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Uttarakhand PMT Uttarakhand PMT Solved Paper-2004

  • question_answer
    If the ratio of specific heats of a gas at constant pressure to that at constant volume is \[\text{ }\!\!\gamma\!\!\text{ ,}\] the change in internal energy of a gas, when the volume changes from V to 2V at constant pressure P, is :

    A)   PV

    B)  \[\frac{\text{R}}{\text{ }\!\!\gamma\!\!\text{ -1}}\]  

    C)  \[\frac{PV}{\gamma -1}\]

    D)  \[\frac{\text{ }\!\!\gamma\!\!\text{ PV}}{\text{ }\!\!\gamma\!\!\text{ -1}}\]

    Correct Answer: C

    Solution :

     The change in internal energy at constant pressure is \[dV=\frac{1}{\gamma -1}({{P}_{2}}{{V}_{2}}-{{P}_{1}}{{V}_{1}})\] \[=\frac{1}{\gamma -1}[P\times 2V-P\times V]\] \[=\frac{PV}{\gamma -1}\]


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