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___

Total net work done during the cycle $$ABCD$$:

$$W_{\text{net}} = \text{Area of rectangle} = (3P_0 - P_0)(2V_0 - V_0) = 2P_0 V_0$$

Heat input $$Q_{\text{in}}$$ occurs during processes where temperature increases ($$AB$$ and $$BC$$):

$$Q_{AB} = nC_v \Delta T_{AB} = \frac{3}{2}V_0(3P_0 - P_0) = 3P_0 V_0$$

$$Q_{BC} = nC_p \Delta T_{BC} = \frac{5}{2}(3P_0)(2V_0 - V_0) = 7.5P_0 V_0$$

Total heat absorbed: $$Q_{\text{in}} = Q_{AB} + Q_{BC} = 3P_0 V_0 + 7.5P_0 V_0 = 10.5P_0 V_0$$

Calculating percentage efficiency:

$$\eta\% = \frac{W_{\text{net}}}{Q_{\text{in}}} \times 100\% = \frac{2P_0 V_0}{10.5P_0 V_0} \times 100\% = \frac{400}{21}\% \approx 19.05\%$$