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

    A)                 \[\frac{R}{(\gamma -1)}\]

    B)                 P V

    C)                 \[\frac{P\,V}{(\gamma -1)}\]

    D)                                            \[\frac{\gamma \,PV}{(\gamma -1)}\]

    Correct Answer: C

    Solution :

                    Change in internal energy is                 \[\Delta U=\frac{1}{(\gamma -1)}({{P}_{2}}{{V}_{2}}-{{P}_{1}}{{V}_{1}})\]                 Here,     \[{{V}_{1}}=V,\,{{V}_{2}}=2V\]                 \[\therefore \Delta U=\frac{1}{\gamma -1}[P\times 2V-P\times V]\]                 \[=\frac{1}{\gamma -1}\times PV\]                 \[=\frac{PV}{\gamma -1}\]                 Note:    The internal energy of an ideal gas depends only on its absolute temperature (T) and is directly proportional to T.

You need to login to perform this action.
You will be redirected in 3 sec spinner