{"id":39903,"date":"2024-09-06T11:35:17","date_gmt":"2024-09-06T09:35:17","guid":{"rendered":"https:\/\/obera.fr\/non-classifiee\/co-je-vratna-adiabaticka-premena\/"},"modified":"2025-04-15T09:43:01","modified_gmt":"2025-04-15T07:43:01","slug":"transformation-adiabatique-reversible","status":"publish","type":"post","link":"https:\/\/obera.fr\/cs\/nase-rady\/transformation-adiabatique-reversible\/","title":{"rendered":"Co je vratn\u00e1 adiabatick\u00e1 p\u0159em\u011bna?"},"content":{"rendered":"\n<p><strong>Vratn\u00e1 adiabatick\u00e1<\/strong> <strong>p\u0159em\u011bna<\/strong> je idealizovan\u00fd termodynamick\u00fd proces, kter\u00fd hraje \u00fast\u0159edn\u00ed roli p\u0159i anal\u00fdze energetick\u00fdch syst\u00e9m\u016f. D\u00edky vylou\u010den\u00ed jak\u00e9hokoli p\u0159enosu tepla s vn\u011bj\u0161\u00edm sv\u011btem se tato p\u0159em\u011bna \u0159\u00edd\u00ed v\u00fdhradn\u011b termodynamick\u00fdmi z\u00e1kony a stavov\u00fdmi rovnicemi. Zvl\u00e1\u0161t\u011b dob\u0159e je pops\u00e1na a aplikov\u00e1na v p\u0159\u00edpad\u011b dokonal\u00fdch plyn\u016f. Jak\u00e9 jsou charakteristick\u00e9 rysy t\u00e9to adiabatick\u00e9 p\u0159em\u011bny? Jak\u00e9 matematick\u00e9 rovnice definuj\u00ed jej\u00ed chov\u00e1n\u00ed? A jak\u00e9 jsou praktick\u00e9 aplikace <strong>adiabatick\u00e9 zvratnosti <\/strong>v tepeln\u00fdch a motorov\u00fdch syst\u00e9mech?     <\/p>\n\n<h2 class=\"wp-block-heading\">Definice a z\u00e1kladn\u00ed principy<\/h2>\n\n<figure class=\"wp-block-image alignright size-full is-resized\"><img decoding=\"async\" width=\"760\" height=\"647\" src=\"https:\/\/obera.fr\/wp-content\/uploads\/2024\/09\/thermodynamique.png\" alt=\"Teplom&#x11B;r s jednou &#x161;ipkou nahoru a druhou dol&#x16F;\" class=\"wp-image-33976\" style=\"width:329px;height:auto\" srcset=\"https:\/\/obera.fr\/wp-content\/uploads\/2024\/09\/thermodynamique.png 760w, https:\/\/obera.fr\/wp-content\/uploads\/2024\/09\/thermodynamique-300x255.png 300w\" sizes=\"(max-width: 760px) 100vw, 760px\" \/><\/figure>\n\n<h3 class=\"wp-block-heading\">Co je to adiabatick\u00e1 transformace?  <\/h3>\n\n<h4 class=\"wp-block-heading\">Definice  <\/h4>\n\n<p><strong>Adiabatick\u00e1 p\u0159em\u011bna <\/strong>je termodynamick\u00fd proces, p\u0159i kter\u00e9m nedoch\u00e1z\u00ed k v\u00fdm\u011bn\u011b tepla s okol\u00edm, tj. Q=0, kde Q p\u0159edstavuje mno\u017estv\u00ed tepla vym\u011bn\u011bn\u00e9ho s okol\u00edm. V d\u016fsledku toho se rovnice v prvn\u00edm principu termodynamiky zjednodu\u0161uje a lze ji vyj\u00e1d\u0159it jako U= W, kde U je zm\u011bna vnit\u0159n\u00ed energie a W je pr\u00e1ce vykonan\u00e1 p\u0159i <a href=\"https:\/\/obera.fr\/cs\/nase-rada\/adiabaticke-chladice-vzduchu-provoz-a-vyhody\/\">adiabatick\u00e9 p\u0159em\u011bn\u011b<\/a>. <\/p>\n\n<h4 class=\"wp-block-heading\">Charakteristiky adiabatick\u00e9 transformace<\/h4>\n\n<p>Vnit\u0159n\u00ed energie syst\u00e9mu se m\u011bn\u00ed pouze v z\u00e1vislosti na pr\u00e1ci vykonan\u00e9 na syst\u00e9mu nebo syst\u00e9mem, bez v\u00fdm\u011bny tepla s okoln\u00edm sv\u011btem.  <\/p>\n\n<p><strong> Adiabatick\u00e1 p\u0159em\u011bna m\u016f\u017ee b\u00fdt vratn\u00e1,<\/strong> pokud proces prob\u00edh\u00e1 ide\u00e1ln\u00edm zp\u016fsobem bez disipace energie, nebo nevratn\u00e1, pokud jsou p\u0159\u00edtomny jevy jako t\u0159en\u00ed, turbulence nebo jin\u00e9 formy disipace.<\/p>\n\n<h3 class=\"wp-block-heading\">Co je vratn\u00e1 adiabatick\u00e1 p\u0159em\u011bna?<\/h3>\n\n<h4 class=\"wp-block-heading\">Definice<\/h4>\n\n<p><strong>Vratn\u00e1 adiabatick\u00e1 p\u0159em\u011bna <\/strong>je termodynamick\u00fd proces, p\u0159i kter\u00e9m se syst\u00e9m vyv\u00edj\u00ed bez v\u00fdm\u011bny tepla s okol\u00edm (adiabaticky) a p\u0159i kter\u00e9m je ka\u017ed\u00e1 f\u00e1ze procesu dokonale vratn\u00e1. Jin\u00fdmi slovy, syst\u00e9m se m\u016f\u017ee vr\u00e1tit do v\u00fdchoz\u00edho stavu, ani\u017e by zanechal trval\u00e9 zm\u011bny v syst\u00e9mu samotn\u00e9m nebo v jeho prost\u0159ed\u00ed. To znamen\u00e1, \u017ee pokud se proces obr\u00e1t\u00ed, syst\u00e9m a jeho prost\u0159ed\u00ed se vr\u00e1t\u00ed p\u0159esn\u011b do sv\u00fdch p\u0159edchoz\u00edch stav\u016f, ani\u017e by do\u0161lo k rozpt\u00fdlen\u00ed energie nebo nevratn\u00fdm zm\u011bn\u00e1m.  <\/p>\n\n<h4 class=\"wp-block-heading\">Charakteristiky vratn\u00e9 adiabatick\u00e9 p\u0159em\u011bny<\/h4>\n\n<p>Z\u00e1kon zachov\u00e1n\u00ed energie: vnit\u0159n\u00ed energie syst\u00e9mu se m\u011bn\u00ed v\u00fdhradn\u011b v z\u00e1vislosti na pr\u00e1ci vykonan\u00e9 na syst\u00e9mu nebo syst\u00e9mem, bez v\u00fdm\u011bny tepla s vn\u011bj\u0161\u00edm sv\u011btem.<\/p>\n\n<ul class=\"wp-block-list\">\n<li><strong>Kvazistatick\u00fd proces<\/strong>: transformace prob\u00edh\u00e1 pomalu, tak\u017ee syst\u00e9m proch\u00e1z\u00ed \u0159adou po sob\u011b jdouc\u00edch rovnov\u00e1\u017en\u00fdch stav\u016f. Jedn\u00e1 se sp\u00ed\u0161e o sled nekone\u010dn\u011b mal\u00fdch operac\u00ed ne\u017e o n\u00e1hlou, prudkou transformaci.   <\/li>\n\n\n\n<li><strong>Termodynamick\u00e1 rovnov\u00e1ha<\/strong>: syst\u00e9m z\u016fst\u00e1v\u00e1 v pr\u016fb\u011bhu cel\u00e9ho procesu v termodynamick\u00e9 rovnov\u00e1ze. Mezi intenzivn\u00edmi veli\u010dinami, jako je tlak a teplota, existuje spojitost, kter\u00e1 zaji\u0161\u0165uje, \u017ee syst\u00e9m je v pr\u016fb\u011bhu p\u0159em\u011bny ve vnit\u0159n\u00ed a vn\u011bj\u0161\u00ed rovnov\u00e1ze. <\/li>\n\n\n\n<li><strong>Izentropick\u00e1 transformace<\/strong>: vzhledem k jej\u00ed vratn\u00e9 povaze a absenci disipativn\u00edch jev\u016f se o procesu \u0159\u00edk\u00e1, \u017ee je izentropick\u00fd. To znamen\u00e1, \u017ee nevznik\u00e1 \u017e\u00e1dn\u00e1 entropie a celkov\u00e1 entropie celku z\u016fst\u00e1v\u00e1 b\u011bhem p\u0159em\u011bny nezm\u011bn\u011bna, tedy S=0. <\/li>\n<\/ul>\n\n<h2 class=\"wp-block-heading\">P\u0159\u00edslu\u0161n\u00e9 rovnice pro vratnou adiabatickou transformaci<\/h2>\n\n<h3 class=\"wp-block-heading\">Obecn\u00e9 vztahy<\/h3>\n\n<p>Pro <strong>vratnou adiabatickou transformaci<\/strong>:<\/p>\n\n<p>Nedoch\u00e1z\u00ed k p\u0159enosu tepla: dQ=0<\/p>\n\n<p>Zm\u011bna entropie je nulov\u00e1: dS=0<\/p>\n\n<p>Rovnice prvn\u00edho termodynamick\u00e9ho z\u00e1kona pro vratnou <a href=\"https:\/\/obera.fr\/cs\/nase-rady\/comprendre-systeme-adiabatique-fonctionnement-applications\/\">adiabatickou<\/a> p\u0159em\u011bnu je: dU = -PdV<\/p>\n\n<p>  s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>U je vnit\u0159n\u00ed energie ;<\/li>\n\n\n\n<li>P je tlak ;<\/li>\n\n\n\n<li>Q p\u0159edstavuje vym\u011bn\u011bn\u00e9 teplo ;<\/li>\n\n\n\n<li>S je entropie ;<\/li>\n\n\n\n<li>V je objem.<\/li>\n<\/ul>\n\n<h3 class=\"wp-block-heading\">Dokonal\u00e9 plyny<\/h3>\n\n<p>Pro dokonal\u00fd plyn, kter\u00fd proch\u00e1z\u00ed <strong>vratnou adiabatickou p\u0159em\u011bnou<\/strong>, je zm\u011bna vnit\u0159n\u00ed energie vyj\u00e1d\u0159ena takto: dU = Cv dT<\/p>\n\n<p>s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Cv je tepeln\u00e1 kapacita p\u0159i konstantn\u00edm objemu ;<\/li>\n\n\n\n<li>dT je zm\u011bna teploty.<\/li>\n<\/ul>\n\n<p>Prvn\u00ed termodynamick\u00fd z\u00e1kon se tedy st\u00e1v\u00e1 : Cv dT = -P dV<\/p>\n\n<h3 class=\"wp-block-heading\">Laplaceovy rovnice<\/h3>\n\n<p>Laplaceovy rovnice se t\u00fdkaj\u00ed tlaku, objemu a teploty dokonal\u00e9ho plynu p\u0159i <strong>vratn\u00e9 adiabatick\u00e9 p\u0159em\u011bn\u011b. <\/strong>Vyjad\u0159uj\u00ed se takto:<\/p>\n\n<p class=\"has-text-align-center\">PV = konstantn\u00ed<\/p>\n\n<p class=\"has-text-align-center\">TV-1 = konstantn\u00ed<\/p>\n\n<p class=\"has-text-align-center\">TP(1-\/) = konstanta<\/p>\n\n<p>S (gama, naz\u00fdvan\u00fdm tak\u00e9 adiabatick\u00fd index nebo Laplace\u016fv koeficient), co\u017e je pom\u011br tepeln\u00fdch kapacit, definovan\u00fd jako = CpCv.<\/p>\n\n<p>s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Cv je tepeln\u00e1 kapacita p\u0159i konstantn\u00edm objemu ;<\/li>\n\n\n\n<li>Cp je tepeln\u00e1 kapacita p\u0159i konstantn\u00edm tlaku.<\/li>\n<\/ul>\n\n<h3 class=\"wp-block-heading\">Vyj\u00e1d\u0159en\u00ed pr\u00e1ce za <strong>vratn\u00fdch adiabatick\u00fdch<\/strong> podm\u00ednek<\/h3>\n\n<p>Kdy\u017e se plyn rozp\u00edn\u00e1, tj. kdy\u017e se zv\u011bt\u0161uje jeho objem (Vf&gt;Vi), kon\u00e1 pr\u00e1ci navenek. V tomto p\u0159\u00edpad\u011b se pr\u00e1ce pova\u017euje za kladnou, proto\u017ee plyn &#8222;odevzd\u00e1v\u00e1&#8220; energii sv\u00e9mu okol\u00ed. V\u00fdraz pro pr\u00e1ci vykonanou plynem p\u0159i t\u00e9to expanzi je d\u00e1n vztahem :  <\/p>\n\n<p class=\"has-text-align-center\">W= PiVi-PfVf-1<\/p>\n\n<p>kde :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Pi a Vi jsou po\u010d\u00e1te\u010dn\u00ed tlak a objem;<\/li>\n\n\n\n<li>Pf a Vf jsou kone\u010dn\u00fd tlak a objem.<\/li>\n<\/ul>\n\n<p>Naopak p\u0159i stla\u010den\u00ed plynu (jeho objem se zmen\u0161\u00ed, Vf<vi un=\"\" travail=\"\" est=\"\" effectu=\"\" sur=\"\" le=\"\" gaz=\"\" par=\"\" l=\"\" toujours=\"\" consid=\"\" comme=\"\" positif=\"\" dans=\"\" ce=\"\" cas=\"\" car=\"\" de=\"\" au=\"\" pour=\"\" comprimer.=\"\" du=\"\" devient=\"\" :=\"\"><\/vi><\/p>\n\n<p class=\"has-text-align-center\">W= PfVf-PiVi-1<\/p>\n\n<h2 class=\"wp-block-heading\">P\u0159\u00edklady aplikac\u00ed  <\/h2>\n\n<p>Rovnice <strong>vratn\u00e9 adiabatick\u00e9 transformace <\/strong>jsou v\u0161udyp\u0159\u00edtomn\u00e9 v oborech, jako je energetika, mechanika plyn\u016f a in\u017een\u00fdrstv\u00ed, a tak\u00e9 v atmosf\u00e9rick\u00fdch a astrofyzik\u00e1ln\u00edch v\u011bd\u00e1ch. V t\u011bchto oborech hraj\u00ed kl\u00ed\u010dovou roli, zejm\u00e9na v termodynamick\u00fdch syst\u00e9mech, kde je c\u00edlem optimalizovat v\u00fdm\u011bnu energie. Tyto transformace, kter\u00e9 se pou\u017e\u00edvaj\u00ed k modelov\u00e1n\u00ed a anal\u00fdze expanze nebo komprese plyn\u016f bez v\u00fdm\u011bny tepla s okol\u00edm, maj\u00ed z\u00e1sadn\u00ed v\u00fdznam pro pochopen\u00ed a optimalizaci mnoha syst\u00e9m\u016f. Zde je n\u011bkolik p\u0159\u00edklad\u016f praktick\u00fdch aplikac\u00ed, kde jsou <strong>vratn\u00e9 adiabatick\u00e9 p\u0159em\u011bny <\/strong>z\u00e1sadn\u00ed:   <\/p>\n\n<h3 class=\"wp-block-heading\">Termodynamick\u00e9 cykly  <\/h3>\n\n<p>Carnot\u016fv cyklus, teoretick\u00fd model tepeln\u00fdch motor\u016f, zahrnuje <strong>reverzibiln\u00ed adiabatick\u00e9 f\u00e1ze, kter\u00e9<\/strong> maximalizuj\u00ed \u00fa\u010dinnost. Tento ide\u00e1ln\u00ed cyklus se skl\u00e1d\u00e1 ze dvou <strong>vratn\u00fdch adiabatick\u00fdch proces\u016f <\/strong>(expanze a komprese) a dvou izotermick\u00fdch proces\u016f (p\u0159i konstantn\u00ed teplot\u011b). <\/p>\n\n<h3 class=\"wp-block-heading\">Kompresory a turb\u00edny<\/h3>\n\n<p>V kompresorech a plynov\u00fdch turb\u00edn\u00e1ch se komprese a expanze plynu \u010dasto modeluj\u00ed jako <strong>vratn\u00e9 adiabatick\u00e9 procesy<\/strong>. T\u00edm se maximalizuje \u00fa\u010dinnost minimalizac\u00ed energetick\u00fdch ztr\u00e1t ve form\u011b tepla. <\/p>\n\n<h3 class=\"wp-block-heading\">Chladni\u010dky a tepeln\u00e1 \u010derpadla<\/h3>\n\n<p>Chladic\u00ed cykly a tepeln\u00e1 \u010derpadla vyu\u017e\u00edvaj\u00ed <strong>vratn\u00e9 adiabatick\u00e9 p\u0159em\u011bny<\/strong> ve f\u00e1z\u00edch komprese a expanze chladic\u00ed kapaliny. Tyto procesy umo\u017e\u0148uj\u00ed efektivn\u00ed p\u0159enos tepeln\u00e9 energie z jednoho m\u00edsta na druh\u00e9, \u010d\u00edm\u017e se optimalizuje energetick\u00e1 \u00fa\u010dinnost syst\u00e9mu. <\/p>\n\n<h3 class=\"wp-block-heading\">Anal\u00fdza pr\u016fmyslov\u00fdch proces\u016f<\/h3>\n\n<p>In\u017een\u00fd\u0159i pou\u017e\u00edvaj\u00ed <a href=\"https:\/\/obera.fr\/cs\/nase-rady\/rafraichisseur-adiabatique-industriel-guide-complet\/\">adiabatickou reverzibilitu<\/a><strong> <\/strong>analyzovat a navrhovat r\u016fzn\u00e9 pr\u016fmyslov\u00e9 procesy, jako je separace plyn\u016f a \u00faprava kapalin. Tyto modely lze pou\u017e\u00edt k optimalizaci v\u00fdkonu a sn\u00ed\u017een\u00ed n\u00e1klad\u016f na energii. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vratn\u00e1 adiabatick\u00e1 p\u0159em\u011bna je idealizovan\u00fd termodynamick\u00fd proces, kter\u00fd hraje \u00fast\u0159edn\u00ed roli p\u0159i anal\u00fdze energetick\u00fdch syst\u00e9m\u016f. D\u00edky vylou\u010den\u00ed jak\u00e9hokoli p\u0159enosu tepla s vn\u011bj\u0161\u00edm sv\u011btem se tato p\u0159em\u011bna \u0159\u00edd\u00ed v\u00fdhradn\u011b termodynamick\u00fdmi z\u00e1kony a stavov\u00fdmi rovnicemi. <\/p>\n","protected":false},"author":4,"featured_media":81214,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_seopress_robots_primary_cat":"none","_seopress_titles_title":"Vratn\u00e1 adiabatick\u00e1 transformace","_seopress_titles_desc":"Vratn\u00e1 adiabatick\u00e1 p\u0159em\u011bna je idealizovan\u00fd termodynamick\u00fd proces, kter\u00fd hraje \u00fast\u0159edn\u00ed roli p\u0159i anal\u00fdze energetick\u00fdch syst\u00e9m\u016f.","_seopress_robots_index":"","footnotes":""},"categories":[310],"tags":[113],"class_list":["post-39903","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nase-rady","tag-entete-male","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50","no-featured-image-padding","resize-featured-image"],"acf":[],"_links":{"self":[{"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/posts\/39903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/comments?post=39903"}],"version-history":[{"count":3,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/posts\/39903\/revisions"}],"predecessor-version":[{"id":81439,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/posts\/39903\/revisions\/81439"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/media\/81214"}],"wp:attachment":[{"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/media?parent=39903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/categories?post=39903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/obera.fr\/cs\/wp-json\/wp\/v2\/tags?post=39903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}