However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go through it:<\/p>\n\n\n\n
\n\n\n\n
Given:<\/strong><\/h3>\n\n\n\n\n- Power output (W) = 10 kW<\/li>\n\n\n\n
- Heat input ( Q_{in} ) = 2250 kJ\/min<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Convert Heat Input to kW<\/strong><\/h3>\n\n\n\nSince:<\/p>\n\n\n\n
\n- 1 kW = 1 kJ\/s<\/li>\n\n\n\n
- 2250 kJ\/min = ( \\frac{2250}{60} ) kJ\/s = 37.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 2: Calculate Thermal Efficiency<\/strong><\/h3>\n\n\n\n[
\\text{Thermal Efficiency} = \\frac{\\text{Power Output}}{\\text{Heat Input}} = \\frac{10}{37.5} = 0.2667
]<\/p>\n\n\n\n
[
\\text{Thermal Efficiency (\\%)} = 0.2667 \\times 100 = \\boxed{26.67\\%}
]<\/p>\n\n\n\n
\n\n\n\nStep 3: Determine Heat Rejection Rate<\/strong><\/h3>\n\n\n\n[
Q_{out} = Q_{in} – W = 37.5 – 10 = \\boxed{27.5\\text{ kW}}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers:<\/strong><\/h3>\n\n\n\n\n- Thermal Efficiency = 26.67%<\/strong><\/li>\n\n\n\n
- Heat Rejection Rate = 27.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\nA heat engine<\/strong> is a system that converts heat (thermal energy) into mechanical work. The performance of a heat engine is primarily evaluated using thermal efficiency<\/strong>, which is the ratio of useful work output to the heat energy input.<\/p>\n\n\n\nIn this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\nThe engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\nThe remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\nThese calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n
\n\n\n\n![\"\"\/](\"https:\/\/tse1.mm.bing.net\/th?id=OIP.Mclflh0YF9IEm-TPfL3ZaQHaKS&w=474&h=474&c=7\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
Step 1: Convert Heat Input to kW<\/strong><\/h3>\n\n\n\nSince:<\/p>\n\n\n\n
\n- 1 kW = 1 kJ\/s<\/li>\n\n\n\n
- 2250 kJ\/min = ( \\frac{2250}{60} ) kJ\/s = 37.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 2: Calculate Thermal Efficiency<\/strong><\/h3>\n\n\n\n[
\\text{Thermal Efficiency} = \\frac{\\text{Power Output}}{\\text{Heat Input}} = \\frac{10}{37.5} = 0.2667
]<\/p>\n\n\n\n
[
\\text{Thermal Efficiency (\\%)} = 0.2667 \\times 100 = \\boxed{26.67\\%}
]<\/p>\n\n\n\n
\n\n\n\nStep 3: Determine Heat Rejection Rate<\/strong><\/h3>\n\n\n\n[
Q_{out} = Q_{in} – W = 37.5 – 10 = \\boxed{27.5\\text{ kW}}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers:<\/strong><\/h3>\n\n\n\n\n- Thermal Efficiency = 26.67%<\/strong><\/li>\n\n\n\n
- Heat Rejection Rate = 27.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\nA heat engine<\/strong> is a system that converts heat (thermal energy) into mechanical work. The performance of a heat engine is primarily evaluated using thermal efficiency<\/strong>, which is the ratio of useful work output to the heat energy input.<\/p>\n\n\n\nIn this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\nThe engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\nThe remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\nThese calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n
\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
Step 2: Calculate Thermal Efficiency<\/strong><\/h3>\n\n\n\n[
\\text{Thermal Efficiency} = \\frac{\\text{Power Output}}{\\text{Heat Input}} = \\frac{10}{37.5} = 0.2667
]<\/p>\n\n\n\n
[
\\text{Thermal Efficiency (\\%)} = 0.2667 \\times 100 = \\boxed{26.67\\%}
]<\/p>\n\n\n\n
\n\n\n\nStep 3: Determine Heat Rejection Rate<\/strong><\/h3>\n\n\n\n[
Q_{out} = Q_{in} – W = 37.5 – 10 = \\boxed{27.5\\text{ kW}}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers:<\/strong><\/h3>\n\n\n\n\n- Thermal Efficiency = 26.67%<\/strong><\/li>\n\n\n\n
- Heat Rejection Rate = 27.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\nA heat engine<\/strong> is a system that converts heat (thermal energy) into mechanical work. The performance of a heat engine is primarily evaluated using thermal efficiency<\/strong>, which is the ratio of useful work output to the heat energy input.<\/p>\n\n\n\nIn this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\nThe engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\nThe remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\nThese calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n
\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{Thermal Efficiency} = \\frac{\\text{Power Output}}{\\text{Heat Input}} = \\frac{10}{37.5} = 0.2667
]<\/p>\n\n\n\n
\\text{Thermal Efficiency (\\%)} = 0.2667 \\times 100 = \\boxed{26.67\\%}
]<\/p>\n\n\n\n
[
Q_{out} = Q_{in} – W = 37.5 – 10 = \\boxed{27.5\\text{ kW}}
]<\/p>\n\n\n\n
\n\n\n\n
Final Answers:<\/strong><\/h3>\n\n\n\n\n- Thermal Efficiency = 26.67%<\/strong><\/li>\n\n\n\n
- Heat Rejection Rate = 27.5 kW<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\nA heat engine<\/strong> is a system that converts heat (thermal energy) into mechanical work. The performance of a heat engine is primarily evaluated using thermal efficiency<\/strong>, which is the ratio of useful work output to the heat energy input.<\/p>\n\n\n\nIn this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\nThe engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\nThe remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\nThese calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n
\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
Explanation (300+ words):<\/strong><\/h3>\n\n\n\nA heat engine<\/strong> is a system that converts heat (thermal energy) into mechanical work. The performance of a heat engine is primarily evaluated using thermal efficiency<\/strong>, which is the ratio of useful work output to the heat energy input.<\/p>\n\n\n\nIn this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\nThe engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\nThe remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\nThese calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n
\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
In this case, the heat engine receives 2250 kJ of heat per minute<\/strong> from an external source. Since power and energy must be expressed in consistent time units for accurate efficiency calculations, we first convert this to kW<\/strong> (kilojoules per second), which is the standard unit for power. Doing so, we find that the engine receives 37.5 kW<\/strong> of thermal energy.<\/p>\n\n\n\n The engine produces 10 kW<\/strong> of useful mechanical power. The thermal efficiency<\/strong> is then calculated by dividing the power output by the heat input: ( \\frac{10}{37.5} = 0.2667 ), or 26.67%<\/strong>. This indicates that only about a quarter of the supplied thermal energy is converted into useful work \u2014 a common occurrence in practical thermodynamic systems due to limitations imposed by the Second Law of Thermodynamics<\/strong>.<\/p>\n\n\n\n The remaining energy<\/strong> (i.e., the part of the input heat that is not converted into work) must be rejected, usually into the environment, in the form of waste heat<\/strong>. This is found by subtracting the useful work output from the total heat input: ( 37.5 – 10 = 27.5 ) kW. This rejected heat needs to be dissipated effectively to maintain continuous engine operation.<\/p>\n\n\n\n These calculations are essential in understanding the effectiveness of real-world engines and are foundational to fields like mechanical engineering<\/strong>, energy management<\/strong>, and environmental engineering<\/strong>.<\/p>\n\n\n\n A heat engine develops 10 KW power when receiving heat at the rate of 2250 KJ\/min. Determine thermal efficiency and the rate of heat rejection. The correct answer and explanation is : However, I can still manually calculate and explain the solution for you step-by-step and generate an image to represent the question. Let\u2019s go […]<\/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-206700","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700","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=206700"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206700\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"