
A monoatomic ideal gas goes through a cyclic process as shown in the figure. The efficiency of this process is

- $19.04 \%$
- $42 \%$
- $62 \%$
- $21 \%$
Solution

Work done in complete cycle $=$ Area under closed curve $=2 P V$ Heat given to the system from $A$ to $B=n C_V \Delta T$ $ =n \frac{3}{2} R \Delta T=\frac{3}{2} \times V \times \Delta P=\frac{3}{2} \times V \times(3 P-P)=3 P V $ Similarly, heat given to the system from $B$ to $C$ $ \begin{aligned} & =n C_P \Delta T \\ & =n\left(\frac{5}{2} R\right) \Delta T=\frac{5}{2}(3 P)(\Delta V) \\ & =\frac{5}{2} \times(3 P) \cdot(2 V-V)=\frac{15}{2} P V \end{aligned} $ The heat is released from $C$ to $D$ and $D$ to $A$. Efficiency $(\eta)=\frac{\text { Work done by gas }}{\text { Heat given to gas }} \times 100$ $ =\frac{2 P V}{3 P V+\frac{15}{2} P V} \times 100=\frac{4}{21} \times 100=19.04 \% $
Asked in: AP EAMCET 2017 (26 Apr Shift 1)