JEE Main & Advanced Physics Thermodynamical Processes Question Bank Topic Test - Thermodynamical Process (2021)

  • question_answer
    The specific heat of hydrogen gas at constant pressure is \[{{C}_{P}}=3.4\times {{10}^{3}}cal/kg{{\,}^{o}}C\] and at constant volume is \[{{C}_{V}}=2.4\times {{10}^{3}}cal/kg{{\,}^{o}}C.\]If one kilogram hydrogen gas is heated from \[{{10}^{o}}C\] to \[{{20}^{o}}C\] at constant pressure, the external work done on the gas to maintain it at constant pressure is

    A) \[{{10}^{5}}\,\]cal

    B) \[{{10}^{4}}\]cal

    C) \[{{10}^{3}}\] cal

    D) \[5\times {{10}^{3}}\]cal

    Correct Answer: B

    Solution :

    [b] From FLOT DQ = DU + DW
    Work done at constant pressure \[{{(\Delta W)}_{P}}={{(\Delta Q)}_{P}}-\Delta U\]
    \[{{(\Delta Q)}_{P}}-{{(\Delta Q)}_{V}}\]           (As we know \[{{(\Delta Q)}_{V}}=\Delta U\])
    Also \[{{(\Delta Q)}_{P}}=m{{c}_{P}}\Delta T\] and \[{{(\Delta Q)}_{V}}=m{{c}_{V}}\Delta T\]
    Þ \[{{(\Delta W)}_{P}}=m({{c}_{P}}-{{c}_{V}})\Delta T\]
                Þ \[{{(\Delta W)}_{P}}=1\times (3.4\times {{10}^{3}}-2.4\times {{10}^{3}})\times 10={{10}^{4}}cal\]

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