{"id":149392,"date":"2022-03-21T10:18:40","date_gmt":"2022-03-21T04:48:40","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/heat-capacity-relation-between-cp-and-cv-derivation-and-equations\/"},"modified":"2024-01-16T13:09:11","modified_gmt":"2024-01-16T07:39:11","slug":"heat-capacity-relation-between-cp-and-cv-derivation-and-equations","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/","title":{"rendered":"Heat Capacity &#8211; Relation between Cp and Cv | Derivation and Equations"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#Define_Heat_Capacity\" title=\"Define Heat Capacity\">Define Heat Capacity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#What_are_Heat_Capacity_C_Cp_and_Cv\" title=\"What are Heat Capacity C, Cp, and Cv?\">What are Heat Capacity C, Cp, and Cv?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#Heat_Capacity_Ratio\" title=\"Heat Capacity Ratio\">Heat Capacity Ratio<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#Why_Cp_Greater_than_Cv\" title=\"Why Cp Greater than Cv?\">Why Cp Greater than Cv?<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#P_CvCp_ln_TT0\" title=\"P = (Cv\/Cp) ( ln (T\/T0))\">P = (Cv\/Cp) ( ln (T\/T0))<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/chemistry\/heat-capacity\/#P_CvCp_ln_TT0-2\" title=\"P = (Cv\/Cp) ( ln (T\/T0))\">P = (Cv\/Cp) ( ln (T\/T0))<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Define_Heat_Capacity\"><\/span>Define Heat Capacity<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Heat Capacity &#8211; Relation between Cp and Cv: Heat capacity is the amount of heat required to raise the temperature of a substance by 1 Kelvin. It usually measured in Joules per Kelvin (J\/K).<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-149391 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/heat-capacity-relation-between-cp-and-cv-derivation-and-equations.jpg\" alt=\"Heat Capacity - Relation between Cp and Cv | Derivation and Equations\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/heat-capacity-relation-between-cp-and-cv-derivation-and-equations.jpg?v=1647838115 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/heat-capacity-relation-between-cp-and-cv-derivation-and-equations-300x212.jpg?v=1647838115 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Heat_Capacity_C_Cp_and_Cv\"><\/span>What are Heat Capacity C, Cp, and Cv?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In physics, the heat capacity (symbol: C) of an object the measure of the amount of heat required to raise the temperature of the object by one unit of temperature. The SI unit of heat capacity is the joule per kelvin (J\/K). The heat capacity of an object can also defined as the amount of energy required to raise the temperature of the object by 1\u00b0C.<\/p>\n<p>An object determined by the type of material the object made of and the size of the object. The heat capacity of a material determined by the amount of energy required to raise the temperature of a unit of the material by 1\u00b0C. The heat capacity of an object also proportional to the object&#8217;s mass.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Heat_Capacity_Ratio\"><\/span>Heat Capacity Ratio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The heat capacity ratio is the ratio of the heat capacities of two substances. It used to measure the thermal conductivity of a material. Therefore the  higher the heat capacity ratio, the better the material is at transferring heat.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Why_Cp_Greater_than_Cv\"><\/span>Why Cp Greater than Cv?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>The Clausius-Clapeyron equation states that the slope of the vapor pressure curve of a liquid proportional to the reciprocal of the absolute temperature. In other words, as the temperature of a liquid increases, the vapor pressure of the liquid also increases. The Clausius-Clapeyron equation is used to calculate the vapor pressure of a liquid as a function of temperature.<\/li>\n<li>Therefore Clausius-Clapeyron equation can rearranged to solve for the vapor pressure of a liquid as a function of temperature:<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"P_CvCp_ln_TT0\"><\/span>P = (Cv\/Cp) ( ln (T\/T0))<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>where P is the vapor pressure of the liquid, Cv is the heat capacity of the vapor, and also Cp is the heat capacity of the liquid.<\/p>\n<ul>\n<li>The Clausius-Clapeyron equation used to calculate the vapor pressure of a liquid as a function of temperature.<\/li>\n<li>The Clausius-Clapeyron equation can rearranged to solve for the vapor pressure of a liquid as a function of temperature:<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"P_CvCp_ln_TT0-2\"><\/span>P = (Cv\/Cp) ( ln (T\/T0))<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>where P is the vapor pressure of the liquid, Cv is the heat capacity of the vapor, and  also Cp is the heat capacity of the liquid.<\/li>\n<li>When the temperature of a liquid increased, the vapor pressure of the liquid also increases. The Clausius-Clapeyron<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Define Heat Capacity Heat Capacity &#8211; Relation between Cp and Cv: Heat capacity is the amount of heat required to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Heat Capacity - Relation between Cp and Cv","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Heat Capacity - Relation between Cp and Cv. 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