{"id":258426,"date":"2025-07-18T06:54:33","date_gmt":"2025-07-18T06:54:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258426"},"modified":"2025-07-18T06:54:35","modified_gmt":"2025-07-18T06:54:35","slug":"a-cube-at-112-c-radiates-heat-at-a-rate-of-92-j-s","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/a-cube-at-112-c-radiates-heat-at-a-rate-of-92-j-s\/","title":{"rendered":"A cube at 112 \u00b0C radiates heat at a rate of 92 J\/s."},"content":{"rendered":"\n<p>A cube at 112 \u00b0C radiates heat at a rate of 92 J\/s. If its surface temperature is increased to 196 \u00b0C, the rate at which it will now radiate is closest to<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The rate at which an object radiates heat is governed by the Stefan-Boltzmann law, which states:P=\u03c3AT4P = \\sigma A T^4P=\u03c3AT4<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PPP is the power radiated (in watts or joules per second, J\/s),<\/li>\n\n\n\n<li>\u03c3\\sigma\u03c3 is the Stefan-Boltzmann constant (5.67\u00d710\u22128\u2009W\/m2K4)(5.67 \\times 10^{-8} \\, \\text{W\/m}^2 \\text{K}^4)(5.67\u00d710\u22128W\/m2K4),<\/li>\n\n\n\n<li>AAA is the surface area of the object,<\/li>\n\n\n\n<li>TTT is the absolute temperature in Kelvin (K).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Key Idea:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The rate of heat radiation is proportional to the <strong>fourth power<\/strong> of the temperature.<\/li>\n\n\n\n<li>The temperatures need to be converted into <strong>Kelvin<\/strong> before using the Stefan-Boltzmann law.<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial temperature: T1=112\u2218C=112+273.15=385.15\u2009KT_1 = 112^\\circ C = 112 + 273.15 = 385.15 \\, KT1\u200b=112\u2218C=112+273.15=385.15K<\/li>\n\n\n\n<li>Final temperature: T2=196\u2218C=196+273.15=469.15\u2009KT_2 = 196^\\circ C = 196 + 273.15 = 469.15 \\, KT2\u200b=196\u2218C=196+273.15=469.15K<\/li>\n\n\n\n<li>Initial power radiated: P1=92\u2009J\/sP_1 = 92 \\, J\/sP1\u200b=92J\/s<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Process:<\/h3>\n\n\n\n<p>The power radiated is proportional to the fourth power of the temperature:P2P1=(T2T1)4\\frac{P_2}{P_1} = \\left( \\frac{T_2}{T_1} \\right)^4P1\u200bP2\u200b\u200b=(T1\u200bT2\u200b\u200b)4<\/p>\n\n\n\n<p>Substitute the known values:P292=(469.15385.15)4\\frac{P_2}{92} = \\left( \\frac{469.15}{385.15} \\right)^492P2\u200b\u200b=(385.15469.15\u200b)4<\/p>\n\n\n\n<p>First, calculate the ratio of temperatures:469.15385.15\u22481.219\\frac{469.15}{385.15} \\approx 1.219385.15469.15\u200b\u22481.219<\/p>\n\n\n\n<p>Raise this ratio to the fourth power:1.2194\u22482.0731.219^4 \\approx 2.0731.2194\u22482.073<\/p>\n\n\n\n<p>Thus,P2=92\u00d72.073\u2248190.7\u2009J\/sP_2 = 92 \\times 2.073 \\approx 190.7 \\, \\text{J\/s}P2\u200b=92\u00d72.073\u2248190.7J\/s<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The rate at which the cube will radiate heat when its surface temperature is increased to 196 \u00b0C is approximately <strong>191 J\/s<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-908.jpeg\" alt=\"\" class=\"wp-image-258429\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A cube at 112 \u00b0C radiates heat at a rate of 92 J\/s. If its surface temperature is increased to 196 \u00b0C, the rate at which it will now radiate is closest to The Correct Answer and Explanation is: The rate at which an object radiates heat is governed by the Stefan-Boltzmann law, which states:P=\u03c3AT4P [&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-258426","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258426","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=258426"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258426\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}