Q. A certain mass of an ideal gas at pressure $P_{1}$ is adiabatically expanded from an initial volume $V_{1}$ to a final volume $V_{2}$. The resulting pressure $P_{2}$ of the gas is given by :

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A

$P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma}$

B

$P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{1 / \gamma}$

C

$P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\frac{\gamma-1}{\gamma}}$

D

$P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\frac{\gamma}{\gamma-1}}$

Solution:

For $P V^{\gamma} $= constant
$P_{1} V_{1}^{\gamma} =P_{2} V_{2}^{\gamma}$
$P_{2} =P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma}$

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