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JCECE Engineering JCECE Engineering Solved Paper-2011

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

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

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

    C)  \[\frac{5}{3}R\]                                               

    D)  \[\frac{6}{5}R\]

    Correct Answer: B

    Solution :

    From the first law of thermodynamic                 \[du=dQ-dW\]                 \[=Q-\frac{Q}{4}=\frac{3Q}{4}\] Also,      \[dU={{C}_{V}}dT=\left( \frac{5}{2}R \right)dT\] For diatomic gas,\[dT=\left( \frac{2}{5}R \right)dU\]                 \[=\frac{2}{5R}\times \frac{3Q}{4}=\frac{3Q}{10R}\] Molar heat capacity                 \[C=\frac{dQ}{dT}=\frac{Q}{3Q/10R}=\frac{10R}{3}\]


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