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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Critical Thinking

  • 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 :

                       \[dU={{C}_{V}}dT=\left( \frac{5}{2}R \right)dT\]or \[dT=\frac{2(dU)}{5R}\]                                       ?..(i)                    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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