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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relatie_met_de_informatietheorie"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Relatie met de informatietheorie</span> </div> </a> <ul id="toc-Relatie_met_de_informatietheorie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zie_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zie_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Zie ook</span> </div> </a> <ul id="toc-Zie_ook-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externe_link" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externe_link"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Externe link</span> </div> </a> <ul id="toc-Externe_link-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Tweede wet van de thermodynamica</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="Ga naar een artikel in een andere taal. Beschikbaar in 64 talen" > <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-64" 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">64 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Tweede_wet_van_termodinamika" title="Tweede wet van termodinamika – Afrikaans" lang="af" hreflang="af" data-title="Tweede wet van termodinamika" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%A7%D9%84%D8%AB%D8%A7%D9%86%D9%8A_%D9%84%D9%84%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D8%A7%D9%84%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A%D8%A9" title="القانون الثاني للديناميكا الحرارية – Arabisch" lang="ar" hreflang="ar" data-title="القانون الثاني للديناميكا الحرارية" data-language-autonym="العربية" data-language-local-name="Arabisch" 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/Segundu_principiu_de_la_termodin%C3%A1mica" title="Segundu principiu de la termodinámica – Asturisch" lang="ast" hreflang="ast" data-title="Segundu principiu de la termodinámica" data-language-autonym="Asturianu" data-language-local-name="Asturisch" 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/Termodinamikan%C4%B1n_ikinci_qanunu" title="Termodinamikanın ikinci qanunu – Azerbeidzjaans" lang="az" hreflang="az" data-title="Termodinamikanın ikinci qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%80%D1%83%D0%B3%D1%96_%D0%BF%D0%B0%D1%87%D0%B0%D1%82%D0%B0%D0%BA_%D1%82%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D1%96" title="Другі пачатак тэрмадынамікі – Belarussisch" lang="be" hreflang="be" data-title="Другі пачатак тэрмадынамікі" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%92%D1%82%D0%BE%D1%80%D0%B8_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BD%D0%B0_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0%D1%82%D0%B0" title="Втори закон на термодинамиката – Bulgaars" lang="bg" hreflang="bg" data-title="Втори закон на термодинамиката" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0_%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%A4%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="তাপগতিবিদ্যার দ্বিতীয় সূত্র – Bengaals" lang="bn" hreflang="bn" data-title="তাপগতিবিদ্যার দ্বিতীয় সূত্র" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – Bosnisch" lang="bs" hreflang="bs" data-title="Drugi zakon termodinamike" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Segon_principi_de_la_termodin%C3%A0mica" title="Segon principi de la termodinàmica – Catalaans" lang="ca" hreflang="ca" data-title="Segon principi de la termodinàmica" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Druh%C3%BD_termodynamick%C3%BD_z%C3%A1kon" title="Druhý termodynamický zákon – Tsjechisch" lang="cs" hreflang="cs" data-title="Druhý termodynamický zákon" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" 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%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%C4%83%D0%BD_%D0%B8%D0%BA%D0%BA%C4%95%D0%BC%C4%95%D1%88_%D0%BF%D1%83%C3%A7%D0%BB%D0%B0%D0%BC%C4%83%D1%88%C4%95" title="Термодинамикăн иккĕмĕш пуçламăшĕ – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Термодинамикăн иккĕмĕш пуçламăшĕ" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Termodynamikkens_2._lov" title="Termodynamikkens 2. lov – Deens" lang="da" hreflang="da" data-title="Termodynamikkens 2. lov" data-language-autonym="Dansk" data-language-local-name="Deens" 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/Zweiter_Hauptsatz_der_Thermodynamik" title="Zweiter Hauptsatz der Thermodynamik – Duits" lang="de" hreflang="de" data-title="Zweiter Hauptsatz der Thermodynamik" data-language-autonym="Deutsch" data-language-local-name="Duits" 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%94%CE%B5%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CF%82_%CE%B8%CE%B5%CF%81%CE%BC%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CF%8C%CF%82_%CE%BD%CF%8C%CE%BC%CE%BF%CF%82" title="Δεύτερος θερμοδυναμικός νόμος – Grieks" lang="el" hreflang="el" data-title="Δεύτερος θερμοδυναμικός νόμος" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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/Second_law_of_thermodynamics" title="Second law of thermodynamics – Engels" lang="en" hreflang="en" data-title="Second law of thermodynamics" data-language-autonym="English" data-language-local-name="Engels" 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/Dua_le%C4%9Do_de_termodinamiko" title="Dua leĝo de termodinamiko – Esperanto" lang="eo" hreflang="eo" data-title="Dua leĝo de termodinamiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Segundo_principio_de_la_termodin%C3%A1mica" title="Segundo principio de la termodinámica – Spaans" lang="es" hreflang="es" data-title="Segundo principio de la termodinámica" data-language-autonym="Español" data-language-local-name="Spaans" 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/Termod%C3%BCnaamika_teine_seadus" title="Termodünaamika teine seadus – Estisch" lang="et" hreflang="et" data-title="Termodünaamika teine seadus" data-language-autonym="Eesti" data-language-local-name="Estisch" 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/Termodinamikaren_bigarren_legea" title="Termodinamikaren bigarren legea – Baskisch" lang="eu" hreflang="eu" data-title="Termodinamikaren bigarren legea" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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%85_%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="قانون دوم ترمودینامیک – Perzisch" lang="fa" hreflang="fa" data-title="قانون دوم ترمودینامیک" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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/Termodynamiikan_toinen_p%C3%A4%C3%A4s%C3%A4%C3%A4nt%C3%B6" title="Termodynamiikan toinen pääsääntö – Fins" lang="fi" hreflang="fi" data-title="Termodynamiikan toinen pääsääntö" data-language-autonym="Suomi" data-language-local-name="Fins" 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/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique – Frans" lang="fr" hreflang="fr" data-title="Deuxième principe de la thermodynamique" data-language-autonym="Français" data-language-local-name="Frans" 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/Segunda_lei_da_termodin%C3%A1mica" title="Segunda lei da termodinámica – Galicisch" lang="gl" hreflang="gl" data-title="Segunda lei da termodinámica" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%97%D7%95%D7%A7_%D7%94%D7%A9%D7%A0%D7%99_%D7%A9%D7%9C_%D7%94%D7%AA%D7%A8%D7%9E%D7%95%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94" title="החוק השני של התרמודינמיקה – Hebreeuws" lang="he" hreflang="he" data-title="החוק השני של התרמודינמיקה" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80_%E0%A4%95%E0%A4%BE_%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊष्मागतिकी का द्वितीय नियम – Hindi" lang="hi" hreflang="hi" data-title="ऊष्मागतिकी का द्वितीय नियम" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – Kroatisch" lang="hr" hreflang="hr" data-title="Drugi zakon termodinamike" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Dezy%C3%A8m_lwa_t%C3%A8modinamik" title="Dezyèm lwa tèmodinamik – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Dezyèm lwa tèmodinamik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/A_termodinamika_m%C3%A1sodik_f%C5%91t%C3%A9tele" title="A termodinamika második főtétele – Hongaars" lang="hu" hreflang="hu" data-title="A termodinamika második főtétele" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1%D5%B5%D5%AB_%D5%A5%D6%80%D5%AF%D6%80%D5%B8%D6%80%D5%A4_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Ջերմադինամիկայի երկրորդ օրենք – Armeens" lang="hy" hreflang="hy" data-title="Ջերմադինամիկայի երկրորդ օրենք" data-language-autonym="Հայերեն" data-language-local-name="Armeens" 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_termodinamika_kedua" title="Hukum termodinamika kedua – Indonesisch" lang="id" hreflang="id" data-title="Hukum termodinamika kedua" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" 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/Secondo_principio_della_termodinamica" title="Secondo principio della termodinamica – Italiaans" lang="it" hreflang="it" data-title="Secondo principio della termodinamica" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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/%E7%86%B1%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%BA%8C%E6%B3%95%E5%89%87" title="熱力学第二法則 – Japans" lang="ja" hreflang="ja" data-title="熱力学第二法則" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%94%E1%83%9D%E1%83%A0%E1%83%94_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="თერმოდინამიკის მეორე კანონი – Georgisch" lang="ka" hreflang="ka" data-title="თერმოდინამიკის მეორე კანონი" data-language-autonym="ქართული" data-language-local-name="Georgisch" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0%D0%BD%D1%8B%D2%A3_%D0%B5%D0%BA%D1%96%D0%BD%D1%88%D1%96_%D0%B7%D0%B0%D2%A3%D1%8B" title="Термодинамиканың екінші заңы – Kazachs" lang="kk" hreflang="kk" data-title="Термодинамиканың екінші заңы" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B4%EC%97%AD%ED%95%99_%EC%A0%9C2%EB%B2%95%EC%B9%99" title="열역학 제2법칙 – Koreaans" lang="ko" hreflang="ko" data-title="열역학 제2법칙" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Altera_lex_thermodynamica" title="Altera lex thermodynamica – Latijn" lang="la" hreflang="la" data-title="Altera lex thermodynamica" data-language-autonym="Latina" data-language-local-name="Latijn" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Otrais_termodinamikas_likums" title="Otrais termodinamikas likums – Lets" lang="lv" hreflang="lv" data-title="Otrais termodinamikas likums" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_termodinamik_kedua" title="Hukum termodinamik kedua – Maleis" lang="ms" hreflang="ms" data-title="Hukum termodinamik kedua" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Termodynamikkens_andre_hovedsetning" title="Termodynamikkens andre hovedsetning – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Termodynamikkens andre hovedsetning" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Segond_principi_de_la_termodinamica" title="Segond principi de la termodinamica – Occitaans" lang="oc" hreflang="oc" data-title="Segond principi de la termodinamica" data-language-autonym="Occitan" data-language-local-name="Occitaans" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A5%E0%A8%B0%E0%A8%AE%E0%A9%8B%E0%A8%A1%E0%A8%BE%E0%A8%87%E0%A8%A8%E0%A8%BE%E0%A8%AE%E0%A8%BF%E0%A8%95%E0%A8%B8_%E0%A8%A6%E0%A8%BE_%E0%A8%A6%E0%A9%82%E0%A8%9C%E0%A8%BE_%E0%A8%A8%E0%A8%BF%E0%A8%AF%E0%A8%AE" title="ਥਰਮੋਡਾਇਨਾਮਿਕਸ ਦਾ ਦੂਜਾ ਨਿਯਮ – Punjabi" lang="pa" hreflang="pa" data-title="ਥਰਮੋਡਾਇਨਾਮਿਕਸ ਦਾ ਦੂਜਾ ਨਿਯਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Druga_zasada_termodynamiki" title="Druga zasada termodynamiki – Pools" lang="pl" hreflang="pl" data-title="Druga zasada termodynamiki" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%DA%BE%D8%B1%D9%85%D9%88%DA%88%D8%A7%D8%A6%D9%86%D8%A7%D9%85%DA%A9%D8%B3_%D8%AF%D8%A7_%D8%AF%D9%88%D8%AC%D8%A7_%D9%82%D9%86%D9%88%D9%86" title="تھرموڈائنامکس دا دوجا قنون – Western Punjabi" lang="pnb" hreflang="pnb" data-title="تھرموڈائنامکس دا دوجا قنون" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Segunda_lei_da_termodin%C3%A2mica" title="Segunda lei da termodinâmica – Portugees" lang="pt" hreflang="pt" data-title="Segunda lei da termodinâmica" data-language-autonym="Português" data-language-local-name="Portugees" 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/Principiul_al_doilea_al_termodinamicii" title="Principiul al doilea al termodinamicii – Roemeens" lang="ro" hreflang="ro" data-title="Principiul al doilea al termodinamicii" data-language-autonym="Română" data-language-local-name="Roemeens" 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%92%D1%82%D0%BE%D1%80%D0%BE%D0%B5_%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%BE_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B8" title="Второе начало термодинамики – Russisch" lang="ru" hreflang="ru" data-title="Второе начало термодинамики" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Drugi zakon termodinamike" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8F%E0%B6%B4%E0%B6%9C%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80%E0%B7%9A_%E0%B6%AF%E0%B7%99%E0%B7%80%E0%B6%B1_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="තාපගති විද්‍යාවේ දෙවන නියමය – Singalees" lang="si" hreflang="si" data-title="තාපගති විද්‍යාවේ දෙවන නියමය" data-language-autonym="සිංහල" data-language-local-name="Singalees" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Second law of thermodynamics" 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/Druh%C3%A1_termodynamick%C3%A1_veta" title="Druhá termodynamická veta – Slowaaks" lang="sk" hreflang="sk" data-title="Druhá termodynamická veta" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike – Sloveens" lang="sl" hreflang="sl" data-title="Drugi zakon termodinamike" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" 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%94%D1%80%D1%83%D0%B3%D0%B8_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B5" title="Други принцип термодинамике – Servisch" lang="sr" hreflang="sr" data-title="Други принцип термодинамике" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" 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/Termodynamikens_andra_huvudsats" title="Termodynamikens andra huvudsats – Zweeds" lang="sv" hreflang="sv" data-title="Termodynamikens andra huvudsats" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA_%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%87%E0%AE%B0%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%BE%E0%AE%AE%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="வெப்ப இயக்கவியலின் இரண்டாம் விதி – Tamil" lang="ta" hreflang="ta" data-title="வெப்ப இயக்கவியலின் இரண்டாம் விதி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%8E%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%AA%E0%B8%AD%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AD%E0%B8%B8%E0%B8%93%E0%B8%AB%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="กฎข้อที่สองของอุณหพลศาสตร์ – Thai" lang="th" hreflang="th" data-title="กฎข้อที่สองของอุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Termodinami%C4%9Fin_ikinci_yasas%C4%B1" title="Termodinamiğin ikinci yasası – Turks" lang="tr" hreflang="tr" data-title="Termodinamiğin ikinci yasası" data-language-autonym="Türkçe" data-language-local-name="Turks" 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%94%D1%80%D1%83%D0%B3%D0%B8%D0%B9_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B8" title="Другий закон термодинаміки – Oekraïens" lang="uk" hreflang="uk" data-title="Другий закон термодинаміки" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA_%DA%A9%D8%A7_%D8%AF%D9%88%D8%B3%D8%B1%D8%A7_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="حرحرکیات کا دوسرا قانون – Urdu" lang="ur" hreflang="ur" data-title="حرحرکیات کا دوسرا قانون" 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/Termodinamikaning_ikkinchi_qonuni" title="Termodinamikaning ikkinchi qonuni – Oezbeeks" lang="uz" hreflang="uz" data-title="Termodinamikaning ikkinchi qonuni" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_lu%E1%BA%ADt_th%E1%BB%A9_hai_c%E1%BB%A7a_nhi%E1%BB%87t_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Định luật thứ hai của nhiệt động lực học – Vietnamees" lang="vi" hreflang="vi" data-title="Định luật thứ hai của nhiệt động lực học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%BA%8C%E5%AE%9A%E5%BE%8B" title="热力学第二定律 – Wuyu" lang="wuu" hreflang="wuu" data-title="热力学第二定律" data-language-autonym="吴语" data-language-local-name="Wuyu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%BA%8C%E5%AE%9A%E5%BE%8B" title="热力学第二定律 – Chinees" lang="zh" hreflang="zh" data-title="热力学第二定律" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8%E7%AC%AC%E4%BA%8C%E5%AE%9A%E5%BE%8B" title="熱力學第二定律 – Klassiek Chinees" lang="lzh" hreflang="lzh" data-title="熱力學第二定律" data-language-autonym="文言" data-language-local-name="Klassiek Chinees" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8%E7%AC%AC%E4%BA%8C%E5%AE%9A%E5%BE%8B" title="熱力學第二定律 – Kantonees" lang="yue" hreflang="yue" data-title="熱力學第二定律" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:Carnot_engine_scheme.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Carnot_engine_scheme.svg/250px-Carnot_engine_scheme.svg.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Carnot_engine_scheme.svg/375px-Carnot_engine_scheme.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Carnot_engine_scheme.svg/500px-Carnot_engine_scheme.svg.png 2x" data-file-width="460" data-file-height="460" /></a><figcaption>Schema voor een warmtemachine: warmte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> stroomt van reservoir 1 met temperatuur <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f304724948a3ef606c4a92459e22b87a954d993" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{1}}"></span> naar het koudere reservoir 2 met temperatuur <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1ba5f12fbb0ff766aec6e22148b429373608555" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{2}}"></span>, en een warmtemotor kan hiermee arbeid <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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> leveren.</figcaption></figure> <p>De <b>tweede wet van de <a href="/wiki/Thermodynamica" title="Thermodynamica">thermodynamica</a></b>, ook wel <b>Tweede Hoofdwet</b> genoemd, is een fundamentele wetmatigheid gebaseerd op de volgende elementaire macroscopische waarnemingen: </p> <ul><li>warmte stroomt van nature van warme naar koude gebieden en nooit spontaan van koud naar warm.</li> <li>arbeid kan wel volledig in warmte, maar omgekeerd kan warmte nooit volledig in arbeid worden omgezet (dit feit werd met name ontdekt bij de ontwikkeling van de <a href="/wiki/Stoommachine" title="Stoommachine">stoommachine</a>)</li></ul> <p>In de tweede helft van de 19e eeuw, toen het bestaan van atomen en moleculen steeds meer bevestigd werd, ontdekte men dat deze macroscopische eigenschappen in wezen zijn terug te voeren tot microscopische eigenschappen, namelijk de chaotische beweging van grote aantallen moleculen of atomen. Met behulp van de <a href="/wiki/Statistische_mechanica" class="mw-redirect" title="Statistische mechanica">statistische mechanica</a>, die vooral door <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a> en <a href="/wiki/Boltzmann" class="mw-redirect" title="Boltzmann">Boltzmann</a> werd ontwikkeld, kon deze hoofdwet worden geherformuleerd in termen van waarschijnlijkheid van de bewegingstoestand van grote aantallen moleculen. Temperatuurverschillen binnen één systeem worden van nature afgevlakt door <a href="/wiki/Dissipatie" title="Dissipatie">dissipatie</a> van <a href="/wiki/Kinetische_energie" title="Kinetische energie">kinetische energie</a> door onderlinge botsingen van moleculen, die uiteindelijk leiden tot een evenwichtstoestand. Nauw hiermee verbonden is het begrip <a href="/wiki/Entropie" title="Entropie">entropie</a> als maat voor de waarschijnlijkheid van een verdeling van microtoestanden, waarbij de evenwichtstoestand de toestand met maximale entropie is. </p><p>Deze wet betekent ook dat <a href="/wiki/Zelforganisatie" title="Zelforganisatie">zelforganisatie</a> in een chaotisch systeem alleen mogelijk is als er energie van buiten het systeem wordt toegevoegd. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overzicht">Overzicht</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=1" title="Bewerk dit kopje: Overzicht" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=1" title="De broncode bewerken van de sectie: Overzicht"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In een algemene zin zegt de tweede wet dat de verschillen in toestandsvariabelen (die niet van de hoeveelheid materie afhangen) als temperatuur en druk tussen twee samen te voegen deelsystemen de neiging hebben uit te middelen naar rato van de hoeveelheden materie in die deelsystemen en dat er arbeid kan worden verkregen uit afwijkingen van de evenwichtstoestand. Als twee systemen alleen contact met elkaar hebben, vormen zij tezamen één geïsoleerd systeem, dat streeft naar gelijkmatige verdeling van de toestandsvariabelen. Een <a href="/wiki/Warmtemachine" title="Warmtemachine">warmtemachine</a> is een mechanisch apparaat dat gebruikmaakt van het verschil in temperatuur van twee systemen en dat omzet in nuttige, bruikbare arbeid. </p><p>De Franse ingenieur <a href="/wiki/Sadi_Carnot" title="Sadi Carnot">Sadi Carnot</a> gaf in <a href="/wiki/1825" title="1825">1825</a> als eerste een formulering van deze wet, die in de loop van de <a href="/wiki/19e_eeuw" title="19e eeuw">19e eeuw</a> verder werd uitgewerkt. De naar Carnot genoemde <a href="/wiki/Carnotcyclus" class="mw-redirect" title="Carnotcyclus">Carnotcyclus</a> werd bestudeerd in samenhang met het mechanische warmte-equivalent van <a href="/wiki/James_Joule" class="mw-redirect" title="James Joule">James Joule</a>. Omdat de werking van elke warmtemotor berust op een temperatuurverschil volgt daar uit dat er geen nuttige arbeid gehaald kan worden uit een geïsoleerd systeem in evenwicht: er moet altijd minstens een warme externe energiebron en een koude warmte-afvoer zijn. De Tweede Wet is de reden dat het <a href="/wiki/Perpetuum_mobile" title="Perpetuum mobile">perpetuum mobile</a> (eeuwigdurende beweging) van de 'tweede soort' niet kan bestaan, zoals de Eerste Wet dat is voor het perpetuum mobile van de 'eerste soort'. </p> <div class="mw-heading mw-heading2"><h2 id="Andere_formuleringen">Andere formuleringen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=2" title="Bewerk dit kopje: Andere formuleringen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=2" title="De broncode bewerken van de sectie: Andere formuleringen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De tweede wet kan op diverse beknopte manieren worden geformuleerd, zoals: </p> <ul><li>Er is geen proces mogelijk dat als <i>enige</i> gevolg heeft dat warmte van een voorwerp met lage temperatuur naar een voorwerp met een hogere temperatuur stroomt.</li> <li>De <a href="/wiki/Entropie" title="Entropie">entropie</a> van een geïsoleerd systeem dat niet in evenwicht is, neemt in de loop van de tijd toe, tot het maximum voor dat geïsoleerde systeem is bereikt. Die toestand met de maximale entropie is de evenwichtstoestand.</li> <li>De formulering van <a href="/wiki/William_Thomson_(natuurkundige)" title="William Thomson (natuurkundige)">Kelvin</a> en <a href="/wiki/Max_Planck" title="Max Planck">Planck</a> is "Het is onmogelijk een machine te construeren die cyclisch op warmte uit een enkel <a href="/wiki/Reservoir_(thermodynamica)" title="Reservoir (thermodynamica)">reservoir</a> werkt en daaruit netto arbeid haalt"</li> <li>"Het is onmogelijk om met een motor, verbonden met twee warmtereservoirs, een cyclisch proces uit te laten voeren dat als enige resultaat heeft de overdracht van een hoeveelheid warmte van het reservoir met lage temperatuur naar het reservoir met hoge temperatuur" (<a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius</a>, 1854).</li> <li>De ideale <a href="/wiki/Koeltechniek" title="Koeltechniek">koelmachine</a> bestaat niet. (Een “ideale” koelmachine “verbruikt” geen energie.)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Wiskundige_beschrijvingen">Wiskundige beschrijvingen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=3" title="Bewerk dit kopje: Wiskundige beschrijvingen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=3" title="De broncode bewerken van de sectie: Wiskundige beschrijvingen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De Duitse fysicus <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> gaf in 1856 de volgende formulering aan wat hij de "tweede fundamentele stelling in de mechanische theorie van hitte " noemde: <sup id="cite_ref-Clausius_1-0" class="reference"><a href="#cite_note-Clausius-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 \int {\frac {\mathrm {d} Q}{T}}=-N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {\mathrm {d} Q}{T}}=-N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/233fefbbd4e5e18091738cb75ee785880bd19449" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.518ex; height:5.843ex;" alt="{\displaystyle \int {\frac {\mathrm {d} Q}{T}}=-N}"></span></dd></dl> <p>waarin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> de toegevoerde warmte, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> de absolute temperatuur en <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> de "gelijkwaardigheids-waarde" van alle niet-compenseerbare omzettingen betrokken bij het cyclisch proces voorstelt. Het quotiënt <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q/T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q/T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/256071b9ddd633090a6659110998c2b5b6a592ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.637ex; height:2.843ex;" alt="{\displaystyle Q/T}"></span> wordt wel de 'gereduceerde warmte' genoemd. Later, in 1865, zou Clausius er toe komen om die "gelijkwaardigheids-waarde" als entropie te definiëren. In datzelfde jaar werd op 24 april de meest geruchtmakende versie van de tweede wet geformuleerd in een presentatie voor de Filosofische Vereniging van Zürich, toen Clausius besloot met: </p> <blockquote><p>De entropie van het heelal neigt naar een maximum.</p></blockquote> <p>Vanwege de beknopte vorm en het ontbreken van specifieke voorwaarden, zoals "gesloten, of geïsoleerd systeem", denken veel mensen niet alleen dat de wanorde in het heelal altijd stijgt, maar ook dat dit op vrijwel elk denkbaar onderwerp van toepassing is; dat is niet waar; de formulering van Clausius is slechts een vereenvoudigde versie van een complexere beschrijving. </p><p>De bij een evenwichtstoestand behorende maximale waarde van de entropie <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> is echter wel een <i>toestandsgrootheid</i>, die evenals andere toestandsgrootheden als druk <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, temperatuur <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>, volume <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> en inwendige energie <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 U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> deel uitmaakt van een voor die evenwichtstoestand kenmerkende combinatie van waarden van die toestandsgrootheden. Het maakt voor die combinatie van waarden dus niet uit via welk proces, omkeerbaar of onomkeerbaar, die toestand bereikt wordt.' Daaruit volgt o.a. dat een <a href="/wiki/Kringintegraal" class="mw-redirect" title="Kringintegraal">kringintegraal</a> van een toestandsgrootheid die een <a href="/wiki/Reversibel_proces" title="Reversibel proces">opeenvolging van omkeerbare toestandsovergangen</a> beschrijft, gelijk is aan nul: </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 \oint \mathrm {d} P=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint \mathrm {d} P=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f33d23b47571885c276390075650e33b001dd037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.88ex; height:5.676ex;" alt="{\displaystyle \oint \mathrm {d} P=0}"></span></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 \oint \mathrm {d} V=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint \mathrm {d} V=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c515bcece693abafbf132f26c3176314cf239fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.921ex; height:5.676ex;" alt="{\displaystyle \oint \mathrm {d} V=0}"></span></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 \oint \mathrm {d} T=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint \mathrm {d} T=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1356e88a9b05585565bdd830ee89c4ebfd3d95be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.77ex; height:5.676ex;" alt="{\displaystyle \oint \mathrm {d} T=0}"></span></dd></dl> <p>en dus ook </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 \oint \mathrm {d} S=\oint {\frac {\mathrm {d} Q}{T}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>=</mo> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint \mathrm {d} S=\oint {\frac {\mathrm {d} Q}{T}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdd2927a366917a3577c3ae2691803ccebcfd16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.28ex; height:5.843ex;" alt="{\displaystyle \oint \mathrm {d} S=\oint {\frac {\mathrm {d} Q}{T}}=0}"></span></dd></dl> <p>Voor omkeerbare processen is <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} Q/T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} Q/T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fae09687f2593cbc4235f21eba6b65cc8e9dab47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.93ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} Q/T}"></span> gelijk aan <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} S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72ba425d7d7a0f229457dea3c0be4a47ea303cc3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.792ex; height:2.176ex;" alt="{\displaystyle \mathrm {d} S}"></span>, de toename van toestandsgrootheid entropie. Voor omkeerbare infinitesimale toestandsveranderingen kan dus <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} Q=T\mathrm {d} S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> <mo>=</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} Q=T\mathrm {d} S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9bca4391cf18d8aec10bea2d95eeef28b1d460" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.657ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} Q=T\mathrm {d} S}"></span> geschreven, waardoor de <a href="/wiki/Eerste_wet_van_de_thermodynamica" title="Eerste wet van de thermodynamica">Eerste (hoofd)wet</a> herschreven kan worden als </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\mathrm {d} S=\mathrm {d} U+\mathrm {d} W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\mathrm {d} S=\mathrm {d} U+\mathrm {d} W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b846ab1dfff2eab546bd1fb9183dcce23a27015" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.17ex; height:2.343ex;" alt="{\displaystyle T\mathrm {d} S=\mathrm {d} U+\mathrm {d} W}"></span>,</dd></dl> <p>waarin <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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> de verrichte uitwendige arbeid is. </p><p><br /> <b>On</b>omkeerbare processen kunnen helemaal niet weergegeven worden als trajecten in een <a href="/wiki/Toestandsdiagram" title="Toestandsdiagram">toestandsdiagram</a>, omdat dat nu eenmaal betrekking heeft op evenwichtstoestanden. Een evenwichtstoestand als resultaat van een onomkeerbaar proces kan wel een plaats worden toegekend in een toestandsdiagram. De kringintegraal </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 \oint {\frac {\mathrm {d} Q_{\text{irreversibel}}}{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>irreversibel</mtext> </mrow> </msub> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint {\frac {\mathrm {d} Q_{\text{irreversibel}}}{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cfc3aca421594cc5595a60db7e3b07786c3d621" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.706ex; height:5.843ex;" alt="{\displaystyle \oint {\frac {\mathrm {d} Q_{\text{irreversibel}}}{T}}}"></span></dd></dl> <p>is wel gedefinieerd, maar die komt dus niet overeen met een gesloten pad in een toestandsdiagram. De waarde ervan is altijd negatief. </p><p>De <a href="/wiki/Statistische_thermodynamica" title="Statistische thermodynamica">statistische thermodynamica</a> kwam op in de tweede helft van de 19e eeuw, toen het bestaan van moleculen steeds serieuzer onder ogen werd gezien. Deze houdt er rekening mee dat elk macroscopisch systeem bestaat uit een groot aantal bewegende deeltjes. De bewegingsvergelijkingen van de deterministische <a href="/wiki/Klassieke_mechanica" title="Klassieke mechanica">klassieke mechanica</a> zijn voor meer dan 2 onafhankelijk bewegende lichamen meestal niet exact oplosbaar. Daarom wordt met behulp van een aantal postulaten een statistische benadering mogelijk gemaakt, die haar rechtvaardiging vindt in empirische bevestiging. Ten eerste wordt gepostuleerd dat een materiaal is samengesteld uit atomen en moleculen die in constante onderling onafhankelijke beweging zijn. De plaatsen en snelheden van al die deeltjes in het systeem op een bepaald moment vormen tezamen een "micro-toestand"; de micro-toestand van een systeem verandert dus voortdurend. Het tweede postulaat luidt dat alle micro-toestanden die binnen de randvoorwaarden mogelijk zijn, even waarschijnlijk zijn. Dit leidt tot een statistische formulering van de tweede wet, waarin volgens de statistische 'wet van de grote getallen' macroscopische grootheden als temperatuur en druk statistische gemiddelden zijn waarvan de <a href="/wiki/Standaarddeviatie" class="mw-redirect" title="Standaarddeviatie">standaarddeviaties</a> evenredig zijn met <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/{\sqrt {N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>N</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/{\sqrt {N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e08dda9c5205a998e3315b9990800e1a27cfe470" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.324ex; height:3.176ex;" alt="{\displaystyle 1/{\sqrt {N}}}"></span>, waarin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> het aantal deeltjes in het systeem is. De combinatie van al deze gemiddelden is de macro-toestand, die overeenkomt met de toestand die in de klassieke thermodynamica beschreven wordt met een toestandsvergelijking.<br /> Het verband tussen de statistische aanpak en de klassieke aanpak komt het kernachtigst tot uitdrukking in de door <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> afgeleide uitdrukking: <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 S=k\cdot \ln(w)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>k</mi> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>w</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=k\cdot \ln(w)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce97a06272b056cb1cab53cbcdcd95e0bf4b176" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.901ex; height:2.843ex;" alt="{\displaystyle S=k\cdot \ln(w)}"></span>, waarin <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> de klassieke toestandsgrootheid entropie is, <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> de constante van Boltzmann en <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> de waarschijnlijkheid van een bepaalde micro-toestand. </p><p>In de statistische aanpak is een tijdafhankelijke wiskundige formulering mogelijk van de Tweede Hoofdwet voor een <i>geïsoleerd systeem</i>, dat dus geen arbeid of energie met de omgeving uitwisselt, en bovendien een <a href="/wiki/Irreversibel_proces" title="Irreversibel proces">onomkeerbaar proces</a> doormaakt, is: </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 {\frac {\mathrm {d} S}{\mathrm {d} t}}\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64e94322067a61b1cc8f61039999df8291182e52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.889ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}\geq 0}"></span></dd></dl> <p>De formulering van de Tweede wet, die overeenkomt met de formulering van Clausius, zegt dus eigenlijk dat een geïsoleerd systeem zich spontaan ontwikkelt in de richting van de meest waarschijnlijke verdeling van micro-toestanden. </p><p>Omdat macroscopische systemen enorme aantallen moleculen, resp. atomen bevatten (ter illustratie: het <a href="/wiki/Getal_van_Avogadro" class="mw-redirect" title="Getal van Avogadro">getal van Avogadro</a> is ongeveer 6,0 × 10<sup>23</sup>) is de waarschijnlijkheid van meetbare afwijkingen van voorspellingen vanuit de klassieke thermodynamica praktisch nul. Nochtans: voor systemen met een klein aantal deeltjes kunnen de thermodynamische grootheden, de entropie inbegrepen, significante tijdafhankelijke statistische variaties vertonen. De klassieke 'fenomenologische' thermodynamische theorie behandelt deze variaties niet. </p> <div class="mw-heading mw-heading2"><h2 id="Relatie_met_de_informatietheorie">Relatie met de informatietheorie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=4" title="Bewerk dit kopje: Relatie met de informatietheorie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=4" title="De broncode bewerken van de sectie: Relatie met de informatietheorie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Maxwell%27s_demon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Maxwell%27s_demon.svg/260px-Maxwell%27s_demon.svg.png" decoding="async" width="260" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Maxwell%27s_demon.svg/390px-Maxwell%27s_demon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Maxwell%27s_demon.svg/520px-Maxwell%27s_demon.svg.png 2x" data-file-width="608" data-file-height="224" /></a><figcaption><a href="/wiki/Maxwells_demon" title="Maxwells demon">Maxwells demon</a> (groen) kan de entropie niet verlagen door snelle moleculen (rood) wel van A naar B en niet van B naar A door te laten en trage moleculen (blauw) wel van B naar A en niet van A naar B door te laten.</figcaption></figure> <p>Entropie in de thermodynamica is equivalent met de entropie zoals die in de <a href="/wiki/Informatietheorie" title="Informatietheorie">informatietheorie</a> wordt gebruikt, de zogenaamde <a href="/wiki/Entropie_(informatietheorie)" title="Entropie (informatietheorie)">Shannon entropie</a>, wanneer je voor de kansen <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_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bab39399bf5424f25d957cdc57c84a0622626d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.059ex; height:2.009ex;" alt="{\displaystyle p_{i}}"></span> de kansverdeling over alle mogelijke microtoestanden van het systeem neemt. Deze equivalentie is algemeen geldig en kan zelfs worden gebruikt voor systemen die niet in <a href="/wiki/Thermodynamisch_evenwicht" title="Thermodynamisch evenwicht">thermodynamisch evenwicht</a> zijn. Wanneer de entropie wordt uitgedrukt in <a href="/wiki/Bit_(eenheid)" title="Bit (eenheid)">bits</a>, dan komt dit overeen met de hoeveelheid informatie die nodig is om de precieze microtoestand van het systeem te specificeren. </p><p>Deze equivalentie maakt het inzichtelijk waarom zelfs <a href="/wiki/Maxwells_demon" title="Maxwells demon">Maxwells demon</a> de <a href="/wiki/Tweede_Hoofdwet" class="mw-redirect" title="Tweede Hoofdwet">Tweede Hoofdwet</a> niet kan overtreden. Om bijvoorbeeld een temperatuurverschil te creëren in een gas door iedere keer een luikje open te doen wanneer er een snelle <a href="/wiki/Molecule" class="mw-redirect" title="Molecule">molecule</a> aankomt, lijkt het alsof je de entropie van een gas kunt verlagen. Nu is het inderdaad zo dat de entropie van het gas verlaagd kan worden, maar de demon moet wel iedere keer een beslissing nemen op grond van de snelheid van de molecule die langs komt. De informatie over de vorige molecule zit dan nog in zijn geheugen, dus op een gegeven moment raakt zijn geheugen vol. Bovendien zou de demon zelf snel in temperatuur oplopen. </p><p>De daling van de entropie van het gas uitgedrukt in bits die een ideale demon kan bereiken is precies gelijk aan de <a href="/w/index.php?title=Geheugencapaciteit&action=edit&redlink=1" class="new" title="Geheugencapaciteit (de pagina bestaat niet)">geheugencapaciteit</a> van de demon. Er is dan dus minder informatie nodig om de <a href="/wiki/Microtoestand" title="Microtoestand">microtoestand</a> van het gas te specificeren maar precies zoveel meer informatie is er nodig om de toestand van het geheugen van de demon te specificeren. Wissen van het geheugen is geen optie, want daardoor neemt de entropie van de omgeving toe met ten minste hetzelfde getal. </p> <div class="mw-heading mw-heading2"><h2 id="Zie_ook">Zie ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=5" title="Bewerk dit kopje: Zie ook" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=5" title="De broncode bewerken van de sectie: Zie ook"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Nulde_wet_van_de_thermodynamica" title="Nulde wet van de thermodynamica">Nulde wet van de thermodynamica</a></li> <li><a href="/wiki/Eerste_wet_van_de_thermodynamica" title="Eerste wet van de thermodynamica">Eerste wet van de thermodynamica</a></li> <li><a href="/wiki/Derde_wet_van_de_thermodynamica" title="Derde wet van de thermodynamica">Derde wet van de thermodynamica</a></li> <li><a href="/wiki/The_2nd_Law" title="The 2nd Law">The 2nd Law</a>, album van <a href="/wiki/Muse" title="Muse">Muse</a> geïnspireerd door deze wet</li></ul> <div class="mw-heading mw-heading2"><h2 id="Externe_link">Externe link</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&veaction=edit&section=6" title="Bewerk dit kopje: Externe link" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Tweede_wet_van_de_thermodynamica&action=edit&section=6" title="De broncode bewerken van de sectie: Externe link"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r67679320">.mw-parser-output .taalaanduiding{font-family:sans-serif;font-size:85%;cursor:help;color:var(--color-subtle,#555)}.mw-parser-output .taalaanduiding span{border-bottom:1px dotted var(--color-subtle,#555)}</style><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090717175331/http://entropysite.oxy.edu/students_approach.html">A Student’s Approach to the Second Law and Entropy</a></li></ul> <div class="toccolours appendix" role="presentation" style="font-size:90%; margin:1em 0 -0.5em; clear:both;"> <div><span style="font-weight:bold">Bronnen, noten en/of referenties</span></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Clausius-1"><span class="mw-cite-backlink"><a href="#cite_ref-Clausius_1-0">↑</a></span> <span class="reference-text">Clausius, R. (1865). "<i>Mechanical Theory of Heat - with its Application to the Steam Engine and the Physical Properties of Bodies</i>." London: John van Voorst.</span> </li> </ol></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="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Tweede_wet_van_de_thermodynamica&oldid=63186528">https://nl.wikipedia.org/w/index.php?title=Tweede_wet_van_de_thermodynamica&oldid=63186528</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorieën</a>: <ul><li><a href="/wiki/Categorie:Natuurkundige_wet" title="Categorie:Natuurkundige wet">Natuurkundige wet</a></li><li><a href="/wiki/Categorie:Thermodynamica" title="Categorie:Thermodynamica">Thermodynamica</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"> Deze pagina is voor het laatst bewerkt op 25 okt 2022 om 17:48.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. 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