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VMMC VMMC Medical Solved Paper-2009

  • question_answer
    The molar heat capacity in a process of a  diatomic gas, if it does a work of \[\frac{Q}{4}\] when a heat of Q is supplied to it is

    A)  \[\frac{2R}{5}\]               

    B)                                                        \[\frac{5R}{2}\]                

    C)                         \[\frac{10R}{3}\]                                             

    D)                        \[\frac{6R}{7}\]

    Correct Answer: C

    Solution :

    \[dU={{C}_{V}}dT=\left[ \frac{5}{2}R \right]dT\] \[\Rightarrow \]               \[dT=\frac{2(dU)}{5R}\] From first law of thermodynamics \[dU=dQ-dW=Q-\frac{Q}{4}=\frac{3Q}{4}\] Now, molar heat capacity \[C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}=\frac{5RQ}{2\left[ \frac{3Q}{4} \right]}=\frac{10}{3}R\]


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