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JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    The molar specific heats of an ideal gas at constant pressure and volume are denoted by \[{{C}_{p}}\] and\[{{C}_{v}}\], respectively. If \[\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}\] and R is the universal gas constant, then Cy is equal to

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

    B) \[\frac{\left( \gamma -1 \right)}{R}\]

    C) \[\gamma R\]     

    D) \[\frac{1+\gamma }{1-\gamma }\]

    Correct Answer: A

    Solution :

    [a] \[{{C}_{p}}-{{C}_{v}}=R\Rightarrow {{C}_{p}}={{C}_{v}}+R\] \[\because \,\,\,\,\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{{{C}_{v}}+R}{{{C}_{p}}}=\frac{{{C}_{v}}}{{{C}_{v}}}+\frac{R}{{{C}_{v}}}\] \[\Rightarrow \gamma =1+\frac{R}{{{C}_{v}}}\Rightarrow \frac{R}{{{C}_{v}}}=\gamma -1\Rightarrow {{C}_{v}}\] \[=\frac{R}{\gamma -1}\]


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