A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V , the efficiency of the engine is

During adiabatic expansion, temperature of the gas decreases.
\(\begin{aligned}
& \mathrm{TV}^{\gamma-1}=\text { constant .i.e. } \mathrm{T} \propto \frac{1}{\mathrm{~V}^{\gamma-1}} \\
\therefore \quad & \mathrm{~T}_{\mathrm{H}} \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_{\mathrm{C}} \mathrm{~V}_2^{\gamma-1}
\end{aligned}\)
As the gas is diatomic, \(\gamma=1.4\)
\(\begin{array}{ll}
\therefore & \frac{\mathrm{T}_{\mathrm{C}}}{\mathrm{~T}_{\mathrm{H}}}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)^{\gamma-1}=\left(\frac{1}{32}\right)^{1.4-1}=\frac{1}{4} \\
\therefore & \eta=1-\frac{\mathrm{T}_{\mathrm{C}}}{\mathrm{~T}_{\mathrm{H}}}=1-\frac{1}{4}=\frac{3}{4}=0.75
\end{array}\)