Water is the working fluid in an ideal Rankine cycle. Dry saturated vapour enters the turbine at 16 MPa, and the condenser pressure is 8 kPa. The mass flow rate of steam entering the turbine is 120 kg\/s, and the expansion is isentropic.
Determine the;
i. power developed (in kW),
ii. rate of heat transfer to the steam passing though the boiler,
iii. thermal efficiency, and
iv. mass flow rate of condenser cooling water, if the cooling water undergoes a temperature increase of 18 OC with negligible pressure change in passing through the condenser. The specific heat capacity of cooling water is 4.179 kJ\/kg.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n Let’s solve each part of the problem step by step for the ideal Rankine cycle:<\/p>\n\n\n\n We will use the steam tables to find the necessary thermodynamic properties at the given pressures.<\/p>\n\n\n\n The turbine power<\/strong> (P) is calculated using:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n From the steam tables:<\/p>\n\n\n\n Thus:<\/p>\n\n\n\n [ Power developed by the turbine = 412.32 MW<\/strong><\/p>\n\n\n\n The heat added to the steam in the boiler is the difference in enthalpies between the saturated liquid at P\u2082 and the saturated steam at P\u2081:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n From the steam tables:<\/p>\n\n\n\n So:<\/p>\n\n\n\n [ Rate of heat transfer to the steam = 413.78 MW<\/strong><\/p>\n\n\n\n The thermal efficiency of the Rankine cycle is given by:<\/p>\n\n\n\n [ Thermal efficiency = 99.7%<\/strong><\/p>\n\n\n\n The rate of heat rejected in the condenser is:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n From the steam tables:<\/p>\n\n\n\n Thus:<\/p>\n\n\n\n [ Now, the rate of heat rejected to the cooling water is:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n Rearranging the equation:<\/p>\n\n\n\n [ Mass flow rate of condenser cooling water = 3,930.5 kg\/s<\/strong><\/p>\n\n\n\n These results reflect the ideal Rankine cycle, assuming no losses and perfect performance in the turbine.<\/p>\n","protected":false},"excerpt":{"rendered":" Water is the working fluid in an ideal Rankine cycle. Dry saturated vapour enters the turbine at 16 MPa, and the condenser pressure is 8 kPa. The mass flow rate of steam entering the turbine is 120 kg\/s, and the expansion is isentropic.Determine the;i. power developed (in kW),ii. rate of heat transfer to the steam […]<\/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-182003","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182003","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=182003"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182003\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given Data:<\/h3>\n\n\n\n
\n
Step 1: Power Developed by the Turbine (Part i)<\/h3>\n\n\n\n
P = \u1e41 \\cdot (h\u2081 – h\u2082)
]<\/p>\n\n\n\n\n
\n
P = 120 \\, \\text{kg\/s} \\cdot (3640 – 204) \\, \\text{kJ\/kg} = 120 \\cdot 3436 \\, \\text{kJ\/s} = 412,320 \\, \\text{kW}
]<\/p>\n\n\n\nStep 2: Rate of Heat Transfer to the Steam (Part ii)<\/h3>\n\n\n\n
Q_{\\text{in}} = \u1e41 \\cdot (h\u2081 – h\u2084)
]<\/p>\n\n\n\n\n
\n
Q_{\\text{in}} = 120 \\, \\text{kg\/s} \\cdot (3640 – 191.81) \\, \\text{kJ\/kg} = 120 \\cdot 3448.19 \\, \\text{kJ\/s} = 413,782.8 \\, \\text{kW}
]<\/p>\n\n\n\nStep 3: Thermal Efficiency (Part iii)<\/h3>\n\n\n\n
\\eta = \\frac{P_{\\text{turbine}}}{Q_{\\text{in}}} = \\frac{412,320}{413,782.8} \\approx 0.997 \\, \\text{or} \\, 99.7\\%
]<\/p>\n\n\n\nStep 4: Mass Flow Rate of Condenser Cooling Water (Part iv)<\/h3>\n\n\n\n
Q_{\\text{out}} = \u1e41 \\cdot (h\u2083 – h\u2082)
]<\/p>\n\n\n\n\n
\n
Q_{\\text{out}} = 120 \\cdot (2676 – 204) = 120 \\cdot 2472 = 296,640 \\, \\text{kJ\/s} = 296.64 MW
]<\/p>\n\n\n\n
Q_{\\text{out}} = m_{\\text{water}} \\cdot c_{\\text{water}} \\cdot \\Delta T
]<\/p>\n\n\n\n\n
m_{\\text{water}} = \\frac{Q_{\\text{out}}}{c_{\\text{water}} \\cdot \\Delta T} = \\frac{296,640}{4.179 \\cdot 18} = 3,930.5 \\, \\text{kg\/s}
]<\/p>\n\n\n\nSummary of Results:<\/h3>\n\n\n\n
\n