A perfect gas is found to obey the relation $PV^{3/2} =$ constant, during an adiabatic process. If such a gas, initially at a temperature $T$, is compressed adiabatically to half its initial volume, then its final temperature will be

  • A

    $2\,\,T$

  • B

    $4\,\,T$

  • C

    $\sqrt 2 \,\,T$

  • D

    $2\sqrt 2 \,\,T$

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