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id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">presunúť do postranného panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skryť</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Začiatok</div> </a> </li> <li id="toc-Aplikácia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplikácia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Aplikácia</span> </div> </a> <button aria-controls="toc-Aplikácia-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Aplikácia</span> </button> <ul id="toc-Aplikácia-sublist" class="vector-toc-list"> <li id="toc-Aplikácia_na_dej_izochorický" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aplikácia_na_dej_izochorický"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Aplikácia na dej izochorický</span> </div> </a> <ul id="toc-Aplikácia_na_dej_izochorický-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplikácia_na_dej_izobarický" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aplikácia_na_dej_izobarický"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Aplikácia na dej izobarický</span> </div> </a> <ul id="toc-Aplikácia_na_dej_izobarický-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplikácia_na_dej_izotermický" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aplikácia_na_dej_izotermický"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Aplikácia na dej izotermický</span> </div> </a> <ul id="toc-Aplikácia_na_dej_izotermický-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplikácia_na_dej_adiabatický" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aplikácia_na_dej_adiabatický"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Aplikácia na dej adiabatický</span> </div> </a> <ul id="toc-Aplikácia_na_dej_adiabatický-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Pozri_aj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pozri_aj"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Pozri aj</span> </div> </a> <ul id="toc-Pozri_aj-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="Obsah" 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="Prepnúť obsah" > <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">Prepnúť obsah</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">Prvá termodynamická veta</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="Prejsť na článok v inom jazyku. Je dostupný v 64 jazykoch" > <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 jazykov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af badge-Q70894304 mw-list-item" title=""><a href="https://af.wikipedia.org/wiki/Eerste_wet_van_termodinamika" title="Eerste wet van termodinamika – afrikánčina" lang="af" hreflang="af" data-title="Eerste wet van termodinamika" data-language-autonym="Afrikaans" data-language-local-name="afrikánčina" 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%A3%D9%88%D9%84_%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 الأول للديناميكا الحرارية – arabčina" lang="ar" hreflang="ar" data-title="القانون الأول للديناميكا الحرارية" data-language-autonym="العربية" data-language-local-name="arabčina" 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/Primer_principiu_de_la_termodin%C3%A1mica" title="Primer principiu de la termodinámica – astúrčina" lang="ast" hreflang="ast" data-title="Primer principiu de la termodinámica" data-language-autonym="Asturianu" data-language-local-name="astúrčina" 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_birinci_qanunu" title="Termodinamikanın birinci qanunu – azerbajdžančina" lang="az" hreflang="az" data-title="Termodinamikanın birinci qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžančina" 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%9F%D0%B5%D1%80%D1%88%D1%8B_%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="Першы пачатак тэрмадынамікі – bieloruština" lang="be" hreflang="be" data-title="Першы пачатак тэрмадынамікі" data-language-autonym="Беларуская" data-language-local-name="bieloruština" 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%9F%D1%8A%D1%80%D0%B2%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="Първи закон на термодинамиката – bulharčina" lang="bg" hreflang="bg" data-title="Първи закон на термодинамиката" data-language-autonym="Български" data-language-local-name="bulharčina" 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%AA%E0%A7%8D%E0%A6%B0%E0%A6%A5%E0%A6%AE_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="তাপগতিবিদ্যার প্রথম সূত্র – bengálčina" lang="bn" hreflang="bn" data-title="তাপগতিবিদ্যার প্রথম সূত্র" data-language-autonym="বাংলা" data-language-local-name="bengálčina" 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – bosniačtina" lang="bs" hreflang="bs" data-title="Prvi zakon termodinamike" data-language-autonym="Bosanski" data-language-local-name="bosniačtina" 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/Primer_principi_de_la_termodin%C3%A0mica" title="Primer principi de la termodinàmica – katalánčina" lang="ca" hreflang="ca" data-title="Primer principi de la termodinàmica" data-language-autonym="Català" data-language-local-name="katalánčina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DB%8C%D8%A7%D8%B3%D8%A7%DB%8C_%DB%8C%DB%95%DA%A9%DB%95%D9%85%DB%8C_%D8%AA%DB%8E%D8%B1%D9%85%DB%86%D8%AF%D8%A7%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="یاسای یەکەمی تێرمۆداینامیک – kurdčina (sorání)" lang="ckb" hreflang="ckb" data-title="یاسای یەکەمی تێرمۆداینامیک" data-language-autonym="کوردی" data-language-local-name="kurdčina (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Prvn%C3%AD_termodynamick%C3%BD_z%C3%A1kon" title="První termodynamický zákon – čeština" lang="cs" hreflang="cs" data-title="První termodynamický zákon" data-language-autonym="Čeština" data-language-local-name="čeština" 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%BF%C4%95%D1%80%D1%80%D0%B5%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 пĕрремĕш пуçламăшĕ – čuvaština" lang="cv" hreflang="cv" data-title="Термодинамикăн пĕрремĕш пуçламăшĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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_1._lov" title="Termodynamikkens 1. lov – dánčina" lang="da" hreflang="da" data-title="Termodynamikkens 1. lov" data-language-autonym="Dansk" data-language-local-name="dánčina" 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/Erster_Hauptsatz_der_Thermodynamik" title="Erster Hauptsatz der Thermodynamik – nemčina" lang="de" hreflang="de" data-title="Erster Hauptsatz der Thermodynamik" data-language-autonym="Deutsch" data-language-local-name="nemčina" 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%A0%CF%81%CF%8E%CF%84%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="Πρώτος θερμοδυναμικός νόμος – gréčtina" lang="el" hreflang="el" data-title="Πρώτος θερμοδυναμικός νόμος" data-language-autonym="Ελληνικά" data-language-local-name="gréčtina" 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/First_law_of_thermodynamics" title="First law of thermodynamics – angličtina" lang="en" hreflang="en" data-title="First law of thermodynamics" data-language-autonym="English" data-language-local-name="angličtina" 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/Unua_le%C4%9Do_de_termodinamiko" title="Unua leĝo de termodinamiko – esperanto" lang="eo" hreflang="eo" data-title="Unua 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/Primer_principio_de_la_termodin%C3%A1mica" title="Primer principio de la termodinámica – španielčina" lang="es" hreflang="es" data-title="Primer principio de la termodinámica" data-language-autonym="Español" data-language-local-name="španielčina" 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_esimene_seadus" title="Termodünaamika esimene seadus – estónčina" lang="et" hreflang="et" data-title="Termodünaamika esimene seadus" data-language-autonym="Eesti" data-language-local-name="estónčina" 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_lehenengo_legea" title="Termodinamikaren lehenengo legea – baskičtina" lang="eu" hreflang="eu" data-title="Termodinamikaren lehenengo legea" data-language-autonym="Euskara" data-language-local-name="baskičtina" 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%A7%D9%88%D9%84_%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="قانون اول ترمودینامیک – perzština" lang="fa" hreflang="fa" data-title="قانون اول ترمودینامیک" data-language-autonym="فارسی" data-language-local-name="perzština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi badge-Q70893996 mw-list-item" title=""><a href="https://fi.wikipedia.org/wiki/Termodynamiikan_ensimm%C3%A4inen_p%C3%A4%C3%A4s%C3%A4%C3%A4nt%C3%B6" title="Termodynamiikan ensimmäinen pääsääntö – fínčina" lang="fi" hreflang="fi" data-title="Termodynamiikan ensimmäinen pääsääntö" data-language-autonym="Suomi" data-language-local-name="fínčina" 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/Premier_principe_de_la_thermodynamique" title="Premier principe de la thermodynamique – francúzština" lang="fr" hreflang="fr" data-title="Premier principe de la thermodynamique" data-language-autonym="Français" data-language-local-name="francúzština" 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/Primeira_lei_da_termodin%C3%A1mica" title="Primeira lei da termodinámica – galícijčina" lang="gl" hreflang="gl" data-title="Primeira lei da termodinámica" data-language-autonym="Galego" data-language-local-name="galícijčina" 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%A8%D7%90%D7%A9%D7%95%D7%9F_%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 הראשון של התרמודינמיקה – hebrejčina" lang="he" hreflang="he" data-title="החוק הראשון של התרמודינמיקה" data-language-autonym="עברית" data-language-local-name="hebrejčina" 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%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊष्मागतिकी का प्रथम नियम – hindčina" lang="hi" hreflang="hi" data-title="ऊष्मागतिकी का प्रथम नियम" data-language-autonym="हिन्दी" data-language-local-name="hindčina" 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/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – chorvátčina" lang="hr" hreflang="hr" data-title="Prvi zakon termodinamike" data-language-autonym="Hrvatski" data-language-local-name="chorvátčina" 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/Premye_lwa_t%C3%A8modinamik" title="Premye lwa tèmodinamik – haitská kreolčina" lang="ht" hreflang="ht" data-title="Premye lwa tèmodinamik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitská kreolčina" 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_els%C5%91_f%C5%91t%C3%A9tele" title="A termodinamika első főtétele – maďarčina" lang="hu" hreflang="hu" data-title="A termodinamika első főtétele" data-language-autonym="Magyar" data-language-local-name="maďarčina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B9%D5%A5%D6%80%D5%B4%D5%B8%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1%D5%B5%D5%AB_%D5%A1%D5%BC%D5%A1%D5%BB%D5%AB%D5%B6_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Թերմոդինամիկայի առաջին օրենք – arménčina" lang="hy" hreflang="hy" data-title="Թերմոդինամիկայի առաջին օրենք" data-language-autonym="Հայերեն" data-language-local-name="arménčina" 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_pertama_termodinamika" title="Hukum pertama termodinamika – indonézština" lang="id" hreflang="id" data-title="Hukum pertama termodinamika" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" 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/Primo_principio_della_termodinamica" title="Primo principio della termodinamica – taliančina" lang="it" hreflang="it" data-title="Primo principio della termodinamica" data-language-autonym="Italiano" data-language-local-name="taliančina" 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%B8%80%E6%B3%95%E5%89%87" title="熱力学第一法則 – japončina" lang="ja" hreflang="ja" data-title="熱力学第一法則" data-language-autonym="日本語" data-language-local-name="japončina" 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%9E%E1%83%98%E1%83%A0%E1%83%95%E1%83%94%E1%83%9A%E1%83%98_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="თერმოდინამიკის პირველი კანონი – gruzínčina" lang="ka" hreflang="ka" data-title="თერმოდინამიკის პირველი კანონი" data-language-autonym="ქართული" data-language-local-name="gruzínčina" 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%B1%D1%96%D1%80%D1%96%D0%BD%D1%88%D1%96_%D0%B1%D0%B0%D1%81%D1%82%D0%B0%D0%BC%D0%B0%D1%81%D1%8B" title="Термодинамиканың бірінші бастамасы – kazaština" lang="kk" hreflang="kk" data-title="Термодинамиканың бірінші бастамасы" data-language-autonym="Қазақша" data-language-local-name="kazaština" 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%9C1%EB%B2%95%EC%B9%99" title="열역학 제1법칙 – kórejčina" lang="ko" hreflang="ko" data-title="열역학 제1법칙" data-language-autonym="한국어" data-language-local-name="kórejčina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Pirmais_termodinamikas_likums" title="Pirmais termodinamikas likums – lotyština" lang="lv" hreflang="lv" data-title="Pirmais termodinamikas likums" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B2_%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="Прв закон на термодинамиката – macedónčina" lang="mk" hreflang="mk" data-title="Прв закон на термодинамиката" data-language-autonym="Македонски" data-language-local-name="macedónčina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A5%87%E0%A4%9A%E0%A5%8D%E0%A4%AF%E0%A4%BE_%E0%A4%85%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%AF%E0%A5%8D%E0%A4%AF%E0%A4%A4%E0%A5%87%E0%A4%9A%E0%A4%BE_%E0%A4%AA%E0%A4%B9%E0%A4%BF%E0%A4%B2%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="ऊर्जेच्या अक्षय्यतेचा पहिला नियम – maráthčina" lang="mr" hreflang="mr" data-title="ऊर्जेच्या अक्षय्यतेचा पहिला नियम" data-language-autonym="मराठी" data-language-local-name="maráthčina" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_termodinamik_pertama" title="Hukum termodinamik pertama – malajčina" lang="ms" hreflang="ms" data-title="Hukum termodinamik pertama" data-language-autonym="Bahasa Melayu" data-language-local-name="malajčina" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Eerste_wet_van_de_thermodynamica" title="Eerste wet van de thermodynamica – holandčina" lang="nl" hreflang="nl" data-title="Eerste wet van de thermodynamica" data-language-autonym="Nederlands" data-language-local-name="holandčina" 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/Den_f%C3%B8rste_termodynamikklova" title="Den første termodynamikklova – nórčina (nynorsk)" lang="nn" hreflang="nn" data-title="Den første termodynamikklova" data-language-autonym="Norsk nynorsk" data-language-local-name="nórčina (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Termodynamikkens_f%C3%B8rste_hovedsetning" title="Termodynamikkens første hovedsetning – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Termodynamikkens første hovedsetning" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" 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/Premier_principi_de_la_termodinamica" title="Premier principi de la termodinamica – okcitánčina" lang="oc" hreflang="oc" data-title="Premier principi de la termodinamica" data-language-autonym="Occitan" data-language-local-name="okcitánčina" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pierwsza_zasada_termodynamiki" title="Pierwsza zasada termodynamiki – poľština" lang="pl" hreflang="pl" data-title="Pierwsza zasada termodynamiki" data-language-autonym="Polski" data-language-local-name="poľština" 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/Primeira_lei_da_termodin%C3%A2mica" title="Primeira lei da termodinâmica – portugalčina" lang="pt" hreflang="pt" data-title="Primeira lei da termodinâmica" data-language-autonym="Português" data-language-local-name="portugalčina" 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_%C3%AEnt%C3%A2i_al_termodinamicii" title="Principiul întâi al termodinamicii – rumunčina" lang="ro" hreflang="ro" data-title="Principiul întâi al termodinamicii" data-language-autonym="Română" data-language-local-name="rumunčina" 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%9F%D0%B5%D1%80%D0%B2%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="Первое начало термодинамики – ruština" lang="ru" hreflang="ru" data-title="Первое начало термодинамики" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/First_law_o_thermodynamics" title="First law o thermodynamics – škótčina" lang="sco" hreflang="sco" data-title="First law o thermodynamics" data-language-autonym="Scots" data-language-local-name="škótčina" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – srbochorvátčina" lang="sh" hreflang="sh" data-title="Prvi zakon termodinamike" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvátčina" 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%B4%E0%B7%85%E0%B6%B8%E0%B7%94_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA" title="තාප ගති විද්‍යාවේ පළමු නියමය – sinhalčina" lang="si" hreflang="si" data-title="තාප ගති විද්‍යාවේ පළමු නියමය" data-language-autonym="සිංහල" data-language-local-name="sinhalčina" 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/First_law_of_thermodynamics" title="First law of thermodynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="First 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Prvi_zakon_termodinamike" title="Prvi zakon termodinamike – slovinčina" lang="sl" hreflang="sl" data-title="Prvi zakon termodinamike" data-language-autonym="Slovenščina" data-language-local-name="slovinčina" 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%9F%D1%80%D0%B2%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="Први принцип термодинамике – srbčina" lang="sr" hreflang="sr" data-title="Први принцип термодинамике" data-language-autonym="Српски / srpski" data-language-local-name="srbčina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%A4%E0%AE%B2%E0%AE%BE%E0%AE%B5%E0%AE%A4%E0%AF%81_%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%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="முதலாவது வெப்ப இயக்கவியல் விதி – tamilčina" lang="ta" hreflang="ta" data-title="முதலாவது வெப்ப இயக்கவியல் விதி" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" 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%AB%E0%B8%99%E0%B8%B6%E0%B9%88%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="กฎข้อที่หนึ่งของอุณหพลศาสตร์ – thajčina" lang="th" hreflang="th" data-title="กฎข้อที่หนึ่งของอุณหพลศาสตร์" data-language-autonym="ไทย" data-language-local-name="thajčina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D1%88%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="Перший закон термодинаміки – ukrajinčina" lang="uk" hreflang="uk" data-title="Перший закон термодинаміки" data-language-autonym="Українська" data-language-local-name="ukrajinčina" 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_%D9%BE%DB%81%D9%84%D8%A7_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="حرحرکیات کا پہلا قانون – urdčina" lang="ur" hreflang="ur" data-title="حرحرکیات کا پہلا قانون" data-language-autonym="اردو" data-language-local-name="urdčina" 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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">z Wikipédie, slobodnej encyklopédie</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="sk" dir="ltr"><p><b>Prvá termodynamická veta</b> alebo <b>prvý termodynamický zákon</b> je vo fyzike nasledujúci <a href="/wiki/Fyzik%C3%A1lny_z%C3%A1kon" title="Fyzikálny zákon">zákon</a>: </p><p>Znenie: </p> <ul><li>formulácia 1: Každá <a href="/wiki/Fyzik%C3%A1lna_s%C3%BAstava" title="Fyzikálna sústava">fyzikálna sústava</a> má <a href="/wiki/Stavov%C3%A1_veli%C4%8Dina" title="Stavová veličina">stavovú veličinu</a> nazývanú <a href="/wiki/Vn%C3%BAtorn%C3%A1_energia" title="Vnútorná energia">vnútorná energia</a> (U), ktorá sa mení len prostredníctvom výmeny <a href="/wiki/Energia" title="Energia">energie</a> s okolím (<a href="/wiki/Pr%C3%A1ca_(fyzika)" title="Práca (fyzika)">objemová práca</a>, <a href="/wiki/Tepeln%C3%A1_v%C3%BDmena" class="mw-redirect" title="Tepelná výmena">tepelná výmena</a>)</li> <li>formulácia 2: ΔU = ΔQ + Δ(W<sub>p</sub> + W<sub>k</sub>) , kde: <ul><li>ΔU: zmena vnútornej energie sústavy</li> <li>ΔQ: zmena <a href="/wiki/Teplo" title="Teplo">tepla</a> sústavy (+ znamená dodanie, - znamená odobratie)</li> <li>Δ(W<sub>p</sub> + W<sub>k</sub>): vykonaná/spotrebovaná objemová práca (+ znamená, že ju sústava vykonala, - znamená, že ju sústava spotrebovala)</li></ul></li> <li>formulácia 3: Nie je možné skonštruovať <a href="/wiki/Perpetuum_mobile" title="Perpetuum mobile">perpetuum mobile</a> prvého druhu (teda stroj, ktorý cyklicky opakuje dej len s počiatočnou energiou)</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Aplikácia"><span id="Aplik.C3.A1cia"></span>Aplikácia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=1" title="Upraviť sekciu: Aplikácia" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=1" title="Editovat zdrojový kód sekce Aplikácia"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Prvý zákon termodynamiky môžeme aplikovať na deje prebiehajúce v uzavretých sústavách. <b>Konvencia:</b> Objemovú prácu <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> budeme označovať súhrnne, nie ako rozdiel spotrebovanej a vykonanej. O tom, o akú prácu ide rozhoduje jej znamienko: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f912b7a62c30a07b7f4a8ededf6c2ab3692cc86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.696ex; height:2.176ex;" alt="{\displaystyle W>0}"></span> — práca bola sústavou spotrebovaná (resp. jej bola dodaná)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e97fbbbe4c17fd7173a57ad232a2ae4d6854f9df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.696ex; height:2.176ex;" alt="{\displaystyle W<0}"></span> — prácu vykonala sústava</li></ul> <div class="mw-heading mw-heading3"><h3 id="Aplikácia_na_dej_izochorický"><span id="Aplik.C3.A1cia_na_dej_izochorick.C3.BD"></span>Aplikácia na dej izochorický</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=2" title="Upraviť sekciu: Aplikácia na dej izochorický" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=2" title="Editovat zdrojový kód sekce Aplikácia na dej izochorický"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri <a href="/wiki/Izochorick%C3%BD_dej" title="Izochorický dej">izochorickom deji</a> platí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta V=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>V</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta V=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7c23b915a91fcc90db716bc3af4c030a238333" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.984ex; height:2.176ex;" alt="{\displaystyle \Delta V=0}"></span>, a preto je objemová práca <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> vykonaná sústavou nulová. Prvý termodynamický zákon nadobúda tvar: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=Q\,\!.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q\,\!.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/257b9d6149d8d160b558a714ce6b347366348ed3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.302ex; height:2.509ex;" alt="{\displaystyle \Delta U=Q\,\!.}"></span></dd></dl> <p>Zmena vnútornej energie sústavy pri izochorickom deji je teda rovná vymenemému <a href="/wiki/Teplo" title="Teplo">teplu</a>. Toto teplo môžeme vztiahnuť na teplotnú zmenu sústavy resp. na jej hmotnosť. Získame tak izochorickú <a href="/wiki/Tepeln%C3%A1_kapacita" title="Tepelná kapacita">mernú tepelnú kapacitu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1a91d7cc559f30152df6280cc1c68884296e914" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.89ex; height:2.009ex;" alt="{\displaystyle c_{V}\,\!}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{V}={\frac {Q}{\Delta T\cdot m}}={\frac {\Delta U}{\Delta T\cdot m}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mrow> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>⋅</mo> <mi>m</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>⋅</mo> <mi>m</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{V}={\frac {Q}{\Delta T\cdot m}}={\frac {\Delta U}{\Delta T\cdot m}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a079a4deaee271d40248c0b9ce4d74c963b86b91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:25.342ex; height:5.509ex;" alt="{\displaystyle c_{V}={\frac {Q}{\Delta T\cdot m}}={\frac {\Delta U}{\Delta T\cdot m}}\,\!}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Aplikácia_na_dej_izobarický"><span id="Aplik.C3.A1cia_na_dej_izobarick.C3.BD"></span>Aplikácia na dej izobarický</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=3" title="Upraviť sekciu: Aplikácia na dej izobarický" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=3" title="Editovat zdrojový kód sekce Aplikácia na dej izobarický"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri <a href="/wiki/Izobarick%C3%BD_dej" title="Izobarický dej">izobarickom deji</a> platí <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=const.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=const.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfdaffd26969be004d725c5919eb1223e5b17672" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:10.463ex; height:2.343ex;" alt="{\displaystyle p=const.}"></span> Aby bola táto podmienka splnená aj pri výmene tepla, musí sústava konať objemovú prácu. Preto platí prvý termodynamický zákon v nezmenenej podobe </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=Q+W\,\!.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>W</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=Q+W\,\!.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da5e7479cb07595080e94cce5693f7ae69c03945" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.578ex; height:2.509ex;" alt="{\displaystyle \Delta U=Q+W\,\!.}"></span></dd></dl> <figure typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Izobara.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Izobara.png/250px-Izobara.png" decoding="async" width="250" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/72/Izobara.png 1.5x" data-file-width="352" data-file-height="308" /></a><figcaption>Znázornenie objemovej práce pri deji izobarickom v p V diagrame.</figcaption></figure> <p>Pre objemovú prácu vykonanú pri <a href="/wiki/Izobarick%C3%BD_dej" title="Izobarický dej">izobarickom deji</a> platí: </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 W=-p\Delta V\,\!.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <mo>−</mo> <mi>p</mi> <mi mathvariant="normal">Δ</mi> <mi>V</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=-p\Delta V\,\!.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9978e00a547f6861bfe04b4d155ee1e702386261" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.881ex; height:2.509ex;" alt="{\displaystyle W=-p\Delta V\,\!.}"></span></dd></dl> <p>Ak si z prvého zákona termodynamiky pre dej izobarický odvodíme <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> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </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/246b4c45ef0ccbcfa3704d5abf071a94ce6bf619" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.225ex; height:2.509ex;" alt="{\displaystyle Q\,\!}"></span>: </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 Q=\Delta U-W=\Delta U+p\Delta V\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>−</mo> <mi>W</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi mathvariant="normal">Δ</mi> <mi>V</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\Delta U-W=\Delta U+p\Delta V\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fc45644d9d188668c62b08012d4aaa26e4747de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:28.868ex; height:2.509ex;" alt="{\displaystyle Q=\Delta U-W=\Delta U+p\Delta V\,\!}"></span></dd></dl> <p>získame vzorec pre výpočet izobaricky vymeneného tepla, ktoré nazývame zmena entalpie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta H\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd187bcc9001bf6ef6d70c07e94b5a0b6fd2b12d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:4.387ex; height:2.176ex;" alt="{\displaystyle \Delta H\,\!}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta H=\Delta U+p\Delta V\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi mathvariant="normal">Δ</mi> <mi>V</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H=\Delta U+p\Delta V\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d377ecb7d2c766502d7608aa05f72a5d77ca87c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:18.936ex; height:2.509ex;" alt="{\displaystyle \Delta H=\Delta U+p\Delta V\,\!}"></span></dd></dl> <p>Aj zmenu <a href="/wiki/Entalpia" title="Entalpia">entalpie</a> pri izobarickom deji môžeme vztiahnuť na zmenu teploty sústavy resp. jej <a href="/wiki/Hmotnos%C5%A5" title="Hmotnosť">hmotnosť</a>, získame tak izobarickú <a href="/wiki/Tepeln%C3%A1_kapacita" title="Tepelná kapacita">mernú tepelnú kapacitu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cea0ffcf977626c0c0ff911b3cc3c63175aa718f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:2.453ex; height:2.343ex;" alt="{\displaystyle c_{p}\,\!}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}={\frac {\Delta U+p\Delta V}{\Delta T\cdot m}}={\frac {\Delta H}{\Delta T\cdot m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>⋅</mo> <mi>m</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>⋅</mo> <mi>m</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{p}={\frac {\Delta U+p\Delta V}{\Delta T\cdot m}}={\frac {\Delta H}{\Delta T\cdot m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707062c28781c9d8e5748f8af0fb4ad071373828" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:28.678ex; height:5.509ex;" alt="{\displaystyle c_{p}={\frac {\Delta U+p\Delta V}{\Delta T\cdot m}}={\frac {\Delta H}{\Delta T\cdot m}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Aplikácia_na_dej_izotermický"><span id="Aplik.C3.A1cia_na_dej_izotermick.C3.BD"></span>Aplikácia na dej izotermický</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=4" title="Upraviť sekciu: Aplikácia na dej izotermický" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=4" title="Editovat zdrojový kód sekce Aplikácia na dej izotermický"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri <a href="/wiki/Izotermick%C3%BD_dej" title="Izotermický dej">izotermickom deji</a> platí <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=const.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=const.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35b9b314a168c7e9d016314201ae84fcaa46662d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.841ex; height:2.176ex;" alt="{\displaystyle T=const.}"></span> a preto nemôže dochádzať ku zmene vnútornej 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 \Delta U=0\qquad (T={\mbox{const.}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mn>0</mn> <mspace width="2em" /> <mo stretchy="false">(</mo> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>const.</mtext> </mstyle> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=0\qquad (T={\mbox{const.}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8637d096668200e3c91e3d3965cb4bf66c5a75c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.124ex; height:2.843ex;" alt="{\displaystyle \Delta U=0\qquad (T={\mbox{const.}})}"></span></dd></dl> <figure typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Izoterma.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Izoterma.png/250px-Izoterma.png" decoding="async" width="250" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Izoterma.png/375px-Izoterma.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Izoterma.png/500px-Izoterma.png 2x" data-file-width="992" data-file-height="959" /></a><figcaption>Znázornenie objemovej práce pri deji izotermickom v p V diagrame.</figcaption></figure> <p>Aj napriek tomu, že pri izotermickom deji nedochádza ku zmene vnútornej energie, dochádza ku výmene energie vo forme tepla aj práce. Aby bolo splnené <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=0\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=0\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78d627b3fa4e711542cca1079d5966fe017cc66f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:8.366ex; height:2.176ex;" alt="{\displaystyle \Delta U=0\,\!}"></span>, musí platiť: </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 Q+W=0\quad \Rightarrow \quad Q=-W\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>+</mo> <mi>W</mi> <mo>=</mo> <mn>0</mn> <mspace width="1em" /> <mo stretchy="false">⇒</mo> <mspace width="1em" /> <mi>Q</mi> <mo>=</mo> <mo>−</mo> <mi>W</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q+W=0\quad \Rightarrow \quad Q=-W\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82141d645887b8f80ccf9a9e1f604bb5576f1fc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:29.201ex; height:2.509ex;" alt="{\displaystyle Q+W=0\quad \Rightarrow \quad Q=-W\,\!}"></span></dd></dl> <p>Objemovú prácu vykonanú pri izotermickom deji vypočítame zo vzorca: </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 W=-nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=-nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <mo>−</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=-nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=-nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68e82a746cac83d9f62126642348e39211281663" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.155ex; height:5.676ex;" alt="{\displaystyle W=-nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=-nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}"></span></dd></dl> <p>Zo vzorca <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=-W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mo>−</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=-W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b2a1601b1524ccdedbfa3372e12899a9a91f87c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.18ex; height:2.509ex;" alt="{\displaystyle Q=-W}"></span> vidíme, že rovnaký vzorec môžeme použiť aj na výpočet vymeneného tepla, len obrátime znamienko: </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 Q=+nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=+nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mo>+</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>+</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=+nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=+nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c2e9f4fa5f0ec23ef7ffc8cca6785b4a1c99be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:35.558ex; height:5.676ex;" alt="{\displaystyle Q=+nRT\cdot \ln {\frac {V_{2}}{V_{1}}}=+nRT\cdot \ln {\frac {p_{1}}{p_{2}}}}"></span></dd></dl> <p>(Výber znamienok je konvenciou.) </p> <div class="mw-heading mw-heading3"><h3 id="Aplikácia_na_dej_adiabatický"><span id="Aplik.C3.A1cia_na_dej_adiabatick.C3.BD"></span>Aplikácia na dej adiabatický</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=5" title="Upraviť sekciu: Aplikácia na dej adiabatický" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=5" title="Editovat zdrojový kód sekce Aplikácia na dej adiabatický"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri <a href="/wiki/Adiabatick%C3%BD_dej" title="Adiabatický dej">adiabatickom deji</a> je sústava dokonale tepelne izolovaná od okolia, platí teda <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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf8c7e37f5856132138ba0dfa88493c21c9b3171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.099ex; height:2.509ex;" alt="{\displaystyle Q=0}"></span>. Pre adiabatický dej platí prvý zákon termodynamický v tvare: </p> <figure typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:AdiabataW.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/AdiabataW.png/250px-AdiabataW.png" decoding="async" width="250" height="216" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/9f/AdiabataW.png 1.5x" data-file-width="352" data-file-height="304" /></a><figcaption>Znázornenie objemovej práce pri deji adiabatickom v p V diagrame.</figcaption></figure> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta U=W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta U=W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69ac1bc6b881415be7241275dfd2314ae474e541" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.252ex; height:2.176ex;" alt="{\displaystyle \Delta U=W}"></span></dd></dl> <p>Takto vykonanú resp. dodanú prácu vnímame ako zmenu teploty sústavy, a preto pre prácu platí: </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 W=\Delta U=nc_{V}\Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>U</mi> <mo>=</mo> <mi>n</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=\Delta U=nc_{V}\Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a67faee342aa57fde1c28d7396d0e202e9296bd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.82ex; height:2.509ex;" alt="{\displaystyle W=\Delta U=nc_{V}\Delta T}"></span></dd></dl> <p>(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> — počet molov plynu) Deje v adiabatických sústavách najlepšie popisuje <a href="/wiki/Poissonov_z%C3%A1kon" class="mw-disambig" title="Poissonov zákon">Poissonov zákon</a>. Za povšimnutie stojí, že krivka adiabaty sa veľmi podobá krivke izotermy, ale je výrazne prudšia. </p> <div class="mw-heading mw-heading2"><h2 id="Pozri_aj">Pozri aj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&veaction=edit&section=6" title="Upraviť sekciu: Pozri aj" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prv%C3%A1_termodynamick%C3%A1_veta&action=edit&section=6" title="Editovat zdrojový kód sekce Pozri aj"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="border: solid #aaa 1px; background: #f9f9f9; padding: 0ex 1ex; font-size: 90%;" class="tright" title="Portály, ktorých súčasťou je táto stránka"> <table style="margin: 0; padding: 0ex"> <tbody><tr> <td style="vertical-align:middle;margin: 0;"><span class="noviewer" typeof="mw:File"><a href="/wiki/S%C3%BAbor:Portal.svg" class="mw-file-description" title="Portal"><img alt="Portal" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/36px-Portal.svg.png" decoding="async" width="36" height="32" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/54px-Portal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/72px-Portal.svg.png 2x" data-file-width="36" data-file-height="32" /></a></span> </td> <td style="text-align:left;font-style:italic; font-weight:bold;"><a href="/wiki/Port%C3%A1l:Fyzika" title="Portál:Fyzika">Fyzikálny portál</a><br /><a href="/wiki/Port%C3%A1l:Ch%C3%A9mia" title="Portál:Chémia">Chemický portál</a> </td></tr></tbody></table></div> <ul><li><a href="/wiki/Nult%C3%A1_termodynamick%C3%A1_veta" title="Nultá termodynamická veta">Nultá termodynamická veta</a></li> <li><a href="/wiki/Druh%C3%A1_termodynamick%C3%A1_veta" title="Druhá termodynamická veta">Druhá termodynamická veta</a></li> <li><a href="/wiki/Tretia_termodynamick%C3%A1_veta" title="Tretia termodynamická veta">Tretia termodynamická veta</a></li></ul>    </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="">Zdroj: „<a dir="ltr" href="https://sk.wikipedia.org/w/index.php?title=Prvá_termodynamická_veta&oldid=6729736">https://sk.wikipedia.org/w/index.php?title=Prvá_termodynamická_veta&oldid=6729736</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C5%A0peci%C3%A1lne:Kateg%C3%B3rie" title="Špeciálne:Kategórie">Kategórie</a>: <ul><li><a href="/wiki/Kateg%C3%B3ria:Termodynamika" title="Kategória:Termodynamika">Termodynamika</a></li><li><a href="/wiki/Kateg%C3%B3ria:Fyzik%C3%A1lne_z%C3%A1kony" title="Kategória:Fyzikálne zákony">Fyzikálne zákony</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skryté kategórie: <ul><li><a href="/wiki/Kateg%C3%B3ria:Port%C3%A1l:Fyzika/Zapojen%C3%A9_%C4%8Dl%C3%A1nky" title="Kategória:Portál:Fyzika/Zapojené články">Portál:Fyzika/Zapojené články</a></li><li><a href="/wiki/Kateg%C3%B3ria:Port%C3%A1l:Ch%C3%A9mia/Zapojen%C3%A9_%C4%8Dl%C3%A1nky" title="Kategória:Portál:Chémia/Zapojené články">Portál:Chémia/Zapojené články</a></li><li><a href="/wiki/Kateg%C3%B3ria:Wikip%C3%A9dia:%C4%8Cl%C3%A1nky_priamo_volaj%C3%BAce_%C5%A1abl%C3%B3nu_Port%C3%A1l" title="Kategória:Wikipédia:Články priamo volajúce šablónu Portál">Wikipédia:Články priamo volajúce šablónu Portál</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"> Dátum a čas poslednej úpravy tejto stránky: 28. september 2018, 16:25.</li> <li id="footer-info-copyright">Text je dostupný za podmienok <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike License 4.0 Unported</a>; prípadne za ďalších podmienok. 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