{"id":203743,"date":"2025-03-20T14:44:33","date_gmt":"2025-03-20T14:44:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=203743"},"modified":"2025-03-20T14:44:35","modified_gmt":"2025-03-20T14:44:35","slug":"the-ratio-of-specific-heat-cp-cv-of-nitrogen-n2-is-1-40","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/20\/the-ratio-of-specific-heat-cp-cv-of-nitrogen-n2-is-1-40\/","title":{"rendered":"The ratio of specific heat (Cp\/Cv) of Nitrogen N2 is 1.40"},"content":{"rendered":"\n

The ratio of specific heat (Cp\/Cv) of Nitrogen N2 is 1.40. Nitrogens gas constant is R = 296.8 [J\/kgK]. Determine the constant volume specific heat Cv and constant pressure specific heat Cp of Nitrogen.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the specific heats at constant volume ((C_v)) and constant pressure ((C_p)) for nitrogen ((N_2)), we use the following thermodynamic relations:<\/p>\n\n\n\n

    \n
  1. Ratio of Specific Heats (Given):<\/strong>
    [
    \\gamma = \\frac{C_p}{C_v} = 1.40
    ]<\/li>\n\n\n\n
  2. Gas Constant (Given):<\/strong>
    [
    R = 296.8 \\text{ J\/kgK}
    ]<\/li>\n\n\n\n
  3. Relationship Between Specific Heats and Gas Constant:<\/strong>
    [
    C_p – C_v = R
    ]<\/li>\n<\/ol>\n\n\n\n

    Step 1: Express ( C_p ) in Terms of ( C_v )<\/h3>\n\n\n\n

    From the definition of (\\gamma):<\/p>\n\n\n\n

    [
    C_p = \\gamma C_v
    ]<\/p>\n\n\n\n

    Substituting (\\gamma = 1.40):<\/p>\n\n\n\n

    [
    C_p = 1.40 C_v
    ]<\/p>\n\n\n\n

    Step 2: Solve for ( C_v )<\/h3>\n\n\n\n

    Using the equation (C_p – C_v = R):<\/p>\n\n\n\n

    [
    (1.40 C_v) – C_v = 296.8
    ]<\/p>\n\n\n\n

    [
    0.40 C_v = 296.8
    ]<\/p>\n\n\n\n

    [
    C_v = \\frac{296.8}{0.40} = 742 \\text{ J\/kgK}
    ]<\/p>\n\n\n\n

    Step 3: Solve for ( C_p )<\/h3>\n\n\n\n

    [
    C_p = 1.40 \\times 742 = 1038.8 \\text{ J\/kgK}
    ]<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n
      \n
    • Constant Volume Specific Heat ((C_v))<\/strong> = 742 J\/kgK<\/strong><\/li>\n\n\n\n
    • Constant Pressure Specific Heat ((C_p))<\/strong> = 1038.8 J\/kgK<\/strong><\/li>\n<\/ul>\n\n\n\n

      Explanation:<\/h3>\n\n\n\n

      The specific heats (C_p) and (C_v) are fundamental properties of gases. (C_v) represents the amount of heat required to raise the temperature of 1 kg of nitrogen by 1K at constant volume, whereas (C_p) represents the same process at constant pressure. The relationship (C_p – C_v = R) arises from the first law of thermodynamics applied to an ideal gas. Since nitrogen behaves as a diatomic ideal gas, its (\\gamma) value is typically around 1.40. By using this ratio and the given gas constant, we solve for (C_v) and then determine (C_p).<\/p>\n","protected":false},"excerpt":{"rendered":"

      The ratio of specific heat (Cp\/Cv) of Nitrogen N2 is 1.40. Nitrogens gas constant is R = 296.8 [J\/kgK]. Determine the constant volume specific heat Cv and constant pressure specific heat Cp of Nitrogen. The correct answer and explanation is : To determine the specific heats at constant volume ((C_v)) and constant pressure ((C_p)) for […]<\/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-203743","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203743","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=203743"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203743\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=203743"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=203743"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=203743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}