# An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ______. Option: 1 19 Option: 2 38 Option: 3 57 Option: 4 76

$\begin{array}{l} \mathrm{W}_{\mathrm{ABCDA}}=2 \mathrm{P}_{0} \mathrm{~V}_{0} \\ \mathrm{Q}_{\mathrm{in}}=\mathrm{Q}_{\mathrm{AB}}+\mathrm{Q}_{\mathrm{BC}} \\ \\ \mathrm{Q}_{\mathrm{AB}}=\mathrm{nC}\left(\mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}\right) \\ \\ =\frac{\mathrm{n} 3 \mathrm{R}}{2}\left(\mathrm{~T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}\right) \\ \\ =\frac{3}{2}\left(\mathrm{P}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}-\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}\right) \\ \\ =\frac{3}{2}\left(3 \mathrm{P}_{\mathrm{B}} \mathrm{V}_{0}=\mathrm{P}_{0} \mathrm{~V}_{0}\right)=3 \mathrm{P}_{0} \mathrm{~V}_{0} \\ \\ \mathrm{Q}_{\mathrm{BC}}=\mathrm{nC}_{\mathrm{P}}\left(\mathrm{T}_{\mathrm{C}}-\mathrm{T}_{\mathrm{B}}\right) \\\\ =\frac{\mathrm{n} 5 \mathrm{R}}{2}\left(\mathrm{~T}_{\mathrm{C}}-\mathrm{T}_{\mathrm{B}}\right) \end{array}$

$\begin{array}{l} =\frac{5}{2}\left(\mathrm{P}_{\mathrm{C}} \mathrm{V}_{\mathrm{C}}-\mathrm{P}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}\right) \\ \\ =\frac{5}{2}\left(6 \mathrm{P}_{0} \mathrm{~V}_{0}-3 \mathrm{P}_{0} \mathrm{~V}_{0}\right)=\frac{15}{2} \mathrm{P}_{0} \mathrm{~V}_{0} \\ \\ \eta=\frac{\mathrm{W}}{\mathrm{Q}_{\text {in }}} \times 100=\frac{2 \mathrm{P}_{0} \mathrm{~V}_{0}}{3 \mathrm{P}_{0} \mathrm{~V}_{0}+\frac{15}{2} \mathrm{P}_{0} \mathrm{~V}_{0}} \times 100 \\\\ \eta=\frac{400}{21}=19.04 \approx 19 \\\\ \mathrm{\eta}=19 \end{array}$

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