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JIPMER Jipmer Medical Solved Paper-2006

  • question_answer
    A perfect gas is found to obey the relation \[P{{V}^{3/2}}=\] constant during an adiabaric process. If such a gas initially at a temperature T, is compressed to half of its initial volume, then its final temperature will be:

    A) \[2T\]                   

    B)        \[4T\]                   

    C) \[{{(2)}^{1/2}}T\]                            

    D) \[2{{(2)}^{1/2}}T\]

    Correct Answer: C

    Solution :

    Gas obeys the equation \[P{{V}^{3/2}}=\] constant Comparing with\[P{{V}^{\gamma }}=\]constant      \[\gamma =\frac{3}{2}\] For adiabatic process \[{{T}_{1}}V_{1}^{\gamma -1}={{T}_{2}}V_{2}^{\gamma -1}\] \[T{{(V)}^{3/2-1}}={{T}_{2}}{{\left( \frac{V}{2} \right)}^{3/2-1}}\] \[{{T}_{2}}=T{{(2)}^{3/2-1}}\]      \[={{(2)}^{1/2}}T\]


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