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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2010

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

    B)  \[\frac{5}{2}R\]

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

    D)         \[\frac{6}{7}R\]

    Correct Answer: C

    Solution :

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


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