The efficiency of an ideal gas with adiabatic exponent γ for the...

$\mathrm{As}, \mathrm{W}_{\mathrm{BC}}=\mathrm{p} \Delta$\mathrm{V}=\mathrm{nR}$\Delta \mathrm{T}=-\mathrm{nR}\left(2 \mathrm{~T}_0-\mathrm{T}_0\right)=\mathrm{nRT}_0$$\begin{aligned} & \text{ and } \quad \mathrm{W}_{\mathrm{CA}}=+2 \mathrm{nRT}_0 \ln 2 \\ & \text{ Work done }=\mathrm{W}_{\mathrm{CA}}+\mathrm{W}_{\mathrm{BC}} \\ & =2 \mathrm{nRT}_0 \ln 2-\mathrm{nRT}_0 \\ & =\operatorname{nRT}_0(2 \ln 2-1) \\ & \end{aligned}$$$Also, input heat,$\Delta \mathrm{Q}_{\mathrm{BC}}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}=\frac{\mathrm{nR} \gamma \mathrm{T}_0}{\gamma-1}$Efficiency$=\frac{\text{ Work }}{\text{ Input heat }}=\frac{(2 \ln 2-1)}{\gamma /(\gamma-1)}$