{"id":249661,"date":"2025-07-09T18:28:57","date_gmt":"2025-07-09T18:28:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249661"},"modified":"2025-07-09T18:28:59","modified_gmt":"2025-07-09T18:28:59","slug":"specific-heat-capacity-of-water-4186-j-kg-1-k-1","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/specific-heat-capacity-of-water-4186-j-kg-1-k-1\/","title":{"rendered":"Specific heat capacity of water = 4186 J kg^-1 K^-1"},"content":{"rendered":"\n<p>Specific heat capacity of water = 4186 J kg^-1 K^-1 Specific heat capacity of ice = 2090 J kg^-1 K^-1 Latent heat of fusion of ice = 335 kJ kg^-1 Latent heat of vaporization of water = 2260 kJ kg^-1 Question: You have 3 kg of ice at -20\u00c2\u00b0C. (i) How much heat is needed to raise the temperature of the ice from -20\u00c2\u00b0C to 0\u00c2\u00b0C? (ii) How much heat is needed to melt all the ice at 0\u00c2\u00b0C to water? (iii) If 1&#215;10^6 J of heat is added to the ice at -20\u00c2\u00b0C, will the ice melt? Explain:<\/p>\n\n\n\n<p><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<p>Let&#8217;s break down each part of the problem step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Heat needed to raise the temperature of ice from -20\u00b0C to 0\u00b0C<\/h3>\n\n\n\n<p>The heat required to change the temperature of a substance is given by the equation: Q=mc\u0394TQ = mc\\Delta TQ=mc\u0394T<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>QQQ is the heat required (in joules, J),<\/li>\n\n\n\n<li>mmm is the mass of the substance (in kg),<\/li>\n\n\n\n<li>ccc is the specific heat capacity of the substance (in J kg\u22121^{-1}\u22121 K\u22121^{-1}\u22121),<\/li>\n\n\n\n<li>\u0394T\\Delta T\u0394T is the change in temperature (in \u00b0C or K).<\/li>\n<\/ul>\n\n\n\n<p>Here:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass of ice, m=3m = 3m=3 kg,<\/li>\n\n\n\n<li>Specific heat capacity of ice, c=2090c = 2090c=2090 J kg\u22121^{-1}\u22121 K\u22121^{-1}\u22121,<\/li>\n\n\n\n<li>Change in temperature, \u0394T=0\u00b0C\u2212(\u221220\u00b0C)=20\u00b0C\\Delta T = 0\u00b0C &#8211; (-20\u00b0C) = 20\u00b0C\u0394T=0\u00b0C\u2212(\u221220\u00b0C)=20\u00b0C.<\/li>\n<\/ul>\n\n\n\n<p>Substituting these values into the formula: Q=3\u00d72090\u00d720=125400&nbsp;JQ = 3 \\times 2090 \\times 20 = 125400 \\text{ J}Q=3\u00d72090\u00d720=125400&nbsp;J<\/p>\n\n\n\n<p>So, the heat required to raise the temperature of the ice from -20\u00b0C to 0\u00b0C is <strong>125400 J<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Heat needed to melt all the ice at 0\u00b0C<\/h3>\n\n\n\n<p>The heat required to melt ice is given by the equation: Q=mLfQ = mL_fQ=mLf\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>QQQ is the heat required (in joules, J),<\/li>\n\n\n\n<li>mmm is the mass of the substance (in kg),<\/li>\n\n\n\n<li>LfL_fLf\u200b is the latent heat of fusion (in J kg\u22121^{-1}\u22121).<\/li>\n<\/ul>\n\n\n\n<p>Here:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass of ice, m=3m = 3m=3 kg,<\/li>\n\n\n\n<li>Latent heat of fusion of ice, Lf=335\u00d7103L_f = 335 \\times 10^3Lf\u200b=335\u00d7103 J kg\u22121^{-1}\u22121.<\/li>\n<\/ul>\n\n\n\n<p>Substituting these values into the formula: Q=3\u00d7335\u00d7103=1005000&nbsp;JQ = 3 \\times 335 \\times 10^3 = 1005000 \\text{ J}Q=3\u00d7335\u00d7103=1005000&nbsp;J<\/p>\n\n\n\n<p>So, the heat required to melt all the ice at 0\u00b0C is <strong>1005000 J<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) Will the ice melt if 1&#215;10^6 J of heat is added?<\/h3>\n\n\n\n<p>To check if the ice will melt, we need to compare the total heat required to raise the temperature of the ice to 0\u00b0C and then melt it. From part (i) and part (ii), we have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Heat required to raise the temperature from -20\u00b0C to 0\u00b0C: <strong>125400 J<\/strong>,<\/li>\n\n\n\n<li>Heat required to melt the ice at 0\u00b0C: <strong>1005000 J<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Total heat required: 125400&nbsp;J+1005000&nbsp;J=1130400&nbsp;J125400 \\text{ J} + 1005000 \\text{ J} = 1130400 \\text{ J}125400&nbsp;J+1005000&nbsp;J=1130400&nbsp;J<\/p>\n\n\n\n<p>Now, if only <strong>1 \\times 10^6 J<\/strong> of heat is provided, it is less than the <strong>1130400 J<\/strong> required. Therefore, the ice will not melt completely with 1 million joules of heat.<\/p>\n\n\n\n<p><strong>Conclusion:<\/strong> 1 million joules of heat will be enough to raise the temperature of the ice from -20\u00b0C to 0\u00b0C, but it will not be enough to melt all the ice. The remaining heat will still be required to overcome the latent heat of fusion and melt the ice.<\/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-banner6-24.jpeg\" alt=\"\" class=\"wp-image-249662\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Specific heat capacity of water = 4186 J kg^-1 K^-1 Specific heat capacity of ice = 2090 J kg^-1 K^-1 Latent heat of fusion of ice = 335 kJ kg^-1 Latent heat of vaporization of water = 2260 kJ kg^-1 Question: You have 3 kg of ice at -20\u00c2\u00b0C. (i) How much heat is needed [&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-249661","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249661","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=249661"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}