{"id":3765,"date":"2016-06-06T12:13:04","date_gmt":"2016-06-06T12:13:04","guid":{"rendered":"http:\/\/www.romconvert.ro\/new\/?post_type=portfolio&#038;p=3765"},"modified":"2016-06-13T18:30:09","modified_gmt":"2016-06-13T15:30:09","slug":"programul-z-pentru-determinarea-factorului-de-abatere-pentru-gazele-reale","status":"publish","type":"portfolio","link":"https:\/\/www.romconvert.ro\/new\/index.php\/portfolio-item\/programul-z-pentru-determinarea-factorului-de-abatere-pentru-gazele-reale\/","title":{"rendered":"Programul Z pentru determinarea factorului de abatere pentru gazele reale"},"content":{"rendered":"\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_section-541a21edc89c4228c055bf0ea5d58e9e\">\n.avia-section.av-av_section-541a21edc89c4228c055bf0ea5d58e9e{\nbackground-color:#303030;\nbackground-image:unset;\n}\n<\/style>\n<div id='av_section_1'  class='avia-section av-av_section-541a21edc89c4228c055bf0ea5d58e9e main_color avia-section-default avia-no-shadow  avia-builder-el-0  el_before_av_section  avia-builder-el-first  avia-bg-style-scroll container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><main  role=\"main\" itemprop=\"mainContentOfPage\"  class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-3765'><div class='entry-content-wrapper clearfix'>\n<section  class='av_textblock_section av-av_textblock-0366cc7376be6c9e82a3e9cc8987b64f '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><h3 style=\"text-align: center;\"><span style=\"color: #ffffff;\">PROGRAMUL Z PENTRU DETERMINAREA FACTORULUI DE ABATERE PENTRU GAZELE REALE<\/span><\/h3>\n<\/div><\/section>\n\n<\/div><\/div><\/main><!-- close content main element --><\/div><\/div><div id='av_section_2'  class='avia-section av-av_section-915b33fd1d6006bfc684ade488387eaf main_color avia-section-default avia-no-border-styling  avia-builder-el-2  el_after_av_section  el_before_av_section  avia-bg-style-scroll container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-3765'><div class='entry-content-wrapper clearfix'>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_heading-d420064b6edf85cb89c2d76bf16ee91a\">\n#top .av-special-heading.av-av_heading-d420064b6edf85cb89c2d76bf16ee91a{\npadding-bottom:20px;\ncolor:#020202;\n}\nbody .av-special-heading.av-av_heading-d420064b6edf85cb89c2d76bf16ee91a .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-av_heading-d420064b6edf85cb89c2d76bf16ee91a .special-heading-inner-border{\nborder-color:#020202;\n}\n.av-special-heading.av-av_heading-d420064b6edf85cb89c2d76bf16ee91a .av-subheading{\nfont-size:16px;\n}\n<\/style>\n<div  class='av-special-heading av-av_heading-d420064b6edf85cb89c2d76bf16ee91a av-special-heading-h2 custom-color-heading blockquote modern-quote modern-centered  avia-builder-el-3  el_before_av_one_fourth  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >1. Considera\u0163ii generale<\/h2><div class='av_custom_color av-subheading av-subheading_below'><p>O evaluare c\u00e2t mai exact\u0103 a m\u0103rimilor de stare pentru gazele reale &#8211; at\u00e2t \u00een faza de proiectare c\u00e2t \u015fi \u00een faza de exploatare &#8211; poate conduce la m\u0103rirea eficien\u0163ei proceselor termodinamice din ma\u015fini \u015fi instala\u0163ii.<\/p>\n<\/div><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_one_fourth-9497bbf8bff73ea4c6992cc17fa9ec36\">\n.flex_column.av-av_one_fourth-9497bbf8bff73ea4c6992cc17fa9ec36{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-av_one_fourth-9497bbf8bff73ea4c6992cc17fa9ec36 av_one_fourth  avia-builder-el-4  el_after_av_heading  el_before_av_one_half  first flex_column_div av-zero-column-padding  '     ><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_one_half-9c1d454dc06f7247226bc4e8f931daae\">\n.flex_column.av-av_one_half-9c1d454dc06f7247226bc4e8f931daae{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-av_one_half-9c1d454dc06f7247226bc4e8f931daae av_one_half  avia-builder-el-5  el_after_av_one_fourth  el_before_av_one_fourth  flex_column_div av-zero-column-padding  '     ><div  class='avia-button-wrap av-av_button-dd5f4d9b3398e34d6299e8ca0fe2e1dc-wrap avia-button-center  avia-builder-el-6  avia-builder-el-no-sibling '>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_button-dd5f4d9b3398e34d6299e8ca0fe2e1dc\">\n#top #wrap_all .avia-button.av-av_button-dd5f4d9b3398e34d6299e8ca0fe2e1dc{\nbackground-color:#ed3636;\nborder-color:#ed3636;\ncolor:#ffffff;\ntransition:all 0.4s ease-in-out;\n}\n#top #wrap_all .avia-button.av-av_button-dd5f4d9b3398e34d6299e8ca0fe2e1dc .avia-svg-icon svg:first-child{\nfill:#ffffff;\nstroke:#ffffff;\n}\n<\/style>\n<a href='http:\/\/www.romconvert.ro\/new\/wp-content\/uploads\/2016\/06\/Programul-Z-pentru-determinarea-factorului-de-abatere-pentru-gazele-reale.pdf'  class='avia-button av-av_button-dd5f4d9b3398e34d6299e8ca0fe2e1dc av-link-btn avia-icon_select-yes-left-icon avia-size-large avia-position-center av-icon-on-hover'  target=\"_blank\"  rel=\"noopener noreferrer\"  aria-label=\"DESC\u0102RCARE ARTICOL\"><span class='avia_button_icon avia_button_icon_left avia-iconfont avia-font-entypo-fontello' data-av_icon='\ue812' data-av_iconfont='entypo-fontello' ><\/span><span class='avia_iconbox_title' >DESC\u0102RCARE ARTICOL<\/span><\/a><\/div><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_one_fourth-9c1d454dc06f7247226bc4e8f931daae\">\n.flex_column.av-av_one_fourth-9c1d454dc06f7247226bc4e8f931daae{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-av_one_fourth-9c1d454dc06f7247226bc4e8f931daae av_one_fourth  avia-builder-el-7  el_after_av_one_half  avia-builder-el-last  flex_column_div av-zero-column-padding  '     ><\/div><\/div><\/div><\/div><!-- close content main div --><\/div><\/div><div id='av_section_3'  class='avia-section av-av_section-d18d8c2c81d10022ebd21ffa95322c35 main_color avia-section-default avia-no-shadow  avia-builder-el-8  el_after_av_section  avia-builder-el-last  avia-bg-style-scroll container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-3765'><div class='entry-content-wrapper clearfix'>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36\">\n.flex_column.av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36 av_one_full  avia-builder-el-9  el_before_av_one_full  avia-builder-el-first  first flex_column_div av-zero-column-padding  '     ><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36\">\n.flex_column.av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-av_one_full-9497bbf8bff73ea4c6992cc17fa9ec36 av_one_full  avia-builder-el-11  el_after_av_one_full  avia-builder-el-last  first flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-av_textblock-0366cc7376be6c9e82a3e9cc8987b64f '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div class=\"bottom-box\">\n<h2 class=\"title\" style=\"text-align: left;\">2. Baza teoretic\u0103 a programului Z<\/h2>\n<div class=\"title-detail\" style=\"text-align: left;\"><\/div>\n<p style=\"text-align: left;\">Ca ecua\u0163ie de stare pentru gazele reale a fost folosit\u0103 ecua\u0163ia Benedict-Webb-Rubin [1], \u00een forma modificat\u0103 de Lee-Kesler:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-1.gif\" \/><\/div>\n<p style=\"text-align: left;\">unde:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-2.gif\" \/><\/div>\n<p style=\"text-align: left;\">Aceast\u0103 ecua\u0163ie (rela\u0163ia 1) are la baz\u0103 12 constante, valorile lor fiind prezentate \u00een Anexa 1. Parametrii redu\u015fi sunt defini\u0163i de rela\u0163iile 5, 6 \u015fi 7.<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-3.gif\" \/><\/div>\n<p style=\"text-align: left;\">O corec\u0163ie suplimentar\u0103 a factorului de compresibilitate se face \u00een func\u0163ie de factorul acentric al gazului definit \u00een rela\u0163ia 8:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-4.gif\" \/><\/div>\n<p style=\"text-align: left;\">Not\u00e2nd cu Z(0) valorile factorului de compresibilitate pentru substan\u0163e simple (Anexa 1), iar cu Z(r) valoarea factorului de compresibilitate pentru o substan\u0163\u0103 de referin\u0163\u0103, se poate defini corec\u0163ia de ordinul 1, consider\u00e2nd o varia\u0163ie liniar\u0103 \u00een raport cu factorul acentric:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-5.gif\" \/><\/div>\n<p style=\"text-align: left;\">Abaterea entalpiei gazului real fa\u0163\u0103 de gazul perfect, definit\u0103 \u015fi prezentat\u0103 \u00een Anexa 2, precum \u015fi abaterea entropiei \u015fi fugacit\u0103\u0163ii se corecteaz\u0103 similar:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-6.gif\" \/><\/div>\n<h2 class=\"title\" style=\"text-align: left;\">3. Probleme remarcabile ap\u0103rute \u00een realizarea programului Z<\/h2>\n<div class=\"title-detail\" style=\"text-align: left;\"><\/div>\n<p style=\"text-align: left;\">Trebuie men\u0163ionat c\u0103 ecua\u0163ia Lee-Kesler are abateri \u00eensemnate at\u00e2t \u00een apropierea punctului critic, c\u00e2t \u015fi \u00een vecin\u0103tatea curbelor de \u00eenceput \u015fi de sf\u00e2r\u015fit de vaporizare.<\/p>\n<p style=\"text-align: left;\">O alt\u0103 problem\u0103 important\u0103 apare datorit\u0103 lu\u0103rii \u00een considerare a influen\u0163ei factorului de acentricitate. \u00cen zona de schimbare de faz\u0103, toate m\u0103rimile variaz\u0103 \u00een func\u0163ie de factorul acentric. \u00cen figura 1 este prezentat\u0103 influen\u0163a factorului acentric asupra func\u0163iei: presiune redus\u0103 \u00een func\u0163ie de temperatura redus\u0103, la satura\u0163ie. Sunt reprezentate curbele pentru factorul acentric 0, 0,25, 0,5 \u015fi 0,75.<\/p>\n<div class=\"box-content\" style=\"text-align: center;\">\n<div class=\"as-image\"><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-7.gif\" \/><\/div>\n<div class=\"as-text\">\n<p style=\"text-align: left;\">Se observ\u0103 c\u0103 pe m\u0103sur\u0103 ce valoarea factorului acentric cre\u015fte, curba devine mai abrupt\u0103, fapt ce modific\u0103 esen\u0163ial comportarea gazului real pentru valori mari ale factorului acentric. Din punct de vedere matematic, func\u0163ia prezentat\u0103 variaz\u0103, la satura\u0163ie, fa\u0163\u0103 de dou\u0103 variabile &#8211; temperatura redus\u0103 \u015fi factorul acentric &#8211; lucru valabil pentru toate m\u0103rimile din aceast\u0103 zon\u0103 (Zlichid, Zvapori, (h*-h)\/(RTc)lichid, (h*-h)\/(RTc)gaz etc.).<\/p>\n<p style=\"text-align: left;\">Pentru a corecta comportarea ecua\u0163iei de stare s-a apelat la valori considerate de \u00eencredere (publicate \u00een [1]), pentru zona de schimbare de faz\u0103 \u015fi vecin\u0103tatea acesteia. Pentru determinarea valorilor au fost verificate dou\u0103 variante: realizarea unor func\u0163ii care s\u0103 descrie comportarea m\u0103rimilor pe zone c\u00e2t mai mari \u015fi realizarea unor func\u0163ii scurte, care permit interpolarea valorilor din 5 \u00een 5 (sau din 10 \u00een 10) puncte aflate \u00een vecin\u0103tatea valorii solicitate. \u00cen acest din urm\u0103 caz s-a definit o re\u0163ea rar\u0103 de puncte de \u00eencredere \u00een zona de interes pe care se utilizeaz\u0103 interpolarea bidimensional\u0103, utiliz\u00e2nd func\u0163ii scurte. F\u0103c\u00e2nd o analiz\u0103 numeric\u0103 am\u0103nun\u0163it\u0103 a valorilor din jurul punctului critic \u015fi din vecin\u0103tatea zonei de lichefiere s-a remarcat faptul c\u0103 nu se poate utiliza o singur\u0103 func\u0163ie, oric\u00e2t de complex\u0103 ar fi ea, astfel \u00eenc\u00e2t eroarea s\u0103 fie rezonabil\u0103. \u00cen acest caz a fost selectat, din circa 3.700 de func\u0163ii, un grup de 10 func\u0163ii care aproximeaz\u0103 foarte bine anumite zone cu probleme. S-a constatat c\u0103 cea mai bun\u0103 metod\u0103 de interpolare se ob\u0163ine cu condi\u0163ia de a alege \u00een permanen\u0163\u0103 func\u0163ia care produce eroarea minim\u0103 la interpolare \u00een domeniul desemnat, reu\u015findu-se astfel ob\u0163inerea unor erori de aproximare mai mici sau egale cu 10-5.<\/p>\n<\/div>\n<\/div>\n<h2 class=\"title\" style=\"text-align: left;\">4. Performan\u0163ele programului Z<\/h2>\n<p>Programul Z permite ob\u0163inerea rapid\u0103, interactiv\u0103, a factorului de compresibilitate \u00een func\u0163ie de presiunea redus\u0103, temperatura redus\u0103 \u015fi factorul acentric. O dat\u0103 cu aceast\u0103 m\u0103rime se ob\u0163in: abaterea entalpiei, a entropiei \u015fi a fugacit\u0103\u0163ii pentru starea cerut\u0103 fa\u0163\u0103 de gazul perfect. Valoarea factorului de compresibilitate este reprezentat\u0103 grafic \u00eentr-o diagram\u0103 logaritmic\u0103, diagram\u0103 care permite identificarea rapid\u0103 a fazei \u00een care se g\u0103se\u015fte substan\u0163a respectiv\u0103.<\/p>\n<p>\u00cen figura 2 este prezent\u0103 diagrama cu starea corespunz\u0103toare punctului: pr = 2, Tr = 1,125.<\/p>\n<div class=\"title-detail\" style=\"text-align: center;\"><\/div>\n<div class=\"box-content\" style=\"text-align: center;\">\n<div class=\"as-image\"><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-8.gif\" \/><\/div>\n<div class=\"as-text\">\n<p style=\"text-align: left;\">Programul permite calcularea valorilor factorului de compresibilitate \u015fi \u00een zona de schimbare de faz\u0103, inclusiv pe curbele limit\u0103. Astfel, pentru toate izotermele care str\u0103bat zona respectiv\u0103, sunt afi\u015fate valorile factorului de compresibilitate, precum \u015fi abaterile entalpiei, entropiei \u015fi fugacit\u0103\u0163ii pentru punctele de \u00eenceput \u015fi sf\u00e2r\u015fit de vaporizare.<\/p>\n<\/div>\n<\/div>\n<p style=\"text-align: left;\">\u00cen zona de schimbare de faz\u0103, influen\u0163a factorului acentric este mare. Figurile 3 \u015fi 4 prezint\u0103 factorul de compresibilitate pentru acelea\u015fi valori ale temperaturii \u015fi presiunii reduse, dar pentru dou\u0103 valori diferite ale factorului acentric. Se remarc\u0103 diferen\u0163a substan\u0163ial\u0103 \u00eentre valorile lui Z:<\/p>\n<p style=\"text-align: left;\">Z=0,80456 pentru w=0<\/p>\n<p style=\"text-align: left;\">\u015fi, respectiv Z=0,04164 pentru w=0,4.<\/p>\n<div class=\"as-images row\" style=\"text-align: center;\">\n<div class=\"as-box col-lg-6 col-md-6 col-sm-6 col-xs-12\">\n<p><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-9.gif\" \/><\/p>\n<p>Figura 3<\/p>\n<\/div>\n<div class=\"as-box col-lg-6 col-md-6 col-sm-6 col-xs-12\">\n<p><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-10.gif\" \/><\/p>\n<p>Figura 4<\/p>\n<\/div>\n<\/div>\n<p style=\"text-align: left;\">\u00cen interiorul zonei de schimbare de faz\u0103, valorile factorului de compresibiliate se ob\u0163in \u00een func\u0163ie de titlu \u015fi temperatura redus\u0103, sau \u00een func\u0163ie de presiune redus\u0103 \u015fi titlu. Figura 5 prezint\u0103 punctul corespunz\u0103tor temperaturii reduse de 0,78 \u015fi titlului 0,85.<\/p>\n<p style=\"text-align: left;\">Programul beneficiaz\u0103 de o baz\u0103 de date care con\u0163ine valorile constantelor critice \u015fi factorul acentric pentru mai mult de 40 de substan\u0163e, ceea ce face posibil\u0103 calcularea interactiv\u0103 a parametrilor redu\u015fi.<\/p>\n<p style=\"text-align: left;\">\u00cen figura 6 sunt prezentate toate datele care pot fi ob\u0163inute pentru un punct de interes, pentru \u00eenceputul \u015fi sf\u00e2r\u015fitul de vaporizare. Utilizatorul poate vizualiza modul \u00een care s-a f\u0103cut corec\u0163ia pentru fiecare valore \u00een parte.<\/p>\n<div class=\"as-images row\" style=\"text-align: center;\">\n<div class=\"as-box col-lg-6 col-md-6 col-sm-6 col-xs-12\">\n<p><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-11.gif\" \/><\/p>\n<p>Figura 5<\/p>\n<\/div>\n<div class=\"as-box col-lg-6 col-md-6 col-sm-6 col-xs-12\">\n<p><img decoding=\"async\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/13-12.gif\" \/><\/p>\n<p>Figura 6<\/p>\n<\/div>\n<\/div>\n<h2 class=\"title\" style=\"text-align: left;\">5. Testarea programului Z<\/h2>\n<div class=\"title-detail\" style=\"text-align: center;\"><\/div>\n<p style=\"text-align: left;\">Testarea programului s-a realizat prin compararea valorilor furnizate de programul Z cu valorile ob\u0163inute cu programul CATT produs de John Wiley &amp; Sons, edi\u0163ie 1994. Rezultatele au fost satisf\u0103c\u0103toare, diferen\u0163ele \u00eentre valorile furnizate de cele dou\u0103 programe fiind mai mici de 0,2% pentru domeniul: pr = 0,01 \u00f7 10, Tr = 0,3 \u00f7 5.<\/p>\n<p style=\"text-align: left;\">Lista nota\u0163iilor utilizate<\/p>\n<p style=\"text-align: left;\">Z &#8211; factorul de compresibilitate; pr &#8211; presiunea redus\u0103; Tr &#8211; temperatura redus\u0103; w &#8211; factorul acentric; h &#8211; entalpia; s &#8211; entropia; u &#8211; energia inern\u0103; f &#8211; fugacitatea; R &#8211; constanta gazului.<\/p>\n<p style=\"text-align: left;\">Indici<\/p>\n<p style=\"text-align: left;\">r &#8211; redus; c &#8211; critic; p &#8211; izobar; v &#8211; izocor; T &#8211; izoterm; * &#8211; gaz perfect.<\/p>\n<div class=\"text-title\" style=\"text-align: left;\"><strong>Anexa 1.<\/strong> Valorile coeficien\u0163ilor ecua\u0163iei Lee-Kesler<\/div>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/as13\/tabel.png\" \/><\/div>\n<div class=\"text-title\" style=\"text-align: center;\"><\/div>\n<div class=\"text-title\" style=\"text-align: left;\"><strong>Anexa 2.<\/strong> Calculul abaterii entalpiei gazului real fa\u0163\u0103 de gazul perfect<\/div>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-13.gif\" \/><\/div>\n<p style=\"text-align: left;\">Expresia diferen\u0163ial\u0103 pentru energia intern\u0103 pentru o izoterm\u0103 (rela\u0163ia A2.3) poate fi evaluat\u0103 cu ajutorul ecua\u0163iei de stare pentru gaze perfecte, corectat\u0103 cu factorul de abatere Z.<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-14.gif\" \/><\/div>\n<p style=\"text-align: left;\">Expresia (A2.6) poate fi scris\u0103 \u00een func\u0163ie de parametrii redu\u015fi, folosind nota\u0163iile: temperatur\u0103 redus\u0103 &#8211; Tr = T\/Tc \u015fi volum redus &#8211; vr = v\/(RTc\/pc)<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-15.gif\" \/><\/div>\n<p style=\"text-align: left;\">Integr\u00e2nd expresia diferen\u0163ial\u0103 (A2.10) \u00eentre o stare a gazului real caracterizat\u0103 de energia intern\u0103 u \u015fi o stare corespunz\u0103toare notat\u0103 u* pentru un gaz perfect \u015fi \u0163in\u00e2nd seama c\u0103 \u00een cazul unui gaz perfect presiunea redus\u0103 tinde la zero, iar volumul redus tinde la infinit, se ob\u0163ine:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-16.gif\" \/><\/div>\n<p style=\"text-align: left;\">Grup\u00e2nd termenii, rezult\u0103 expresia (A2.12) care reprezint\u0103 abaterea energiei, \u00eentr-o stare oarecare, fa\u0163\u0103 de o stare corespunz\u0103toare, dar pentru un gaz perfect:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-17.gif\" \/><\/div>\n<p>Pornind de la defini\u0163ia entalpiei, se poate scrie expresia abaterii entalpiei gazului real fa\u0163\u0103 de gazul perfect:<\/p>\n<div class=\"math-image\" style=\"text-align: center;\"><img decoding=\"async\" class=\"as-image\" src=\"http:\/\/romconvert.azurewebsites.net\/images\/formule\/13-18.gif\" \/><\/div>\n<p>Ra\u0163ion\u00e2nd asem\u0103n\u0103tor se poate calcula abaterea entropiei si fugacit\u0103\u0163ii fa\u0163\u0103 de gazul perfect.<\/p>\n<div class=\"as-bibliografie\" style=\"text-align: left;\">Bibliografie:<\/div>\n<ol>\n<li style=\"text-align: left;\">Van Wylen, G.; Sonntag, R.; Borgnakke, C.: Fundamentals of Classical Thermodynamics, John Wiley &amp; Sons Inc., New York, 1994.<\/li>\n<li style=\"text-align: left;\">Vidal, J.: Thermodynamique &#8211; Methodes appliquees au raffinage et au genie chimique, Edition Techniq, Paris, 1973.<\/li>\n<li style=\"text-align: left;\">Marinescu, M.; B\u0103ran, N.; Radcenco, V.: Termodinamic\u0103 tehnic\u0103, MatrixRom, Bucure\u015fti, 1998.<\/li>\n<li style=\"text-align: left;\">Neac\u015fu, S.: Programul APAB.<\/li>\n<li style=\"text-align: left;\">Neac\u015fu, S.: Programul MetanTS.<\/li>\n<\/ol>\n<\/div>\n<\/div><\/section><\/div>\n<\/div><\/div><\/div><!-- close content main div --><\/div><\/div><div id='after_section_3'  class='main_color av_default_container_wrap container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-3765'><div class='entry-content-wrapper clearfix'><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3766,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"portfolio_entries":[74],"class_list":["post-3765","portfolio","type-portfolio","status-publish","has-post-thumbnail","hentry","portfolio_entries-programul-z-pentru-determinarea-factorului-de-abatere-pentru-gazele-reale"],"_links":{"self":[{"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/portfolio\/3765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/portfolio"}],"about":[{"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/types\/portfolio"}],"author":[{"embeddable":true,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/comments?post=3765"}],"version-history":[{"count":2,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/portfolio\/3765\/revisions"}],"predecessor-version":[{"id":3884,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/portfolio\/3765\/revisions\/3884"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/media\/3766"}],"wp:attachment":[{"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/media?parent=3765"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/tags?post=3765"},{"taxonomy":"portfolio_entries","embeddable":true,"href":"https:\/\/www.romconvert.ro\/new\/index.php\/wp-json\/wp\/v2\/portfolio_entries?post=3765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}