A sample of gas at temperature T is adiabatically expanded to double… | MHT CET 2026 (13 Apr, Shift 2)

Q36MHT CET 2026 · 13 APR · SHIFT 2Medium

Thermodynamic Processes

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma = \frac{3}{2}$ ):

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Answer: (d)

Adiabatic: $TV^{\gamma-1} = \text{const}$ , so $T_2 = T\left(\frac{1}{2}\right)^{1/2} = \frac{T}{\sqrt{2}}$ .
Work by gas (taking 1 mole): $W = \frac{R(T_1 - T_2)}{\gamma - 1} = \frac{RT(1 - 1/\sqrt{2})}{1/2}$
$W = 2RT\left(1 - \frac{1}{\sqrt{2}}\right) = RT(2 - \sqrt{2})$
So the answer is (d) $W = RT[2 - \sqrt{2}]$ .

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