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A certain mass of an ideal gas at pressure \( P_{1} \) is
\( \mathrm{P} \) adiabatically expanded from an initial volume \( V_{1} \) to a final volume

W \( V_{2} \). The resulting pressure \( P_{2} \) of the gas is given by :
(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) \( P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\frac{\gamma}{\gamma-1}} \)
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