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class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-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="Cuprins" 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="Comută cuprinsul" > <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">Comută cuprinsul</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">Legea Dulong-Petit</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" 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Disponibil în 28 limbi" > <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-28" 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">28 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%AF%D9%88%D9%84%D9%88%D9%86-%D8%A8%D8%AA%D9%8A" title="قانون دولون-بتي – arabă" lang="ar" hreflang="ar" data-title="قانون دولون-بتي" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%94%D0%B7%D1%8E%D0%BB%D0%BE%D0%BD%D0%B3%D0%B0_%E2%80%94_%D0%9F%D1%86%D1%96" title="Закон Дзюлонга — Пці – belarusă" lang="be" hreflang="be" data-title="Закон Дзюлонга — Пці" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Llei_de_Dulong_i_Petit" title="Llei de Dulong i Petit – catalană" lang="ca" hreflang="ca" data-title="Llei de Dulong i Petit" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dulong-Petit-Gesetz" title="Dulong-Petit-Gesetz – germană" lang="de" hreflang="de" data-title="Dulong-Petit-Gesetz" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_Dulong-Petit" title="Νόμος Dulong-Petit – greacă" lang="el" hreflang="el" data-title="Νόμος Dulong-Petit" data-language-autonym="Ελληνικά" data-language-local-name="greacă" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Dulong%E2%80%93Petit_law" title="Dulong–Petit law – engleză" lang="en" hreflang="en" data-title="Dulong–Petit law" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ley_de_Dulong-Petit" title="Ley de Dulong-Petit – spaniolă" lang="es" hreflang="es" data-title="Ley de Dulong-Petit" data-language-autonym="Español" data-language-local-name="spaniolă" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Dulong-Petiten_legea" title="Dulong-Petiten legea – bască" lang="eu" hreflang="eu" data-title="Dulong-Petiten legea" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%AF%D9%88%D9%84%D9%88%D9%86%E2%80%93%D9%BE%D8%AA%DB%8C" title="قانون دولون–پتی – persană" lang="fa" hreflang="fa" data-title="قانون دولون–پتی" data-language-autonym="فارسی" data-language-local-name="persană" 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/Dulongin_ja_Petit%E2%80%99n_laki" title="Dulongin ja Petit’n laki – finlandeză" lang="fi" hreflang="fi" data-title="Dulongin ja Petit’n laki" data-language-autonym="Suomi" data-language-local-name="finlandeză" 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/Loi_de_Dulong_et_Petit" title="Loi de Dulong et Petit – franceză" lang="fr" hreflang="fr" data-title="Loi de Dulong et Petit" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%95%D7%A7_%D7%93%D7%95%D7%9C%D7%95%D7%9F-%D7%A4%D7%98%D7%99" title="חוק דולון-פטי – ebraică" lang="he" hreflang="he" data-title="חוק דולון-פטי" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%B5%D5%B8%D6%82%D5%AC%D5%B8%D5%B6%D5%A3%D5%AB_%D6%87_%D5%8A%D5%BF%D5%AB%D5%AB_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Դյուլոնգի և Պտիի օրենք – armeană" lang="hy" hreflang="hy" data-title="Դյուլոնգի և Պտիի օրենք" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_Dulong%E2%80%93Petit" title="Hukum Dulong–Petit – indoneziană" lang="id" hreflang="id" data-title="Hukum Dulong–Petit" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Legge_di_Dulong-Petit" title="Legge di Dulong-Petit – italiană" lang="it" hreflang="it" data-title="Legge di Dulong-Petit" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%87%E3%83%A5%E3%83%AD%E3%83%B3%EF%BC%9D%E3%83%97%E3%83%86%E3%82%A3%E3%81%AE%E6%B3%95%E5%89%87" title="デュロン＝プティの法則 – japoneză" lang="ja" hreflang="ja" data-title="デュロン＝プティの法則" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%92%AC%EB%A1%B1-%ED%94%84%ED%8B%B0_%EB%B2%95%EC%B9%99" title="뒬롱-프티 법칙 – coreeană" lang="ko" hreflang="ko" data-title="뒬롱-프티 법칙" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D1%8E%D0%BB%D0%BE%D0%BD%D0%B3-%D0%9F%D1%82%D0%B8_%D0%BC%D1%8B%D0%B9%D0%B7%D0%B0%D0%BC%D1%8B" title="Дюлонг-Пти мыйзамы – kârgâză" lang="ky" hreflang="ky" data-title="Дюлонг-Пти мыйзамы" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_van_Dulong_en_Petit" title="Wet van Dulong en Petit – neerlandeză" lang="nl" hreflang="nl" data-title="Wet van Dulong en Petit" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" 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/Dulong%E2%80%93Petit-lova" title="Dulong–Petit-lova – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Dulong–Petit-lova" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_Dulonga-Petita" title="Prawo Dulonga-Petita – poloneză" lang="pl" hreflang="pl" data-title="Prawo Dulonga-Petita" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Lei_de_Dulong-Petit" title="Lei de Dulong-Petit – portugheză" lang="pt" hreflang="pt" data-title="Lei de Dulong-Petit" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%94%D1%8E%D0%BB%D0%BE%D0%BD%D0%B3%D0%B0_%E2%80%94_%D0%9F%D1%82%D0%B8" title="Закон Дюлонга — Пти – rusă" lang="ru" hreflang="ru" data-title="Закон Дюлонга — Пти" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dulong%E2%80%93Petits_lag" title="Dulong–Petits lag – suedeză" lang="sv" hreflang="sv" data-title="Dulong–Petits lag" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Dulong-Petit_Yasas%C4%B1" title="Dulong-Petit Yasası – turcă" lang="tr" hreflang="tr" data-title="Dulong-Petit Yasası" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%94%D1%8E%D0%BB%D0%BE%D0%BD%D0%B3%D0%B0_%E2%80%94_%D0%9F%D1%82%D1%96" title="Закон Дюлонга — Пті – ucraineană" lang="uk" hreflang="uk" data-title="Закон Дюлонга — Пті" data-language-autonym="Українська" data-language-local-name="ucraineană" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Dyulong_va_Pti_qonuni" title="Dyulong va Pti qonuni – uzbecă" lang="uz" hreflang="uz" data-title="Dyulong va Pti qonuni" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9D%9C%E9%9A%86-%E7%8F%80%E8%92%82%E5%AE%9A%E5%BE%8B" title="杜隆-珀蒂定律 – chineză" lang="zh" hreflang="zh" data-title="杜隆-珀蒂定律" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</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/Q515546#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</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="Spații de nume"> <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 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dir="ltr"><p><b>Legea Dulong-Petit</b> este o lege empirică descoperită în <a href="/wiki/1819" title="1819">1819</a> de fizicienii francezi <a href="/wiki/Pierre_Louis_Dulong" title="Pierre Louis Dulong">Pierre Louis Dulong</a> și <a href="/w/index.php?title=Alexis_Th%C3%A9r%C3%A8se_Petit&action=edit&redlink=1" class="new" title="Alexis Thérèse Petit — pagină inexistentă">Alexis Thérèse Petit</a>. Ea afirmă că, pentru o clasă largă de corpuri solide alcătuite dintr-o singură specie de atomi, <a href="/wiki/Termodinamic%C4%83#Schimb_de_căldură" title="Termodinamică">capacitatea termică la volum constant</a> pe <a href="/wiki/Mol" title="Mol">mol</a> are o valoare aproximativ constantă. Conform <a href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">mecanicii statistice clasice</a>, această valoare rezultă egală cu <b>3R</b>, unde <b>R</b> este <a href="/wiki/Constanta_universal%C4%83_a_gazului_ideal" title="Constanta universală a gazului ideal">constanta universală a gazului ideal</a>. </p><p>La temperaturi joase, rezultatele experimentale se abat semnificativ de la legea Dulong-Petit: capacitatea termică a solidelor tinde la zero când temperatura tinde la <b>0 K</b>, în conformitate cu <a href="/wiki/Termodinamic%C4%83#Principiul_al_treilea_al_termodinamicii" title="Termodinamică">principiul al treilea al termodinamicii</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formulări_echivalente"><span id="Formul.C4.83ri_echivalente"></span>Formulări echivalente</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Legea_Dulong-Petit&veaction=edit&section=1" 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.ambox-delete,html.skin-theme-clientpref-os .mw-parser-output .ambox-content,html.skin-theme-clientpref-os .mw-parser-output .ambox-style,html.skin-theme-clientpref-os .mw-parser-output .ambox-move,html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{background-color:#202122!important}}</style><table class="metadata plainlinks ambox ambox ambox-notice ambox-content" style=""> <tbody><tr><td class="mbox-image"><div style="width: 52px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/44px-Wiki_letter_w.svg.png" decoding="async" width="44" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/66px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/88px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text" style=""><span class="mbox-text-span"><b>Vă rugăm să contribuiți <a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Legea_Dulong-Petit&action=edit">la îmbunătățirea articolului</a> ajutând la extinderea lui.</b> Informații suplimentare pot fi găsite pe <a href="/w/index.php?title=Discu%C8%9Bie:Legea_Dulong-Petit&action=edit&redlink=1" class="new" title="Discuție:Legea Dulong-Petit — pagină inexistentă">pagina de discuții</a>. <small></small><span class="hide-when-compact"> </span><span class="hide-when-compact"> </span></span></td></tr></tbody></table> <p>Un sistem de vibrații într-o rețea cristalină poate fi modelat considerând potențialele unui oscilator armonic pe fiecare <a href="/wiki/Grad_de_libertate_(mecanic%C4%83)" title="Grad de libertate (mecanică)">grad de libertate</a>. Atunci, energia liberă a sistemului poate fi scrisă ca<sup id="cite_ref-landau_1-0" class="reference"><a href="#cite_note-landau-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 F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left(1-e^{-\hbar \omega _{\alpha }/k_{B}T}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </munder> <mi>log</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left(1-e^{-\hbar \omega _{\alpha }/k_{B}T}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba1b414453e1f1bc8d0a187e2c320ee3780dda4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:39.658ex; height:6.009ex;" alt="{\displaystyle F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left(1-e^{-\hbar \omega _{\alpha }/k_{B}T}\right)}"></span></dd></dl> <p>unde indicele <i>α</i> se sumează pe toate gradele de libertate. În modelul lui Einstein din 1907 (opus modelului Debye, care avea să apară mai târziu) se consideră numai limită de înaltă energie: </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 k_{B}T\gg \hbar \omega _{\alpha }.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo>≫</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}T\gg \hbar \omega _{\alpha }.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5a0d8a292ef08bdba07879cbcc0fb16d050be35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.012ex; height:2.509ex;" alt="{\displaystyle k_{B}T\gg \hbar \omega _{\alpha }.\,}"></span></dd></dl> <p>atunci </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 1-e^{-\hbar \omega _{\alpha }/k_{B}T}\approx \hbar \omega _{\alpha }/k_{B}T.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </msup> <mo>≈</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1-e^{-\hbar \omega _{\alpha }/k_{B}T}\approx \hbar \omega _{\alpha }/k_{B}T.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f973874f542103469955beb128a4ef5888a11db3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.232ex; height:3.343ex;" alt="{\displaystyle 1-e^{-\hbar \omega _{\alpha }/k_{B}T}\approx \hbar \omega _{\alpha }/k_{B}T.\,}"></span></dd></dl> <p>rezultând </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 F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left({\frac {\hbar \omega _{\alpha }}{k_{B}T}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </munder> <mi>log</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left({\frac {\hbar \omega _{\alpha }}{k_{B}T}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a42d16cdda18b1bc7ef1bb8b1fde408b9a7679f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.893ex; height:6.676ex;" alt="{\displaystyle F=N\varepsilon _{0}+k_{B}T\sum _{\alpha }\log \left({\frac {\hbar \omega _{\alpha }}{k_{B}T}}\right)}"></span></dd></dl> <p>Definind <i> frecvența medie geometrică</i> prin </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 \log {\bar {\omega }}={\frac {1}{M}}\sum _{\alpha }\log \omega _{\alpha },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </munder> <mi>log</mi> <mo>⁡</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log {\bar {\omega }}={\frac {1}{M}}\sum _{\alpha }\log \omega _{\alpha },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b66669ae328e2989e9f2943c60e98fc3e53cdb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.046ex; height:6.343ex;" alt="{\displaystyle \log {\bar {\omega }}={\frac {1}{M}}\sum _{\alpha }\log \omega _{\alpha },}"></span></dd></dl> <p>unde <i>M</i> e numărul total de grade de libertate ale systemului. </p><p><br /> </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 F=N\varepsilon _{0}-Mk_{B}T\log k_{B}T+Mk_{B}T\log \hbar {\bar {\omega }}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>M</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mi>log</mi> <mo>⁡</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo>+</mo> <mi>M</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mi>log</mi> <mo>⁡</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=N\varepsilon _{0}-Mk_{B}T\log k_{B}T+Mk_{B}T\log \hbar {\bar {\omega }}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29ba2d2d7cf83369d022e98374841724f5962b79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:43.218ex; height:2.509ex;" alt="{\displaystyle F=N\varepsilon _{0}-Mk_{B}T\log k_{B}T+Mk_{B}T\log \hbar {\bar {\omega }}\,}"></span></dd></dl> <p>Folosind energia </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 E=F-T\left({\frac {\partial F}{\partial T}}\right)_{V},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>F</mi> <mo>−</mo> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</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> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=F-T\left({\frac {\partial F}{\partial T}}\right)_{V},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb9344cbac2bd43b2b18dd585641ef94ec8d43e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.551ex; height:6.176ex;" alt="{\displaystyle E=F-T\left({\frac {\partial F}{\partial T}}\right)_{V},}"></span></dd></dl> <p>rezultă </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 E=N\varepsilon _{0}+Mk_{B}T.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>N</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>M</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=N\varepsilon _{0}+Mk_{B}T.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4706210e45b9f8ffbe6221061dd4b1a607e6bac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.719ex; height:2.509ex;" alt="{\displaystyle E=N\varepsilon _{0}+Mk_{B}T.\,}"></span></dd></dl> <p><br /> </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}=\left({\frac {\partial E}{\partial T}}\right)_{V}=Mk_{B},}"> <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> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>E</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> <mo>=</mo> <mi>M</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{V}=\left({\frac {\partial E}{\partial T}}\right)_{V}=Mk_{B},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24e3a7648da67912f7940d8ac54bc1abdc1b8555" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.982ex; height:6.176ex;" alt="{\displaystyle C_{V}=\left({\frac {\partial E}{\partial T}}\right)_{V}=Mk_{B},}"></span></dd></dl> <p>care e independent de temperatură. </p> <div class="mw-heading mw-heading2"><h2 id="Vezi_și"><span id="Vezi_.C8.99i"></span>Vezi și</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Legea_Dulong-Petit&veaction=edit&section=3" title="Modifică secțiunea: Vezi și" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Legea_Dulong-Petit&action=edit&section=3" title="Edit section's source code: Vezi și"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Rela%C8%9Bia_lui_Mayer" title="Relația lui Mayer">Relația lui Mayer</a></li> <li><a href="/wiki/Termochimie" title="Termochimie">Termochimie</a></li></ul> <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=Legea_Dulong-Petit&veaction=edit&section=4" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Legea_Dulong-Petit&action=edit&section=4" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-landau-1"><b><a href="#cite_ref-landau_1-0">^</a></b> <span class="reference-text"><cite class="citation book"><a href="/wiki/Lev_Landau" title="Lev Landau">Landau, L. D.</a>; <a href="/wiki/Evgheni_Lif%C8%99i%C8%9B" title="Evgheni Lifșiț">Lifshitz, E. M.</a> (<time datetime="1980">1980</time>). <i>Statistical Physics Pt. 1</i>. Course in Theoretical Physics. <b>5</b> (ed. 3rd). Oxford: Pergamon Press. p. 193,196. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0750633727" title="Special:Referințe în cărți/0750633727">0750633727</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Physics+Pt.+1&rft.place=Oxford&rft.series=Course+in+Theoretical+Physics&rft.pages=193%2C196&rft.edition=3rd&rft.pub=Pergamon+Press&rft.date=1980&rft.isbn=0750633727&rft.aulast=Landau&rft.aufirst=L.+D.&rft.au=Lifshitz%2C+E.+M.&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALegea+Dulong-Petit" class="Z3988"><span style="display:none;"> </span></span><style data-mw-deduplicate="TemplateStyles:r16236537">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"„""”""«""»"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Legea_Dulong-Petit&veaction=edit&section=5" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Legea_Dulong-Petit&action=edit&section=5" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Țițeica, Șerban: <i>Curs de fizică statistică și teoria cuantelor</i>, All Educational, Timișoara, 2000. <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/973684319X" class="internal mw-magiclink-isbn">ISBN 973-684-319-X</a></li></ul> <p><br /> </p> <table class="navbox" cellspacing="0" style=""> <tbody><tr> <td style="padding:2px;"> <table cellspacing="0" class="nowraplinks collapsible collapsed" style="width:100%;background:transparent;color:inherit;;"> <tbody><tr> <th style=";" colspan="2" class="navbox-title"><div style="float:left; width:6em;text-align:left;"><div class="noprint plainlinks" style="padding:0; font-size:xx-small; color:var(--color-base, #000); white-space:nowrap; ;"><span style=";;border:none;"><a href="/wiki/Format:Fizic%C4%83_statistic%C4%83" title="Format:Fizică statistică"><span title="Vizualizare format" style=";;border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a href="/w/index.php?title=Discu%C8%9Bie_Format:Fizic%C4%83_statistic%C4%83&action=edit&redlink=1" class="new" title="Discuție Format:Fizică statistică — pagină inexistentă"><span title="Discuție format" style=";;border:none;;">d</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Fizic%C4%83_statistic%C4%83&action=edit"><span title="Acest format se poate modifica. Folosiți butonul de previzualizare înainte de a salva." style=";;border:none;;">m</span></a></span></div></div><span class="" style="font-size: 110%;"><a href="/wiki/Fizic%C4%83_statistic%C4%83" title="Fizică statistică">Fizică statistică</a></span> </th></tr> <tr style="height:2px;"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Termodinamică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"> <div style="padding:0em 0.25em"> <a href="/wiki/Calorimetrie" title="Calorimetrie">Calorimetrie</a> • <a href="/wiki/Capacitate_termic%C4%83" title="Capacitate termică">Capacitate termică</a> • <a href="/wiki/C%C4%83ldur%C4%83_latent%C4%83" title="Căldură latentă">Căldură latentă</a> • <a href="/wiki/Ciclu_termodinamic" title="Ciclu termodinamic">Ciclu termodinamic</a> • <a href="/wiki/Ciclul_Carnot" title="Ciclul Carnot">Ciclul Carnot</a> • <a href="/wiki/Ciclul_Clausius-Rankine" title="Ciclul Clausius-Rankine">Ciclul Clausius-Rankine</a> • <a href="/wiki/Coeficient_de_transformare_adiabatic%C4%83" title="Coeficient de transformare adiabatică">Coeficient de transformare adiabatică</a> • <a href="/wiki/Constanta_universal%C4%83_a_gazului_ideal" title="Constanta universală a gazului ideal">Constanta universală a gazului ideal</a> • <a href="/wiki/Echilibru_termodinamic" title="Echilibru termodinamic">Echilibru termodinamic</a> • <a href="/wiki/Energie_intern%C4%83" title="Energie internă">Energie internă</a> • <a href="/wiki/Energie_liber%C4%83" title="Energie liberă">Energie liberă</a> • <a href="/wiki/Entalpie" title="Entalpie">Entalpie</a> • <a href="/wiki/Entalpie_liber%C4%83" title="Entalpie liberă">Entalpie liberă</a> • <a href="/wiki/Entropia_radia%C8%9Biei_electromagnetice" title="Entropia radiației electromagnetice">Entropia radiației electromagnetice</a> • <a href="/wiki/Entropia_termodinamic%C4%83_(dup%C4%83_Carath%C3%A9odory)" title="Entropia termodinamică (după Carathéodory)">Entropia termodinamică (după Carathéodory)</a> • <a href="/wiki/Entropie" title="Entropie">Entropie</a> • <a href="/wiki/Entropie_termodinamic%C4%83" title="Entropie termodinamică">Entropie termodinamică</a> • <a href="/wiki/Evaporare" title="Evaporare">Evaporare</a> • <a href="/wiki/Faz%C4%83_(termodinamic%C4%83)" title="Fază (termodinamică)">Fază (termodinamică)</a> • <a href="/wiki/Fierbere" title="Fierbere">Fierbere</a> • <a href="/wiki/Formula_lui_Planck" title="Formula lui Planck">Formula lui Planck</a> • <a href="/wiki/Frac%C8%9Bie_molar%C4%83" title="Fracție molară">Fracție molară</a> • <a href="/wiki/Gaz_ideal" title="Gaz ideal">Gaz ideal</a> • <a href="/wiki/Gaz_perfect" title="Gaz perfect">Gaz perfect</a> • <a href="/wiki/Gaz_real" title="Gaz real">Gaz real</a> • <a href="/wiki/Legea_Boyle-Mariotte" title="Legea Boyle-Mariotte">Legea Boyle-Mariotte</a> • <a class="mw-selflink selflink">Legea Dulong-Petit</a> • <a href="/wiki/Legea_lui_Avogadro" title="Legea lui Avogadro">Legea lui Avogadro</a> • <a href="/wiki/Legea_lui_Dalton" title="Legea lui Dalton">Legea lui Dalton</a> • <a href="/wiki/Legea_lui_Henry" title="Legea lui Henry">Legea lui Henry</a> • <a href="/wiki/Legea_lui_Raoult" title="Legea lui Raoult">Legea lui Raoult</a> • <a href="/wiki/Legile_de_deplasare_ale_lui_Wien" title="Legile de deplasare ale lui Wien">Legile de deplasare ale lui Wien</a> • <a href="/wiki/Legile_lui_Kirchhoff_(radia%C8%9Bie)" title="Legile lui Kirchhoff (radiație)">Legile lui Kirchhoff (radiație)</a> • <a href="/wiki/Lema_lui_Carath%C3%A9odory_(termodinamic%C4%83)" title="Lema lui Carathéodory (termodinamică)">Lema lui Carathéodory (termodinamică)</a> • <a href="/wiki/M%C4%83rimi_molare_de_exces" title="Mărimi molare de exces">Mărimi molare de exces</a> • <a href="/wiki/Paradoxul_lui_Gibbs_(termodinamic%C4%83)" title="Paradoxul lui Gibbs (termodinamică)">Paradoxul lui Gibbs (termodinamică)</a> • <a href="/wiki/Perpetuum_mobile" title="Perpetuum mobile">Perpetuum mobile</a> • <a href="/wiki/Poten%C8%9Bial_chimic" title="Potențial chimic">Potențial chimic</a> • <a href="/wiki/Poten%C8%9Bial_termodinamic" title="Potențial termodinamic">Potențial termodinamic</a> • <a href="/wiki/Presiune_de_vapori" title="Presiune de vapori">Presiune de vapori</a> • <a href="/wiki/Principiile_termodinamicii" title="Principiile termodinamicii">Principiile termodinamicii</a> • <a href="/wiki/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii">Principiul al doilea al termodinamicii</a> • <a href="/wiki/Principiul_al_doilea_al_termodinamicii:_Planck_versus_Carath%C3%A9odory" title="Principiul al doilea al termodinamicii: Planck versus Carathéodory">Principiul al doilea al termodinamicii: Planck versus Carathéodory</a> • <a href="/wiki/Principiul_al_treilea_al_termodinamicii" title="Principiul al treilea al termodinamicii">Principiul al treilea al termodinamicii</a> • <a href="/wiki/Principiul_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii">Principiul întâi al termodinamicii</a> • <a href="/wiki/Principiul_zero_al_termodinamicii" title="Principiul zero al termodinamicii">Principiul zero al termodinamicii</a> • <a href="/wiki/Proces_adiabatic" title="Proces adiabatic">Proces adiabatic</a> • <a href="/wiki/Punct_de_fierbere" title="Punct de fierbere">Punct de fierbere</a> • <a href="/wiki/Punct_de_topire" title="Punct de topire">Punct de topire</a> • <a href="/wiki/Radia%C8%9Bie_termic%C4%83" title="Radiație termică">Radiație termică</a> • <a href="/wiki/Rela%C8%9Bia_lui_Mayer" title="Relația lui Mayer">Relația lui Mayer</a> • <a href="/wiki/Rezonatorul_lui_Planck" title="Rezonatorul lui Planck">Rezonatorul lui Planck</a> • <a href="/wiki/Sistem_termodinamic" title="Sistem termodinamic">Sistem termodinamic</a> • <a href="/wiki/Temperatur%C4%83" title="Temperatură">Temperatură</a> • <a href="/wiki/Termochimie" title="Termochimie">Termochimie</a> • <a href="/wiki/Termodinamic%C4%83" title="Termodinamică">Termodinamică</a> • <a href="/wiki/Transformare_Legendre" title="Transformare Legendre">Transformare Legendre</a> • <a href="/wiki/Transformare_termodinamic%C4%83" title="Transformare termodinamică">Transformare termodinamică</a> • <a href="/wiki/Termodinamic%C4%83_chimic%C4%83" title="Termodinamică chimică">Termodinamică chimică</a> •</div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Mecanică statistică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-even"><div style="padding:0em 0.25em"> <a href="/wiki/Entropie_statistic%C4%83" title="Entropie statistică">Entropie statistică</a> • <a href="/wiki/Faz%C4%83_(mecanic%C4%83_statistic%C4%83)" title="Fază (mecanică statistică)">Fază (mecanică statistică)</a> • <a href="/wiki/Grad_de_libertate" title="Grad de libertate">Grad de libertate</a> • <a href="/wiki/Mecanic%C4%83_statistic%C4%83" title="Mecanică statistică">Mecanică statistică</a> • <a href="/wiki/Operator_statistic" title="Operator statistic">Operator statistic</a></div> </td></tr> <tr style="height:2px"> <td> </td></tr> <tr> <td class="navbox-group" style=";;">Teorie cinetică </td> <td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"><div style="padding:0em 0.25em"> <a href="/wiki/Agita%C8%9Bie_termic%C4%83" class="mw-redirect" title="Agitație termică">Agitație termică</a> • <a href="/wiki/Constanta_Boltzmann" title="Constanta Boltzmann">Constanta Boltzmann</a> • <a href="/wiki/Demonul_lui_Maxwell" title="Demonul lui Maxwell">Demonul lui Maxwell</a> • <a href="/wiki/Num%C4%83rul_lui_Avogadro" title="Numărul lui Avogadro">Numărul lui Avogadro</a> • <a href="/wiki/Teoria_cinetic%C4%83_a_gazelor" title="Teoria cinetică a gazelor">Teoria cinetică a gazelor</a> • <a href="/wiki/Teoria_haosului" title="Teoria haosului">Teoria haosului</a></div> </td></tr></tbody></table> </td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r16513826">.mw-parser-output .navbox{margin:0 auto 0}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox-abovebelow[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-group[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-image[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-list[style]{background:inherit!important;color:inherit!important;border-top:2px solid #fdfdfd!important}html.skin-theme-clientpref-night .mw-parser-output .navbox[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-subgroup[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-group[style],html.skin-theme-clientpref-night .mw-parser-output .navbox-even[style],html.skin-theme-clientpref-night .mw-parser-output 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