In an adiabatic change for an ideal gas, show that the work done in an adiabatic expansion

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In an adiabatic change for an ideal gas, show that the work done in an adiabatic expansion

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

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