If $T_{2}$ and $T_{2}^{'}$ are the respective temperatures of a gas undergoing adiabatic reversible and irreversible expansions from the volume $V_{1}$ to $V_{2}$ , which of the following facts holds good:
where $γ$ is the ratio $C_{p, m} / C_{V, m}$ of the gas.

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$V_{1} T_{1}^{γ} = V_{1} T_{2}^{γ}$

$T_{2} > T_{2}^{'}$

$T_{2} < T_{2}^{'}$

$T_{2} = T_{2}^{'}$

answer is B.

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Detailed Solution

The magnitude of work is larger in reversible expansion, hence, larger will be decrease in temperature, $T_{2} < T_{2}^{'}$

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