An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is

$\mathrm{A}\to \mathrm{B}:\mathrm{V}=\text{ (constant })$

$\Rightarrow {\mathrm{Q}}_{A\to B}={\mathrm{nC}}_{\mathrm{v}}\cdot \mathrm{\Delta T}=\mathrm{n}\left(\frac{3}{2}\mathrm{R}\right)\left(\mathrm{\Delta T}\right)=\frac{3}{2}\mathrm{nR}\left(\mathrm{\Delta T}\right)=\frac{3}{2}\left(\mathrm{\Delta P}\right)\mathrm{V}$

$\Rightarrow {\mathrm{Q}}_{A\to B}=3{\mathrm{P}}_0{\mathrm{V}}_0$

$\mathrm{B}\to \mathrm{C}:\mathrm{P}=\left(\text{ constant }\right)$

$\Rightarrow {\mathrm{Q}}_{\mathrm{B}\to \mathrm{C}}=n{C}_P\left(∆T\right)=n\left(\frac{5}{2}R\right)\left(∆T\right)=\frac{5}{2}nR\left(∆T\right)=\frac{5}{2}\times P\left(∆V\right)$

$\Rightarrow {\mathrm{Q}}_{\mathrm{B}\to \mathrm{C}}=\frac{15}{2}{P}_0{V}_0$

$W=area(\square ABCD)=2P_0{V}_0$

$\Rightarrow \eta =\frac{W}{Q_{in}}=\frac{W}{Q_{A\to B}+Q_{B\to C}}=\frac{4}{21}$