{"id":227259,"date":"2025-06-06T03:54:24","date_gmt":"2025-06-06T03:54:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227259"},"modified":"2025-06-06T03:54:26","modified_gmt":"2025-06-06T03:54:26","slug":"in-the-problem-below-a-thermodynamics-student-wants-to-know-how-to-find-in-order-for-her-to-calculate-the-isentropic-efficiency-of-the-turbine","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/in-the-problem-below-a-thermodynamics-student-wants-to-know-how-to-find-in-order-for-her-to-calculate-the-isentropic-efficiency-of-the-turbine\/","title":{"rendered":"In the problem below, a thermodynamics student wants to know how to find, in order for her to calculate the isentropic efficiency of the turbine"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In the problem below, a thermodynamics student wants to know how to find<br>, in order for her to calculate the isentropic efficiency of the turbine. What is the step she must do to eventually find<br>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">400 3 MPa Actual process Isentropic process Steam turbine 100 50 kPa<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">she has to find the efficiency of the compressor in order for her to find the efficiency of the turbine through the direct x calculation she first has to use<br>at 3MPa as well as sf and sfg at 50 kPa to find x she has to find<br>and use it with hf and hfg at 3 MPa using x she first has to use<br>at 50 kPa as well as hf and hfg at 3 MPa to find<br>to find x she first has to use<br>at 50 kPa as well as hf and hfg at 3 MPa to find<br>directly she must first find hf at 3 MPa and hg at the 50 kPa to solve for<br>she has to first realize this is an actual (real) process and therefore she must use the value of h at 2a together with<br>in the same equation to find<br>she can&#8217;t there is missing information<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-195.png\" alt=\"\" class=\"wp-image-227260\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Correct Answer:<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>She first has to use s\u2081 at 3 MPa as well as sf and sfg at 50 kPa to find x.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation <\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To calculate the <strong>isentropic efficiency of the turbine<\/strong>, the student must find <strong>h\u2082s<\/strong>, the enthalpy at the turbine outlet assuming an <strong>isentropic process<\/strong> (idealized, no entropy generation). The isentropic efficiency is defined as: \u03b7turbine=h1\u2212h2ah1\u2212h2s\\eta_{turbine} = \\frac{h_1 &#8211; h_{2a}}{h_1 &#8211; h_{2s}}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>h1h_1 = Enthalpy at turbine inlet (given or can be found from T\u2081 and P\u2081)<\/li>\n\n\n\n<li>h2ah_{2a} = Enthalpy at turbine outlet (actual, given as 100\u00b0C at 50 kPa)<\/li>\n\n\n\n<li>h2sh_{2s} = Enthalpy at turbine outlet under isentropic conditions (to be found)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step-by-Step to Find h2sh_{2s}:<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Determine s\u2081 (entropy at state 1):<\/strong><br>Since state 1 is superheated steam at 3 MPa and 440\u00b0C, use steam tables to find entropy s1s_1.<\/li>\n\n\n\n<li><strong>Use s\u2081 = s\u2082s (isentropic assumption):<\/strong><br>For isentropic processes, entropy remains constant. Therefore, s2s=s1s_2s = s_1.<\/li>\n\n\n\n<li><strong>At 50 kPa, determine the quality (x):<\/strong><br>Look up saturated properties at 50 kPa:<ul><li>sfs_f: entropy of saturated liquid<\/li><li>sfgs_{fg}: difference in entropy between saturated vapor and liquid<\/li><\/ul>Use the formula: x=s1\u2212sfsfgx = \\frac{s_1 &#8211; s_f}{s_{fg}}<\/li>\n\n\n\n<li><strong>Find h2sh_{2s}:<\/strong><br>Use the quality (x) found above to determine h2sh_{2s} from: h2s=hf+xhfgh_{2s} = h_f + x h_{fg}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>hfh_f: enthalpy of saturated liquid at 50 kPa<\/li>\n\n\n\n<li>hfgh_{fg}: latent heat of vaporization at 50 kPa<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">This method uses the <strong>isentropic relation of constant entropy<\/strong> and applies steam table data to compute the thermodynamic quality and enthalpy of the steam under ideal conditions at turbine exit pressure.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, <strong>the correct step<\/strong> is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><em>She first has to use s\u2081 at 3 MPa as well as sf and sfg at 50 kPa to find x.<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-119.jpeg\" alt=\"\" class=\"wp-image-227261\"\/><\/figure>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>In the problem below, a thermodynamics student wants to know how to find, in order for her to calculate the isentropic efficiency of the turbine. What is the step she must do to eventually find? 400 3 MPa Actual process Isentropic process Steam turbine 100 50 kPa she has to find the efficiency of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-227259","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=227259"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227259\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}