Question

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ______.

Answer 1

From the figure,
Work, $W=(3P_0-P_0)(2V_0-V_0)=2P_0{V}_0$

Heat given, $Q_{in}=Q_{AB}+Q_{BC}=n{C}_V\Delta T_{AB}+n{C}_p\Delta T_{BC}$

$=n\frac{3R}{2}(T_B-T_A)+n\frac{5R}{2}(T_C-T_B)$

$(\because C_v=\frac{3R}{2}\text{and}{C}_P=\frac{5R}{2})$

$=\frac{3}{2}(P_B{V}_B-P_A{V}_A)+\frac{5}{2}(P_C{V}_C-P_B{V}_B)$

$=\frac{3}{2}\times [3P_0{V}_0-P_0{V}_0]+\frac{5}{2}[6P_0{V}_0-3P_0{V}_0]$

$=3P_0{V}_0+\frac{15}{2}{P}_0{V}_0=\frac{21}{2}{P}_0{V}_0$

Efficiency, $\eta =\frac{W}{Q_{in}}=\frac{2P_0{V}_0}{\frac{21}{2}}=\frac{4}{21}$

$\eta \%=\frac{400}{21}\approx 19$