A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\right.$ given, $\left.\gamma=\frac{3}{2}\right)$ :
JEE MAIN 2023, Medium
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$T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$
$T V^{1 / 2}=T_2(2 V)^{1 / 2}$
$T_2=\frac{T}{\sqrt{2}}$
$W=\frac{R\left(T_1-T_2\right)}{\gamma-1}=\frac{R\left(T-\frac{T}{\sqrt{2}}\right)}{\frac{1}{2}}=R T(2-\sqrt{2})$
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