Physics - Heat & Thermo Question with Solution | TestHub

Work done in complete cycle $=$ Area under $\mathrm{P}-\mathrm{V}$ graph $={\mathrm{P}}_0{\mathrm{V}}_0$ from $A$ to $B$, heat given to the gas $={\mathrm{nC}}_{\mathrm{v}}\Delta \mathrm{T}=\mathrm{n}\frac{3}{2}\mathrm{R}\Delta \mathrm{T}=\frac{3}{2}{\mathrm{V}}_0\Delta \mathrm{P}=\frac{3}{2}{\mathrm{P}}_0{\mathrm{V}}_0$ from $B$ to $C$, heat given to the system $=n{C}_{\mathrm{p}}\Delta \mathrm{T}=\mathrm{n}\left(\frac{5}{2}\mathrm{R}\right)\Delta \mathrm{T}$ $=\frac{5}{2}\left(2{\mathrm{P}}_0\right)\Delta \mathrm{V}=5{\mathrm{P}}_0{\mathrm{V}}_0$ from $C$ to $D$ and $D$ to $A$, heat is rejected. $\text{ efficiency, }\eta =\frac{\text{ work done by gas }}{\text{ heat given to the gas }}\times 100$ $\eta =\frac{P_0{V}_0}{\frac{3}{2}{P}_0{V}_0+5P_0{V}_0}=15.4\%$