{"id":39874,"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":"2025-04-15T09:41:01","modified_gmt":"2025-04-15T07:41:01","slug":"transformation-adiabatique-reversible","status":"publish","type":"post","link":"https:\/\/obera.fr\/sk\/nasa-rada\/transformation-adiabatique-reversible\/","title":{"rendered":"\u010co je vratn\u00e1 adiabatick\u00e1 premena?"},"content":{"rendered":"\n<p><strong>Vratn\u00e1 adiabatick\u00e1<\/strong> <strong>premena<\/strong> je idealizovan\u00fd termodynamick\u00fd proces, ktor\u00fd zohr\u00e1va \u00fastredn\u00fa \u00falohu pri anal\u00fdze energetick\u00fdch syst\u00e9mov. V\u010faka vyl\u00fa\u010deniu ak\u00e9hoko\u013evek prenosu tepla s vonkaj\u0161\u00edm svetom sa t\u00e1to premena riadi v\u00fdlu\u010dne z\u00e1konmi termodynamiky a stavov\u00fdmi rovnicami. Je obzvl\u00e1\u0161\u0165 dobre op\u00edsan\u00e1 a aplikovan\u00e1 v pr\u00edpade dokonal\u00fdch plynov. Ak\u00e9 s\u00fa charakteristick\u00e9 znaky tejto adiabatickej premeny? Ak\u00e9 matematick\u00e9 rovnice definuj\u00fa jej spr\u00e1vanie? A ak\u00e9 s\u00fa praktick\u00e9 aplik\u00e1cie <strong>adiabatickej reverzibility <\/strong>v tepeln\u00fdch a motorov\u00fdch syst\u00e9moch?     <\/p>\n\n<h2 class=\"wp-block-heading\">Defin\u00edcia a z\u00e1kladn\u00e9 z\u00e1sady<\/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=\"Teplomer s jednou &#x161;&#xED;pkou smerom nahor a druhou smerom nadol\" 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\">\u010co je to adiabatick\u00e1 transform\u00e1cia?  <\/h3>\n\n<h4 class=\"wp-block-heading\">Defin\u00edcia  <\/h4>\n\n<p><strong>Adiabatick\u00e1 premena <\/strong>je termodynamick\u00fd proces, pri ktorom nedoch\u00e1dza k v\u00fdmene tepla s okol\u00edm, t. j. Q=0, kde Q predstavuje mno\u017estvo tepla vymenen\u00e9ho s okol\u00edm. V d\u00f4sledku toho sa rovnica v prvom princ\u00edpe termodynamiky zjednodu\u0161uje a mo\u017eno ju vyjadri\u0165 ako U = W, kde U je zmena vn\u00fatornej energie a W je pr\u00e1ca vykonan\u00e1 po\u010das <a href=\"https:\/\/obera.fr\/sk\/nasa-rada\/adiabaticke-chladice-vzduchu-prevadzka-a-vyhody\/\">adiabatickej premeny<\/a>. <\/p>\n\n<h4 class=\"wp-block-heading\">Charakteristika adiabatickej transform\u00e1cie<\/h4>\n\n<p>Vn\u00fatorn\u00e1 energia syst\u00e9mu sa men\u00ed len v z\u00e1vislosti od pr\u00e1ce vykonanej na syst\u00e9me alebo syst\u00e9mom, bez v\u00fdmeny tepla s vonkaj\u0161\u00edm svetom.  <\/p>\n\n<p><strong> Adiabatick\u00e1 premena m\u00f4\u017ee by\u0165 vratn\u00e1,<\/strong> ke\u010f proces prebieha ide\u00e1lnym sp\u00f4sobom bez disip\u00e1cie energie, alebo nevratn\u00e1, ke\u010f s\u00fa pr\u00edtomn\u00e9 javy ako trenie, turbulencia alebo in\u00e9 formy disip\u00e1cie.<\/p>\n\n<h3 class=\"wp-block-heading\">\u010co je vratn\u00e1 adiabatick\u00e1 premena?<\/h3>\n\n<h4 class=\"wp-block-heading\">Defin\u00edcia<\/h4>\n\n<p><strong>Vratn\u00e1 adiabatick\u00e1 premena <\/strong>je termodynamick\u00fd proces, pri ktorom sa syst\u00e9m vyv\u00edja bez v\u00fdmeny tepla s okol\u00edm (adiabaticky) a pri ktorom je ka\u017ed\u00e1 f\u00e1za procesu dokonale vratn\u00e1. In\u00fdmi slovami, syst\u00e9m sa m\u00f4\u017ee vr\u00e1ti\u0165 do svojho po\u010diato\u010dn\u00e9ho stavu bez toho, aby zanechal trval\u00e9 zmeny v samotnom syst\u00e9me alebo v jeho prostred\u00ed. To znamen\u00e1, \u017ee ak sa proces zvr\u00e1ti, syst\u00e9m a jeho prostredie sa vr\u00e1tia presne do svojich predch\u00e1dzaj\u00facich stavov bez ak\u00e9hoko\u013evek rozptylu energie alebo nevratnej zmeny.  <\/p>\n\n<h4 class=\"wp-block-heading\">Charakteristika vratnej adiabatickej premeny<\/h4>\n\n<p>Z\u00e1kon zachovania energie: vn\u00fatorn\u00e1 energia syst\u00e9mu sa men\u00ed v\u00fdlu\u010dne ako funkcia pr\u00e1ce vykonanej na syst\u00e9me alebo syst\u00e9mom, bez v\u00fdmeny tepla s vonkaj\u0161\u00edm svetom.<\/p>\n\n<ul class=\"wp-block-list\">\n<li><strong>Kv\u00e1zi-statick\u00fd proces<\/strong>: transform\u00e1cia prebieha pomaly, \u010do umo\u017e\u0148uje, aby syst\u00e9m pre\u0161iel s\u00e9riou po sebe nasleduj\u00facich rovnov\u00e1\u017enych stavov. Je to sk\u00f4r postupnos\u0165 nekone\u010dne mal\u00fdch oper\u00e1ci\u00ed ako n\u00e1hla, prudk\u00e1 transform\u00e1cia.   <\/li>\n\n\n\n<li><strong>Termodynamick\u00e1 rovnov\u00e1ha<\/strong>: po\u010das cel\u00e9ho procesu zost\u00e1va syst\u00e9m v termodynamickej rovnov\u00e1he. Medzi intenz\u00edvnymi veli\u010dinami, ako je tlak a teplota, existuje spojitos\u0165, ktor\u00e1 zabezpe\u010duje, \u017ee syst\u00e9m je po\u010das celej premeny vo vn\u00fatornej a vonkaj\u0161ej rovnov\u00e1he. <\/li>\n\n\n\n<li><strong>Izentropick\u00e1 transform\u00e1cia<\/strong>: vzh\u013eadom na jej vratn\u00fd charakter a absenciu disipat\u00edvnych javov sa hovor\u00ed, \u017ee proces je izentropick\u00fd. Znamen\u00e1 to, \u017ee nevznik\u00e1 \u017eiadna entropia a celkov\u00e1 entropia celku zost\u00e1va po\u010das premeny nezmenen\u00e1, t. j. S=0. <\/li>\n<\/ul>\n\n<h2 class=\"wp-block-heading\">Pr\u00edslu\u0161n\u00e9 rovnice pre vratn\u00fa adiabatick\u00fa transform\u00e1ciu<\/h2>\n\n<h3 class=\"wp-block-heading\">V\u0161eobecn\u00e9 vz\u0165ahy<\/h3>\n\n<p>Pre <strong>vratn\u00fa adiabatick\u00fa transform\u00e1ciu<\/strong>:<\/p>\n\n<p>Nedoch\u00e1dza k prenosu tepla: dQ=0<\/p>\n\n<p>Zmena entropie je nulov\u00e1: dS=0<\/p>\n\n<p>Rovnica prv\u00e9ho termodynamick\u00e9ho z\u00e1kona pre vratn\u00fa <a href=\"https:\/\/obera.fr\/sk\/nasa-rada\/comprendre-systeme-adiabatique-fonctionnement-applications\/\">adiabatick\u00fa<\/a> premenu je: dU = -PdV<\/p>\n\n<p>  s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>U je vn\u00fatorn\u00e1 energia ;<\/li>\n\n\n\n<li>P je tlak ;<\/li>\n\n\n\n<li>Q predstavuje vymenen\u00e9 teplo;<\/li>\n\n\n\n<li>S je entropia ;<\/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>Pre dokonal\u00fd plyn, ktor\u00fd prech\u00e1dza <strong>vratnou adiabatickou premenou<\/strong>, sa zmena vn\u00fatornej energie vyjadruje ako: dU = Cv dT<\/p>\n\n<p>s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Cv je tepeln\u00e1 kapacita pri kon\u0161tantnom objeme ;<\/li>\n\n\n\n<li>dT je zmena teploty.<\/li>\n<\/ul>\n\n<p>Prv\u00fd z\u00e1kon termodynamiky sa preto st\u00e1va : Cv dT = -P dV<\/p>\n\n<h3 class=\"wp-block-heading\">Laplaceove rovnice<\/h3>\n\n<p>Laplaceove rovnice vyjadruj\u00fa tlak, objem a teplotu dokonal\u00e9ho plynu po\u010das <strong>vratnej adiabatickej premeny. <\/strong>S\u00fa vyjadren\u00e9 takto:<\/p>\n\n<p class=\"has-text-align-center\">PV = kon\u0161tantn\u00fd<\/p>\n\n<p class=\"has-text-align-center\">TV-1 = kon\u0161tantn\u00fd<\/p>\n\n<p class=\"has-text-align-center\">TP(1-\/) = kon\u0161tanta<\/p>\n\n<p>S (gama, naz\u00fdvan\u00fd aj adiabatick\u00fd index alebo Laplaceov koeficient), ktor\u00fd je pomerom tepeln\u00fdch kapac\u00edt, definovan\u00fdm ako = CpCv.<\/p>\n\n<p>s :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Cv je tepeln\u00e1 kapacita pri kon\u0161tantnom objeme ;<\/li>\n\n\n\n<li>Cp je tepeln\u00e1 kapacita pri kon\u0161tantnom tlaku.<\/li>\n<\/ul>\n\n<h3 class=\"wp-block-heading\">Vyjadrenie pr\u00e1ce v <strong>reverzibiln\u00fdch adiabatick\u00fdch<\/strong> podmienkach<\/h3>\n\n<p>Ke\u010f sa plyn rozp\u00edna, t. j. ke\u010f sa zv\u00e4\u010d\u0161\u00ed jeho objem (Vf&gt;Vi), vykon\u00e1 pr\u00e1cu navonok. V tomto pr\u00edpade sa pr\u00e1ca pova\u017euje za kladn\u00fa, preto\u017ee plyn &#8222;odovzd\u00e1va&#8220; energiu svojmu okoliu. V\u00fdraz pre pr\u00e1cu vykonan\u00fa plynom po\u010das tejto expanzie je dan\u00fd vz\u0165ahom :  <\/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 s\u00fa po\u010diato\u010dn\u00fd tlak a objem;<\/li>\n\n\n\n<li>Pf a Vf s\u00fa kone\u010dn\u00fd tlak a objem.<\/li>\n<\/ul>\n\n<p>Naopak, ke\u010f sa plyn stla\u010d\u00ed (jeho objem sa 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\">Pr\u00edklady aplik\u00e1ci\u00ed  <\/h2>\n\n<p>Rovnice <strong>vratnej adiabatickej premeny <\/strong>s\u00fa v\u0161adepr\u00edtomn\u00e9 v oblastiach, ako je energetika, mechanika plynov a in\u017einierstvo, ako aj v atmosf\u00e9rick\u00fdch a astrofyzik\u00e1lnych ved\u00e1ch. V t\u00fdchto discipl\u00ednach zohr\u00e1vaj\u00fa k\u013e\u00fa\u010dov\u00fa \u00falohu, najm\u00e4 v termodynamick\u00fdch syst\u00e9moch, kde je cie\u013eom optimalizova\u0165 v\u00fdmenu energie. Tieto premeny, ktor\u00e9 sa pou\u017e\u00edvaj\u00fa na modelovanie a anal\u00fdzu expanzie alebo kompresie plynov bez v\u00fdmeny tepla s okol\u00edm, s\u00fa nevyhnutn\u00e9 na pochopenie a optimaliz\u00e1ciu mnoh\u00fdch syst\u00e9mov. Uv\u00e1dzame nieko\u013eko pr\u00edkladov praktick\u00fdch aplik\u00e1ci\u00ed, v ktor\u00fdch maj\u00fa <strong>vratn\u00e9 adiabatick\u00e9 premeny <\/strong>z\u00e1sadn\u00fd v\u00fdznam:   <\/p>\n\n<h3 class=\"wp-block-heading\">Termodynamick\u00e9 cykly  <\/h3>\n\n<p>Carnotov cyklus, teoretick\u00fd model tepeln\u00fdch motorov, zah\u0155\u0148a <strong>reverzibiln\u00e9 adiabatick\u00e9 f\u00e1zy<\/strong> s cie\u013eom maximalizova\u0165 \u00fa\u010dinnos\u0165. Tento ide\u00e1lny cyklus pozost\u00e1va z dvoch <strong>vratn\u00fdch adiabatick\u00fdch procesov <\/strong>(expanzia a kompresia) a dvoch izotermick\u00fdch procesov (pri kon\u0161tantnej teplote). <\/p>\n\n<h3 class=\"wp-block-heading\">Kompresory a turb\u00edny<\/h3>\n\n<p>V kompresoroch a plynov\u00fdch turb\u00ednach sa kompresia a expanzia plynu \u010dasto modeluj\u00fa ako <strong>vratn\u00e9 adiabatick\u00e9 procesy<\/strong>. T\u00fdm sa maximalizuje \u00fa\u010dinnos\u0165 minimalizovan\u00edm str\u00e1t energie vo forme tepla. <\/p>\n\n<h3 class=\"wp-block-heading\">Chladni\u010dky a tepeln\u00e9 \u010derpadl\u00e1<\/h3>\n\n<p>Chladiace cykly a tepeln\u00e9 \u010derpadl\u00e1 vyu\u017e\u00edvaj\u00fa <strong>vratn\u00e9 adiabatick\u00e9 premeny<\/strong> po\u010das f\u00e1z kompresie a expanzie chladiacej kvapaliny. Tieto procesy umo\u017e\u0148uj\u00fa \u00fa\u010dinn\u00fd prenos tepelnej energie z jedn\u00e9ho miesta na druh\u00e9, \u010d\u00edm sa optimalizuje energetick\u00e1 \u00fa\u010dinnos\u0165 syst\u00e9mu. <\/p>\n\n<h3 class=\"wp-block-heading\">Anal\u00fdza priemyseln\u00fdch procesov<\/h3>\n\n<p>In\u017einieri pou\u017e\u00edvaj\u00fa <a href=\"https:\/\/obera.fr\/sk\/nasa-rada\/rafraichisseur-adiabatique-industriel-guide-complet\/\">adiabatick\u00fa reverzibilitu<\/a><strong> <\/strong>analyzova\u0165 a navrhova\u0165 r\u00f4zne priemyseln\u00e9 procesy, ako napr\u00edklad separ\u00e1ciu plynov a \u00fapravu kvapal\u00edn. Tieto modely mo\u017eno pou\u017ei\u0165 na optimaliz\u00e1ciu v\u00fdkonu a zn\u00ed\u017eenie n\u00e1kladov na energiu. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vratn\u00e1 adiabatick\u00e1 premena je idealizovan\u00fd termodynamick\u00fd proces, ktor\u00fd zohr\u00e1va \u00fastredn\u00fa \u00falohu pri anal\u00fdze energetick\u00fdch syst\u00e9mov. V\u010faka vyl\u00fa\u010deniu ak\u00e9hoko\u013evek prenosu tepla s vonkaj\u0161\u00edm svetom sa t\u00e1to premena riadi v\u00fdlu\u010dne z\u00e1konmi termodynamiky a stavov\u00fdmi rovnicami. <\/p>\n","protected":false},"author":4,"featured_media":81229,"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 transform\u00e1cia","_seopress_titles_desc":"Vratn\u00e1 adiabatick\u00e1 premena je idealizovan\u00fd termodynamick\u00fd proces, ktor\u00fd zohr\u00e1va \u00fastredn\u00fa \u00falohu pri anal\u00fdze energetick\u00fdch syst\u00e9mov.","_seopress_robots_index":"","footnotes":""},"categories":[141],"tags":[142],"class_list":["post-39874","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nasa-rada","tag-entete-male-sk","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\/sk\/wp-json\/wp\/v2\/posts\/39874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/comments?post=39874"}],"version-history":[{"count":3,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/posts\/39874\/revisions"}],"predecessor-version":[{"id":81414,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/posts\/39874\/revisions\/81414"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/media\/81229"}],"wp:attachment":[{"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/media?parent=39874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/categories?post=39874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/obera.fr\/sk\/wp-json\/wp\/v2\/tags?post=39874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}