}{\partial T}}+F\left({\frac {\partial q}{\partial T}}\right)_{p}}"></span></dd></dl> <p>Sebbene i solidi e i liquidi siano poco dilatabili, la differenza tra <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1ed5361b532828e1bda88a5282706a31b5d082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.503ex; height:2.009ex;" alt="{\displaystyle c_{V}}"></span> non è trascurabile: infatti, per i solidi è <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}/c_{V}\approx 1,05}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>≈</mo> <mn>1</mn> <mo>,</mo> <mn>05</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}/c_{V}\approx 1,05}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edf3cc6028a208636cb67c54b0c6dfce6482c2ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.351ex; height:3.009ex;" alt="{\displaystyle c_{p}/c_{V}\approx 1,05}"></span> mentre per i liquidi in molti casi è <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}/c_{V}\approx 1,2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>≈</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}/c_{V}\approx 1,2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e96227c5854e253b724cf1c9bbfc0886aba1b84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.189ex; height:3.009ex;" alt="{\displaystyle c_{p}/c_{V}\approx 1,2}"></span> ma si hanno anche liquidi con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}/c_{V}>1,5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>></mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}/c_{V}>1,5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/639adc5a240afd33630954141db9b238551cf7aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.189ex; height:3.009ex;" alt="{\displaystyle c_{p}/c_{V}>1,5}"></span>. Per un aeriforme il calore specifico a pressione costante differisce da quello a <a href="/wiki/Volume" title="Volume">volume</a> costante per il lavoro di <a href="/wiki/Trasformazione_isobara" class="mw-redirect" title="Trasformazione isobara">espansione</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Dipendenza_dalla_temperatura">Dipendenza dalla temperatura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=3" title="Modifica la sezione Dipendenza dalla temperatura" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=3" title="Edit section's source code: Dipendenza dalla temperatura"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Grafico_calori_specifici_gas.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Grafico_calori_specifici_gas.png/310px-Grafico_calori_specifici_gas.png" decoding="async" width="310" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Grafico_calori_specifici_gas.png/465px-Grafico_calori_specifici_gas.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Grafico_calori_specifici_gas.png/620px-Grafico_calori_specifici_gas.png 2x" data-file-width="667" data-file-height="394" /></a><figcaption>Grafico dei calori specifici di gas perfetto a volume costante di alcuni gas</figcaption></figure> <p>Il calore specifico è una grandezza in generale dipendente dalla temperatura. Le correlazioni semiempiriche sono solitamente sviluppate in <a href="/wiki/Serie_di_Taylor" title="Serie di Taylor">serie di Taylor</a> fino al quarto ordine:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c^{0}=a+bT+cT^{2}+dT^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>T</mi> <mo>+</mo> <mi>c</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>d</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c^{0}=a+bT+cT^{2}+dT^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fac2ba2b2a3b5c7757454ddc01736df7188904f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.316ex; height:2.843ex;" alt="{\displaystyle c^{0}=a+bT+cT^{2}+dT^{3}}"></span></dd></dl> <p>con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddd708c4ec8b8a343be52c5a7e8d8e0a0148aeb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.061ex; height:2.676ex;" alt="{\displaystyle c^{0}}"></span> in <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[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> <mo>⋅</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <msup> <mi mathvariant="normal">l</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi mathvariant="normal">K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a239835e1d2eaf84216c8f57ed12a0092210a805" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.711ex; height:3.343ex;" alt="{\displaystyle \left[\mathrm {J\cdot mol^{-1}\cdot K^{-1}} \right]}"></span> dove <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> sono tabulate per sostanza e <i>T</i> è la <a href="/wiki/Temperatura_assoluta" title="Temperatura assoluta">temperatura assoluta</a>.<sup id="cite_ref-Cengel_4-0" class="reference"><a href="#cite_note-Cengel-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Come si nota dalla figura a fianco, per alcuni gas, in determinati intervalli di temperatura, un tipo di calore specifico può considerarsi costante con essa e questo è particolarmente vero per i gas monoatomici, come i <a href="/wiki/Gas_nobili" title="Gas nobili">gas nobili</a>.<sup id="cite_ref-Cengel_4-1" class="reference"><a href="#cite_note-Cengel-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Relazioni_di_Mayer">Relazioni di Mayer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=4" title="Modifica la sezione Relazioni di Mayer" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=4" title="Edit section's source code: Relazioni di Mayer"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In base alla <a href="/wiki/Relazioni_di_Maxwell" title="Relazioni di Maxwell">relazione di Maxwell</a> in entropia e temperatura i calori specifici o molari o le capacità termiche rispettivamente a coordinata costante e forza coniugata costante sono legati: </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 {\begin{aligned}x_{i}\neq s,&\quad F_{i}\neq T\\[4pt]\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}&=\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\\[4pt]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.7em 0.7em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≠</mo> <mi>s</mi> <mo>,</mo> </mtd> <mtd> <mspace width="1em" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≠</mo> <mi>T</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x_{i}\neq s,&\quad F_{i}\neq T\\[4pt]\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}&=\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\\[4pt]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca628da4f8c60eb8bd1f4220b30765706cc4d66d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.408ex; margin-bottom: -0.263ex; width:22.611ex; height:10.509ex;" alt="{\displaystyle {\begin{aligned}x_{i}\neq s,&\quad F_{i}\neq T\\[4pt]\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}&=\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\\[4pt]\end{aligned}}}"></span></dd></dl> <p>che sostituita nell'identità: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial s}{\partial T}}\right)_{F_{i}}=\left({\frac {\partial s}{\partial T}}\right)_{x_{i}}+\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}"> <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>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial s}{\partial T}}\right)_{F_{i}}=\left({\frac {\partial s}{\partial T}}\right)_{x_{i}}+\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df5aec84c6c20854252ddf70a9b75a3d7733b54e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:42.786ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial s}{\partial T}}\right)_{F_{i}}=\left({\frac {\partial s}{\partial T}}\right)_{x_{i}}+\left({\frac {\partial s}{\partial x_{i}}}\right)_{T}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}"></span></dd></dl> <p>porta, tenendo conto della definizione di calore specifico alle <i>relazioni di <a href="/wiki/Julius_Robert_von_Mayer" title="Julius Robert von Mayer">Mayer</a></i><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>: </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 c_{F_{i}}-c_{x_{i}}=T\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{F_{i}}-c_{x_{i}}=T\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72015634c45441b059470623b5f594325962d63a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:32.586ex; height:6.509ex;" alt="{\displaystyle c_{F_{i}}-c_{x_{i}}=T\left({\frac {\partial F_{i}}{\partial T}}\right)_{x_{i}}\left({\frac {\partial x_{i}}{\partial T}}\right)_{F_{i}}}"></span></dd></dl> <p>Per un <b>sistema termodinamico semplice</b> abbiamo una sola relazione: </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 c_{p}-c_{V}=T\left({\frac {\partial p}{\partial T}}\right)_{V}\left({\frac {\partial V}{\partial T}}\right)_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}-c_{V}=T\left({\frac {\partial p}{\partial T}}\right)_{V}\left({\frac {\partial V}{\partial T}}\right)_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2934fcf32846ae8b75562bc019cf702dfb5da31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:29.273ex; height:6.509ex;" alt="{\displaystyle c_{p}-c_{V}=T\left({\frac {\partial p}{\partial T}}\right)_{V}\left({\frac {\partial V}{\partial T}}\right)_{p}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Gas_perfetto">Gas perfetto</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=5" title="Modifica la sezione Gas perfetto" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=5" title="Edit section's source code: Gas perfetto"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per un <a href="/wiki/Gas_perfetto" class="mw-redirect" title="Gas perfetto">gas perfetto</a>, che appartiene ai sistemi termodinamici semplici, la relazione di Mayer ha le seguenti espressioni: </p> <ol><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 c_{p}=c_{V}+\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}=c_{V}+\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8aca707f4b8972c7cd51b0a3c28cf22d2594a7f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.432ex; height:2.843ex;" alt="{\displaystyle c_{p}=c_{V}+\Re }"></span><br />con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1ed5361b532828e1bda88a5282706a31b5d082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.503ex; height:2.009ex;" alt="{\displaystyle c_{V}}"></span> i calori molari rispettivamente a pressione e volume costante e <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 \Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc5a2cb7aa22f6d765976edb1daebefaf408142" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle \Re }"></span> costante dei gas perfetti;</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 c_{p}=c_{V}+R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>+</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}=c_{V}+R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eff3e5a0d218065f297e85dd8cc2e6ec898505d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.272ex; height:2.843ex;" alt="{\displaystyle c_{p}=c_{V}+R}"></span><br />con <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> costante specifica dei gas perfetti pari 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 R={\Re /M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">ℜ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R={\Re /M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43c757b8376bb35ceda27cd65b4e2e770125c5e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.391ex; height:2.843ex;" alt="{\displaystyle R={\Re /M}}"></span> dove <i>M</i> è il peso molare della sostanza, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd3e4dfd14610335b7e1fe0a498410dba4f0e6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.036ex; height:2.009ex;" alt="{\displaystyle c_{v}}"></span> i calori specifici rispettivamente a pressione e volume costante.</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 C_{p}=C_{V}+n\Re =C_{V}+mR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi mathvariant="normal">ℜ</mi> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>+</mo> <mi>m</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{p}=C_{V}+n\Re =C_{V}+mR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab14e4b31de71a7f77098fc7bfe1153e0d6eec37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.038ex; height:2.843ex;" alt="{\displaystyle C_{p}=C_{V}+n\Re =C_{V}+mR}"></span><br />con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc37470431fbf62081b69ba870ad3f855178361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.721ex; height:2.843ex;" alt="{\displaystyle C_{p}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c18988639f2937d3fe4dc00dfa0b0bd7e0bec1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.158ex; height:2.509ex;" alt="{\displaystyle C_{V}}"></span> le capacità termiche rispettivamente a pressione e volume costante e <i>n</i> e <i>m</i> sono rispettimavente le moli e la massa di sostanza.</li></ol> <p>Per ottenere questa relazione ad esempio tra calori molari si considerino <i>n</i> <a href="/wiki/Mole" title="Mole">moli</a> di gas perfetto che acquistano una certa quantità di calore infinitesima a pressione costante: </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 \delta Q_{p}=n\cdot c_{p}\ \mathrm {d} T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{p}=n\cdot c_{p}\ \mathrm {d} T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a19264f1c294a47573e422a14381bf5bd394dbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.694ex; height:3.009ex;" alt="{\displaystyle \delta Q_{p}=n\cdot c_{p}\ \mathrm {d} T}"></span></dd></dl> <p>si avrà una variazione della temperatura corrispondente 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 \mathrm {d} T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/309833548168052f2696ca961149df099b5d1f80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.929ex; height:2.176ex;" alt="{\displaystyle \mathrm {d} T}"></span> proporzionale al <a href="/wiki/Calore_molare" class="mw-redirect" title="Calore molare">calore molare</a> a pressione costante <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77463f4fbb953a6f1fe19d83708e553f6d21457f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}"></span>. Il <a href="/wiki/Primo_principio_della_termodinamica" title="Primo principio della termodinamica">primo principio della termodinamica</a> per questa trasformazione si esprime: </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 \delta Q_{p}=\mathrm {d} U+\delta W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mi>δ</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{p}=\mathrm {d} U+\delta W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07aa03e0569085b21761a25644d948d3cc1d68a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.444ex; height:3.009ex;" alt="{\displaystyle \delta Q_{p}=\mathrm {d} U+\delta W}"></span></dd></dl> <p>da cui: </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 nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+p\ \mathrm {d} V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>=</mo> <mi>n</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <mi>p</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+p\ \mathrm {d} V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52a678216a7dc164c828d344ee682c1a34d75e25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.146ex; height:2.843ex;" alt="{\displaystyle nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+p\ \mathrm {d} V}"></span></dd></dl> <p>per l'<a href="/wiki/Equazione_di_stato_dei_gas" class="mw-redirect" title="Equazione di stato dei gas">equazione di stato dei gas</a> ideali, l'ultimo termine si può scrivere: </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\ \mathrm {d} V=n\Re \ \mathrm {d} T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>=</mo> <mi>n</mi> <mi mathvariant="normal">ℜ</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\ \mathrm {d} V=n\Re \ \mathrm {d} T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd668c6175c9a7bd5b67fdfeb73c5d5982e50b5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:14.846ex; height:2.509ex;" alt="{\displaystyle p\ \mathrm {d} V=n\Re \ \mathrm {d} T}"></span></dd></dl> <p>per cui abbiamo: </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 nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+n\Re \ \mathrm {d} T=n(c_{V}+\Re )\ \mathrm {d} T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>=</mo> <mi>n</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <mi>n</mi> <mi mathvariant="normal">ℜ</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>=</mo> <mi>n</mi> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">ℜ</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+n\Re \ \mathrm {d} T=n(c_{V}+\Re )\ \mathrm {d} T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7d692226f382c577cbe36e93a1701d04f0dced5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:44.224ex; height:3.009ex;" alt="{\displaystyle nc_{p}\ \mathrm {d} T=nc_{V}\ \mathrm {d} T+n\Re \ \mathrm {d} T=n(c_{V}+\Re )\ \mathrm {d} T}"></span></dd></dl> <p>semplificando si ottiene la <i>relazione di Mayer</i> tra i calori molari.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Determinazione_sperimentale">Determinazione sperimentale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=6" title="Modifica la sezione Determinazione sperimentale" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=6" title="Edit section's source code: Determinazione sperimentale"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il <a href="/wiki/Teorema_di_equipartizione_dell%27energia" title="Teorema di equipartizione dell'energia">teorema di equipartizione dell'energia</a> permette di calcolare agevolmente il calore specifico di un <a href="/wiki/Gas_ideale" title="Gas ideale">gas con comportamento ideale</a>, su basi di <a href="/wiki/Meccanica_classica" title="Meccanica classica">meccanica classica</a>. </p><p>La <a href="/wiki/Legge_di_Dulong-Petit" title="Legge di Dulong-Petit">legge di Dulong-Petit</a> stabilisce, su base classica, che il calore molare di tutti i solidi è lo stesso, indipendentemente dalla temperatura. <a href="/wiki/IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a> e <a href="/wiki/IUPAP" class="mw-redirect" title="IUPAP">IUPAP</a> utilizzano il termine capacità termica specifica o molare, anziché calore specifico e calore molare. </p><p>Il calore specifico dipende dalla natura chimica della sostanza considerata e dalla temperatura. Si può ritenere costante solo per piccole variazioni di temperatura e lontano dalle temperature di <a href="/wiki/Transizione_di_fase" title="Transizione di fase">transizione di fase</a>. Brusche variazioni del calore specifico vengono infatti prese come indice di una transizione di fase solido-liquido, liquido-vapore e anche transizioni cristalline o transizioni strutturali di una <a href="/wiki/Molecola" title="Molecola">molecola</a>. </p><p>Anche se per scopi pratici questa definizione è sufficientemente precisa, dal punto di vista teorico essa è solo di un'approssimazione, poiché in realtà il calore specifico dipende dalla temperatura stessa. Per una trattazione più rigorosa ci si può basare sulla <a href="/wiki/Capacit%C3%A0_termica" title="Capacità termica">capacità termica</a> e definire il calore specifico come la capacità termica per unità di <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>. </p><p>L'<a href="/wiki/Acqua" title="Acqua">acqua</a> a 15 °C ha un calore specifico di 1 cal / (<a href="/wiki/Grammo" title="Grammo">g</a> × °C) mentre quello dell'alcol etilico è di 0,581 cal / (g × °C). </p><p>Il calore specifico a pressione e volume costante vengono definiti rispettivamente a partire dall'<a href="/wiki/Entalpia" title="Entalpia">entalpia</a> e dall'<a href="/wiki/Energia_interna" title="Energia interna">energia interna</a>. Da queste definizioni si ricavano due relazioni valide per qualunque fluido: </p><p>Per l'energia interna: </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 \Delta U=mc_{V}(T_{2}-T_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>m</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=mc_{V}(T_{2}-T_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb05f7f7b12f7d0053a142232e8ae5d3821d38f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.833ex; height:2.843ex;" alt="{\displaystyle \Delta U=mc_{V}(T_{2}-T_{1})}"></span>,</dd></dl> <p>dove: </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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>: è la <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a> (kg) di <a href="/wiki/Fluido" title="Fluido">fluido</a> coinvolta</dd> <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 \Delta T=(T_{2}-T_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T=(T_{2}-T_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48b790914bc566f262e14490f87c35f8553a09da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.144ex; height:2.843ex;" alt="{\displaystyle \Delta T=(T_{2}-T_{1})}"></span>: è la variazione di temperatura (K).</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1ed5361b532828e1bda88a5282706a31b5d082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.503ex; height:2.009ex;" alt="{\displaystyle c_{V}}"></span>: è il calore specifico a <a href="/wiki/Volume" title="Volume">volume</a> costante.</dd></dl> <p>E per l'entalpia: </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 \Delta H=mc_{p}(T_{2}-T_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>=</mo> <mi>m</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H=mc_{p}(T_{2}-T_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd517a5768880fb9734b10d74de8ff7dc97e8aa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.678ex; height:3.009ex;" alt="{\displaystyle \Delta H=mc_{p}(T_{2}-T_{1})}"></span><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>.</dd></dl> <p>Nel modello teorico del <a href="/wiki/Gas_perfetto" class="mw-redirect" title="Gas perfetto">gas perfetto</a> il valore del calore molare vale: </p> <ul><li>Nel caso di gas monoatomici <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 {3 \over 2}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {3 \over 2}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/806e81862726ba8bd910f559ce3dfa79d9afdb67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.923ex; height:5.176ex;" alt="{\displaystyle {3 \over 2}\Re }"></span> (a volume costante) e <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 {5 \over 2}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {5 \over 2}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8091b3a482f313cab21ea5b513becb7aed5a1c49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.923ex; height:5.176ex;" alt="{\displaystyle {5 \over 2}\Re }"></span> (a pressione costante).</li> <li>Nel caso di gas biatomici o poliatomici con molecola allineata <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 {5 \over 2}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {5 \over 2}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8091b3a482f313cab21ea5b513becb7aed5a1c49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.923ex; height:5.176ex;" alt="{\displaystyle {5 \over 2}\Re }"></span> (a volume costante) e <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 {7 \over 2}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {7 \over 2}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc93c840eddb4b9f922ea5901e20c2057b511aae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.923ex; height:5.176ex;" alt="{\displaystyle {7 \over 2}\Re }"></span> (a pressione costante).</li> <li>Nel caso di gas poliatomici con molecola non allineata <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 {3}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {3}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65800ff3cfcf16ae1d1b39c51c4382d87301bf7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.087ex; height:2.176ex;" alt="{\displaystyle {3}\Re }"></span> (a volume costante) e <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 {4}\Re }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mi mathvariant="normal">ℜ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {4}\Re }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/faa52a8821232dbf92cf3a5d8719c84b6a443e69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.087ex; height:2.176ex;" alt="{\displaystyle {4}\Re }"></span> (a pressione costante).</li></ul> <p>Spesso il gas monoatomico perfetto viene immaginato come uno pseudo-<a href="/wiki/Idrogeno" title="Idrogeno">idrogeno</a>, con peso molecolare uguale a 1. </p> <div class="mw-heading mw-heading2"><h2 id="Calore_specifico_isobaro_di_alcune_sostanze">Calore specifico isobaro di alcune sostanze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=7" title="Modifica la sezione Calore specifico isobaro di alcune sostanze" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=7" title="Edit section's source code: Calore specifico isobaro di alcune sostanze"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable"> <tbody><tr> <th>Sostanza </th> <th><a href="/wiki/Stato_della_materia" title="Stato della materia">Stato</a> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc37470431fbf62081b69ba870ad3f855178361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.721ex; height:2.843ex;" alt="{\displaystyle C_{p}}"></span><br />kcal/(kg·K) </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc37470431fbf62081b69ba870ad3f855178361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.721ex; height:2.843ex;" alt="{\displaystyle C_{p}}"></span><br />J/(kg·K) </th></tr> <tr> <td><a href="/wiki/Alluminio" title="Alluminio">Alluminio</a></td> <td>solido </td> <td>0,210</td> <td align="right">880 </td></tr> <tr> <td><a href="/wiki/Acciaio_inox" class="mw-redirect" title="Acciaio inox">Acciaio inox</a></td> <td>solido </td> <td>0,120</td> <td align="right">502 </td></tr> <tr> <td><a href="/wiki/Acqua" title="Acqua">Acqua</a></td> <td>liquido </td> <td>1,000</td> <td align="right">4186 </td></tr> <tr> <td>Acqua (<a href="/wiki/Ghiaccio" title="Ghiaccio">Ghiaccio</a>)</td> <td>solido (0 °C) </td> <td>0,499</td> <td align="right">2090 </td></tr> <tr> <td><a href="/wiki/Anidride_carbonica" title="Anidride carbonica">Anidride carbonica</a></td> <td>gassoso </td> <td>0,200</td> <td align="right">838 </td></tr> <tr> <td><a href="/wiki/Aria" title="Aria">Aria</a> (secca)</td> <td>gassoso </td> <td>0,240</td> <td align="right">1005 </td></tr> <tr> <td><a href="/wiki/Aria" title="Aria">Aria</a> (100% umidità relativa)</td> <td>gassoso </td> <td>0,246</td> <td align="right">~ 1030 </td></tr> <tr> <td><a href="/wiki/Azoto" title="Azoto">Azoto</a></td> <td>gassoso </td> <td>0,249</td> <td align="right">1042 </td></tr> <tr> <td><a href="/wiki/Berillio" title="Berillio">Berillio</a></td> <td>solido </td> <td>0,436</td> <td align="right">1824 </td></tr> <tr> <td><a href="/wiki/Diamante" title="Diamante">Diamante</a></td> <td>solido </td> <td>0,120</td> <td align="right">502 </td></tr> <tr> <td><a href="/wiki/Elio" title="Elio">Elio</a></td> <td>gassoso </td> <td>1,240</td> <td align="right">5190 </td></tr> <tr> <td><a href="/wiki/Etanolo" title="Etanolo">Etanolo</a></td> <td>liquido </td> <td>0,588</td> <td align="right">2460 </td></tr> <tr> <td><a href="/wiki/Ferro" title="Ferro">Ferro</a></td> <td>solido </td> <td>0,110</td> <td align="right">460 </td></tr> <tr> <td><a href="/wiki/Glicerina" class="mw-redirect" title="Glicerina">Glicerina</a></td> <td>liquido </td> <td>0,540</td> <td align="right">2260 </td></tr> <tr> <td><a href="/wiki/Grafite" title="Grafite">Grafite</a></td> <td>solido </td> <td>0,172</td> <td align="right">720 </td></tr> <tr> <td><a href="/wiki/Idrogeno" title="Idrogeno">Idrogeno</a></td> <td>gassoso </td> <td>3,448</td> <td align="right">14435 </td></tr> <tr> <td><a href="/wiki/Litio" title="Litio">Litio</a></td> <td>solido </td> <td>0,856</td> <td align="right">3582 </td></tr> <tr> <td><a href="/wiki/Marmo" title="Marmo">Marmo</a></td> <td>solido </td> <td>0,210</td> <td align="right">880 </td></tr> <tr> <td><a href="/wiki/Mercurio_(elemento_chimico)" title="Mercurio (elemento chimico)">Mercurio</a></td> <td>liquido </td> <td>0,033</td> <td align="right">139 </td></tr> <tr> <td><a href="/wiki/Olio" title="Olio">Olio</a></td> <td>liquido </td> <td>0,478</td> <td align="right">~ 2000 </td></tr> <tr> <td><a href="/wiki/Ossigeno" title="Ossigeno">Ossigeno</a></td> <td>gassoso </td> <td>0,220</td> <td align="right">920 </td></tr> <tr> <td><a href="/wiki/Oro" title="Oro">Oro</a></td> <td>solido </td> <td>0,031</td> <td align="right">129 </td></tr> <tr> <td><a href="/wiki/Ottone_(lega)" title="Ottone (lega)">Ottone</a></td> <td>solido </td> <td>0,090</td> <td align="right">377 </td></tr> <tr> <td><a href="/wiki/Piombo" title="Piombo">Piombo</a></td> <td>solido </td> <td>0,031</td> <td align="right">130 </td></tr> <tr> <td><a href="/wiki/Polistirene" title="Polistirene">Polistirene</a></td> <td>solido </td> <td>0,346</td> <td align="right">1450 </td></tr> <tr> <td><a href="/wiki/Rame" title="Rame">Rame</a></td> <td>solido </td> <td>0,092</td> <td align="right">385 </td></tr> <tr> <td><a href="/wiki/Silice" title="Silice">Silice</a> (fuso)</td> <td>liquido </td> <td>0,168</td> <td align="right">703 </td></tr> <tr> <td><a href="/wiki/Silice" title="Silice">Silice</a></td> <td>solido </td> <td>0,483</td> <td align="right">2020 </td></tr> <tr> <td><a href="/wiki/Stagno_(elemento_chimico)" title="Stagno (elemento chimico)">Stagno</a></td> <td>solido </td> <td>0,054</td> <td align="right">228 </td></tr> <tr> <td><a href="/wiki/Zinco" title="Zinco">Zinco</a></td> <td>solido </td> <td>0,093</td> <td align="right">388 </td></tr> <tr> <th colspan="4" style="text-align: center; font-size: small"><a href="/wiki/Condizioni_standard" title="Condizioni standard">Condizioni standard</a> (salvo diversa indicazione).<br />Per i solidi il valore del calore specifico a pressione costante coincide col calore specifico a volume costante </th></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Calore_specifico_negativo">Calore specifico negativo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=8" title="Modifica la sezione Calore specifico negativo" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=8" title="Edit section's source code: Calore specifico negativo"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il concetto di "calore specifico negativo", noto implicitamente in astrofisica fin dai lavori di <a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a> degli anni '30, compare in maniera marginale nel classico testo di Fisica Statistica di L.D.Landau ed E.M. Lifshitz, fu diffuso nella comunità dei fisici da <a href="/w/index.php?title=Walter_Thirring&action=edit&redlink=1" class="new" title="Walter Thirring (la pagina non esiste)">Walter Thirring</a> nel <a href="/wiki/1970" title="1970">1970</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Recentemente ci si è accorti che un qualsiasi sistema con interazioni a lungo raggio (come sistemi autogravitanti, plasmi a una componente) può avere calore specifico negativo<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>. La richiesta più basilare affinché un sistema possa avere calore specifico negativo è che tale sistema non sia additivo. Tranne che per le osservazioni astrofisiche, ad ora non è chiara la verifica sperimentale di tale possibilità. </p><p>In altro contesto, all'interno della meccanica statistica di non equilibrio, è stato osservato calore specifico negativo in alcuni sistemi<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> (in particolare in reazioni di multiframmentazione nucleare, nei cluster atomici e in oggetti stellari auto-gravitanti<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>). </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=9" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=9" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text">Sycev, Sistemi termodinamici complessi, Editori Riuniti 1985</span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text">È uso comune (ma non sempre adottato) in termodinamica scrivere con lettere minuscole le grandezze specifiche e molari, e con lettere maiuscole le grandezze totali.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFCoulson_&_Richardson">Coulson & Richardson</a>, p. 324</cite>.</span> </li> <li id="cite_note-Cengel-4"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-Cengel_4-0">a</a></i></sup> <sup><i><a href="#cite_ref-Cengel_4-1">b</a></i></sup></span> <span class="reference-text"><cite class="citation libro" style="font-style:normal"> Yunus A. Çengel, <span style="font-style:italic;">Termodinamica e trasmissione del calore</span>, Milano, McGraw-Hill Companies, 2005, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-386-6203-7" title="Speciale:RicercaISBN/88-386-6203-7">88-386-6203-7</a>.</cite></span> </li> <li id="cite_note-5"><a href="#cite_ref-5"><b>^</b></a> <span class="reference-text"><Sycev, Sistemi termodinamici complessi, Editori Riuniti 1985, cap. 2, p.45</span> </li> <li id="cite_note-6"><a href="#cite_ref-6"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFSilvestroni">Silvestroni</a>, p. 169</cite>.</span> </li> <li id="cite_note-7"><a href="#cite_ref-7"><b>^</b></a> <span class="reference-text">Alcuni testi di fisica, con minor rigore, definiscono l'energia interna e l'entalpia con queste relazioni, partendo dai calori specifici, che invece sono definiti da queste due grandezze.</span> </li> <li id="cite_note-8"><a href="#cite_ref-8"><b>^</b></a> <span class="reference-text">W. Thirring, <i>Systems with negative specific heat</i>, Z. Phys. 235, pp. 339-352 (1970).</span> </li> <li id="cite_note-9"><a href="#cite_ref-9"><b>^</b></a> <span class="reference-text">A. Campa, S. Ruffo, T. Dauxois, <i>Statistical mechanics and dynamics of solvable models with long-range interactions</i>, Phys. Rep. 480, pp. 57-159 (2009).</span> </li> <li id="cite_note-10"><a href="#cite_ref-10"><b>^</b></a> <span class="reference-text"><a rel="nofollow" class="external free" href="http://siba.unipv.it/fisica/ScientificaActa/volume_2_1/Villain_ita.pdf">http://siba.unipv.it/fisica/ScientificaActa/volume_2_1/Villain_ita.pdf</a></span> </li> <li id="cite_note-11"><a href="#cite_ref-11"><b>^</b></a> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.pluchino.it/scienza/talks-html/TALK%20DOTTORATO-1.pdf">Microsoft PowerPoint - TALK DOTTORATO-1.ppt</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=10" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=10" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFSilvestroni" class="citation libro" style="font-style:normal"> Paolo Silvestroni, <span style="font-style:italic;">Fondamenti di chimica</span>, 10ª ed., Milano, CEA, 1996, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-408-0998-8" title="Speciale:RicercaISBN/88-408-0998-8">88-408-0998-8</a>.</cite></li> <li><cite id="CITEREFMazzone" class="citation libro" style="font-style:normal"> Giorgio Mazzone, <span style="font-style:italic;"><a rel="nofollow" class="external text" href="http://old.enea.it/produzione_scientifica/pdf_volumi/V2006_06TermoSolidi.pdf">Appunti di termodinamica dei solidi, vol. 1</a></span>, 1ª ed., Roma, ENEA, 2006, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-8286-141-4" title="Speciale:RicercaISBN/88-8286-141-4">88-8286-141-4</a>.</cite>, cap. 13 Il calore specifico dei solidi, pp. 103–108.</li> <li><cite id="CITEREFSycev" class="citation libro" style="font-style:normal"> Sycev, <span style="font-style:italic;">Sistemi termodinamici complessi</span>, Roma, Editori Riuniti, 1985, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-359-2883-4" title="Speciale:RicercaISBN/88-359-2883-4">88-359-2883-4</a>.</cite>, cap. 2, p. 45</li> <li><cite id="CITEREFCoulson_&_Richardson" class="citation libro" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) J.M. Coulson, J.F. Richardson, <a rel="nofollow" class="external text" href="https://www.amazon.com/Chemical-Engineering-Volume-Third-Edition/dp/0750641428"><span style="font-style:italic;">Chemical Engineering</span></a>, vol. 6, 3ª ed., Butterworth-Heinemann, 1999, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/0-7506-4142-8" title="Speciale:RicercaISBN/0-7506-4142-8">0-7506-4142-8</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=11" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=11" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Calore" title="Calore">Calore</a></li> <li><a href="/wiki/Calore_latente" title="Calore latente">Calore latente</a></li> <li><a href="/wiki/Calore_sensibile" title="Calore sensibile">Calore sensibile</a></li> <li><a href="/wiki/Capacit%C3%A0_termica" title="Capacità termica">Capacità termica</a></li> <li><a href="/wiki/Coefficiente_di_dilatazione_adiabatica" title="Coefficiente di dilatazione adiabatica">Coefficiente di dilatazione adiabatica</a></li> <li><a href="/wiki/Entalpia" title="Entalpia">Entalpia</a></li> <li><a href="/wiki/Energia_interna" title="Energia interna">Energia interna</a></li> <li><a href="/wiki/Equazione_di_Kirchhoff" title="Equazione di Kirchhoff">Equazione di Kirchhoff</a></li> <li><a href="/wiki/Legge_di_Dulong_Petit" class="mw-redirect" title="Legge di Dulong Petit">Legge di Dulong Petit</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=12" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=12" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><span class="plainlinks" title="commons:Category:Specific heat capacity"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Specific_heat_capacity?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file su <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Specific_heat_capacity?uselang=it">calore specifico</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calore_specifico&veaction=edit&section=13" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Calore_specifico&action=edit&section=13" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/science/specific-heat"><span style="font-style:italic;">specific heat</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q487756#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://www.interfred.it/Scuola/Progettare_freddo/Sensibile_scambiato/Tabella_cs.asp"><span style="font-style:italic;">Calore specifico per alcuni tipi di sostanze</span></a>, su <span style="font-style:italic;">interfred.it</span>.</cite></li> <li><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://www.itchiavari.org/chimica/tabelle/calospec.html"><span style="font-style:italic;">Calori specifici di alcune sostanze</span></a>, su <span style="font-style:italic;">itchiavari.org</span>.</cite></li></ul> <style data-mw-deduplicate="TemplateStyles:r140554510">.mw-parser-output .CdA{border:1px solid #aaa;width:100%;margin:auto;font-size:90%;padding:2px}.mw-parser-output .CdA th{background-color:#f2f2f2;font-weight:bold;width:20%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .CdA th{background-color:#202122}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .CdA th{background-color:#202122}}</style><table class="CdA"><tbody><tr><th><a href="/wiki/Aiuto:Controllo_di_autorit%C3%A0" title="Aiuto:Controllo di autorità">Controllo di autorità</a></th><td><a href="/wiki/Nuovo_soggettario" title="Nuovo soggettario">Thesaurus BNCF</a> <span class="uid"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=31408">31408</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/subjects/sh85126389">sh85126389</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="tedesco">DE</abbr></span>) <a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4182218-3">4182218-3</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Biblioteca_nazionale_di_Francia" title="Biblioteca nazionale di Francia">BNF</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="francese">FR</abbr></span>) <a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12274423z">cb12274423z</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12274423z">(data)</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Biblioteca_nazionale_di_Israele" title="Biblioteca nazionale di Israele">J9U</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr>, <abbr title="ebraico">HE</abbr></span>) <a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007565726505171">987007565726505171</a></span></td></tr></tbody></table> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-basis: calc( 100% / 2 - 8px / 2 );"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Gnome-applications-science.svg" class="mw-file-description" title="Chimica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Gnome-applications-science.svg/25px-Gnome-applications-science.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Gnome-applications-science.svg/38px-Gnome-applications-science.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Gnome-applications-science.svg/50px-Gnome-applications-science.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> <b><a href="/wiki/Portale:Chimica" title="Portale:Chimica">Portale Chimica</a></b></div></div><div style="flex-basis: calc( 100% / 2 - 8px / 2 );"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r140555418"><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Thermodynamics_icon.svg" class="mw-file-description" title="Termodinamica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/25px-Thermodynamics_icon.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/38px-Thermodynamics_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/50px-Thermodynamics_icon.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <b><a href="/wiki/Portale:Termodinamica" title="Portale:Termodinamica">Portale Termodinamica</a></b></div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Estratto da "<a dir="ltr" href="https://it.wikipedia.org/w/index.php?title=Calore_specifico&oldid=141673924">https://it.wikipedia.org/w/index.php?title=Calore_specifico&oldid=141673924</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categoria:Categorie" title="Categoria:Categorie">Categoria</a>: <ul><li><a href="/wiki/Categoria:Grandezze_termodinamiche" title="Categoria:Grandezze termodinamiche">Grandezze termodinamiche</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorie nascoste: <ul><li><a href="/wiki/Categoria:Voci_con_modulo_citazione_e_parametro_coautori" title="Categoria:Voci con modulo citazione e parametro coautori">Voci con modulo citazione e parametro coautori</a></li><li><a href="/wiki/Categoria:P1417_letta_da_Wikidata" title="Categoria:P1417 letta da Wikidata">P1417 letta da Wikidata</a></li><li><a href="/wiki/Categoria:Voci_con_codice_Thesaurus_BNCF" title="Categoria:Voci con codice Thesaurus BNCF">Voci con codice Thesaurus BNCF</a></li><li><a href="/wiki/Categoria:Voci_con_codice_LCCN" title="Categoria:Voci con codice LCCN">Voci con codice LCCN</a></li><li><a href="/wiki/Categoria:Voci_con_codice_GND" title="Categoria:Voci con codice GND">Voci con codice GND</a></li><li><a href="/wiki/Categoria:Voci_con_codice_BNF" title="Categoria:Voci con codice BNF">Voci con codice BNF</a></li><li><a href="/wiki/Categoria:Voci_con_codice_J9U" title="Categoria:Voci con codice J9U">Voci con codice J9U</a></li><li><a href="/wiki/Categoria:Voci_non_biografiche_con_codici_di_controllo_di_autorit%C3%A0" title="Categoria:Voci non biografiche con codici di controllo di autorità">Voci non biografiche con codici di controllo di autorità</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Questa pagina è stata modificata per l'ultima volta il 17 ott 2024 alle 15:59.</li> <li id="footer-info-copyright">Il testo è disponibile secondo la <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.it">licenza Creative Commons Attribuzione-Condividi allo stesso modo</a>; 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Calore specifico - Wikipedia