{"id":245666,"date":"2025-07-06T10:47:10","date_gmt":"2025-07-06T10:47:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245666"},"modified":"2025-07-06T10:47:12","modified_gmt":"2025-07-06T10:47:12","slug":"a-refrigeration-system-requires-1-3-kw-of-power-for-a-refrigeration-rate-of-3-kj-s-and-a-heat-rejection-at-60-ac","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/a-refrigeration-system-requires-1-3-kw-of-power-for-a-refrigeration-rate-of-3-kj-s-and-a-heat-rejection-at-60-ac\/","title":{"rendered":"A refrigeration system requires 1.3 kW of power for a refrigeration rate of 3 kJ\/s and a heat rejection at 60 \u00c2\u00b0C."},"content":{"rendered":"\n
A refrigeration system requires 1.3 kW of power for a refrigeration rate of 3 kJ\/s and a heat rejection at 60 \u00c2\u00b0C. Calculate the coefficient of performance and lowest temperature the system can possibly operate at, a) 4.30, 232.18 K b) 2.30, 232.18 K c) 2.30, 352.18 K d) 3.30, 252.18 K<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To solve this problem, we’ll first need to understand the coefficient of performance (COP) for a refrigeration system and the lowest temperature the system can possibly operate at.<\/p>\n\n\n\n
1. Coefficient of Performance (COP)<\/strong><\/h3>\n\n\n\n
The COP of a refrigeration system is the ratio of the refrigeration effect (cooling rate) to the work input required by the system. Mathematically, it can be expressed as:COP=QLWCOP = \\frac{Q_L}{W}COP=WQL\u200b\u200b<\/p>\n\n\n\n
Where:<\/p>\n\n\n\n
\n
QLQ_LQL\u200b is the refrigeration rate or the amount of heat removed from the cold reservoir (in kJ\/s).<\/li>\n\n\n\n
WWW is the power input required to operate the system (in kW).<\/li>\n<\/ul>\n\n\n\n
Now, calculate the COP:COP=31.3=2.30COP = \\frac{3}{1.3} = 2.30COP=1.33\u200b=2.30<\/p>\n\n\n\n
So, the COP<\/strong> is 2.30.<\/p>\n\n\n\n
2. Lowest Temperature of Operation<\/strong><\/h3>\n\n\n\n
To calculate the lowest temperature the system can operate at, we can use the thermodynamic relationship between the COP, the temperatures of the cold and hot reservoirs. For a refrigeration cycle, the COP is related to the temperatures by:COP=TLTH\u2212TLCOP = \\frac{T_L}{T_H – T_L}COP=TH\u200b\u2212TL\u200bTL\u200b\u200b<\/p>\n\n\n\n
Where:<\/p>\n\n\n\n
\n
TLT_LTL\u200b is the temperature of the cold reservoir (in Kelvin).<\/li>\n\n\n\n
THT_HTH\u200b is the temperature of the hot reservoir (in Kelvin).<\/li>\n<\/ul>\n\n\n\n
We are given that the heat rejection temperature is 60\u00b0C. Converting this to Kelvin:TH=60+273.15=333.15\u2009KT_H = 60 + 273.15 = 333.15 \\, \\text{K}TH\u200b=60+273.15=333.15K<\/p>\n\n\n\n
Now, rearranging the COP formula to solve for TLT_LTL\u200b:COP=TLTH\u2212TL\u21d22.30=TL333.15\u2212TLCOP = \\frac{T_L}{T_H – T_L} \\quad \\Rightarrow \\quad 2.30 = \\frac{T_L}{333.15 – T_L}COP=TH\u200b\u2212TL\u200bTL\u200b\u200b\u21d22.30=333.15\u2212TL\u200bTL\u200b\u200b<\/p>\n\n\n\n
Thus, the lowest temperature<\/strong> TLT_LTL\u200b is 232.18 K.<\/p>\n\n\n\n
3. Answer<\/strong><\/h3>\n\n\n\n
Based on these calculations:<\/p>\n\n\n\n
\n
The COP<\/strong> is 2.30.<\/li>\n\n\n\n
The lowest temperature<\/strong> the system can operate at is 232.18 K.<\/li>\n<\/ul>\n\n\n\n
Thus, the correct answer is (b) 2.30, 232.18 K<\/strong>.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
A refrigeration system requires 1.3 kW of power for a refrigeration rate of 3 kJ\/s and a heat rejection at 60 \u00c2\u00b0C. Calculate the coefficient of performance and lowest temperature the system can possibly operate at, a) 4.30, 232.18 K b) 2.30, 232.18 K c) 2.30, 352.18 K d) 3.30, 252.18 K The Correct Answer […]<\/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-245666","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245666","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=245666"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245666\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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