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

  • question_answer
    Certain perfect gas is found to obey \[P{{V}^{3/2}}=\] constant during adiabatic process. If such a gas at initial temperature T is adiabatically compressed to half the initial volume, its final temperature will be

    A) \[\sqrt{2}\,\cdot T\]

    B) 2T

    C) \[2\sqrt{2}\,\cdot T\]

    D) 4T

    Correct Answer: A

    Solution :

    [a] \[P{{V}^{3/2}}=\] Constant, \[PV=RT\] or \[P=\frac{RT}{V};\]
    \[\left( \frac{RT}{V} \right)\times {{V}^{3/2}}=\] Constant or \[T{{V}^{1/2}}=\] Constant.
    \[\therefore \] Thus V changes to V/2, the temp. becomes \[\sqrt{2T}\].


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