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AMU Medical AMU Solved Paper-1996

  • question_answer
    An ideal gas with pressure\[{{P}_{1}},\]volume V and temperature T is expanded isothermally to a volume\[2V\]and a final pressure P. The same gas is expanded adiabatically to a volume 2V, the final pressure is\[{{P}_{A}}\]. In terms of the ratio of the two specific heats for the gas\[\gamma \]the ration\[{{P}_{1}}/{{P}_{A}}\]is

    A)  \[{{2}^{\gamma -1}}\]

    B)  \[{{2}^{1-\gamma }}\]

    C)  \[2\gamma \]

    D)  \[{{2}^{\gamma }}\]

    Correct Answer: D

    Solution :

    : For adiabatic change,\[P{{V}^{\gamma }}=\]constant. \[\therefore \] \[{{P}_{1}}{{V}^{\gamma }}={{P}_{A}}{{(2V)}^{\gamma }}\] or \[{{P}_{1}}{{V}^{\gamma }}={{P}_{A}}{{2}^{\gamma }}{{V}^{\gamma }}\] or \[{{P}_{1}}={{P}_{A}}{{2}^{\gamma }}\] or \[\frac{{{P}_{1}}}{{{P}_{A}}}={{2}^{\gamma }}\]


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