JEE Main & Advanced Physics Thermodynamical Processes Question Bank Topic Test - Thermodynamical Processes

  • question_answer
    A gas expands adiabatically at constant pressure such that its temperature \[T\,\propto \,a/\sqrt{V}.\] The value of \[\gamma =({{C}_{p}}/{{C}_{V}})\] of the gas is

    A) 1.30     

    B) 1.50

    C) 1.67

    D) 2.00

    Correct Answer: B

    Solution :

    [b] In adiabatic expansion,
                \[p{{V}^{\gamma }}=\,\]constant put \[p=\,\frac{RT}{V}\]
                            \[\left( \frac{RT}{V} \right)\,{{V}^{\gamma }}=\,\,\text{constant}\,\,\]
                \[T{{V}^{\gamma -1}}=\]constant or \[T\propto \,{{V}^{1-\gamma }}\]
                \[\because \]     \[T\propto \,\frac{1}{\sqrt{V}}\]
                \[\therefore \]    \[1-\gamma =-\frac{1}{2}\]
                or         \[\gamma =1+\frac{1}{2}\,=\frac{3}{2}\,=1.5\]

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