If T2 and T2′ are the respective temperatures of a gas undergoing adiabatic reversible and irreversible expansions from the volume V1 to V2 , which of the following facts holds good:where  γ is the ratio Cp,m/CV,m of the gas.

# If ${T}_{2}$ and ${T}_{2}^{\mathrm{\prime }}$ 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  $\gamma$ is the ratio ${C}_{p,\mathrm{m}}/{C}_{V,\mathrm{m}}$ of the gas.

1. A

${T}_{2}>{T}_{2}^{\mathrm{\prime }}$

2. B

${T}_{2}<{T}_{2}^{\mathrm{\prime }}$

3. C

${T}_{2}={T}_{2}^{\mathrm{\prime }}$

4. D

${V}_{1}{T}_{1}^{\gamma }={V}_{1}{T}_{2}^{\gamma }$

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### Solution:

The magnitude of work is larger in reversible expansion, hence, larger will be decrease in temperature, ${T}_{2}<{T}_{2}^{\mathrm{\prime }}$  