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

(Round off to nearest integer)

From the figure,

Work, W = 2P₀V₀

Heat given, Q_in = W_AB + W_BC ${\text{=\hspace{0.17em}n\hspace{0.17em}.\hspace{0.17em}C}}_{\text{V}}{\text{\hspace{0.17em}ΔT}}_{\text{AB}}{\text{\hspace{0.17em}+\hspace{0.17em}nC}}_{\text{P}}{\text{ΔT}}_{\text{BC}}$

$\text{=\hspace{0.17em}n\hspace{0.17em}}\frac{\text{3R}}{\text{2}}\left({\text{T}}_{\text{B}}{\text{-T}}_{\text{A}}\right)\text{+}\frac{\text{n5R}}{\text{2}}\left({\text{T}}_{\text{C}}{\text{-T}}_{\text{B}}\right)$

$(\therefore {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}C}}_{\text{V}}\text{=}\frac{\text{3R}}{\text{2}}{\text{and\hspace{0.17em}\hspace{0.17em}C}}_{\text{P}}\text{=}\frac{\text{5R}}{\text{2}})$

$\text{=}\frac{\text{3}}{\text{2}}\left({\text{P}}_{\text{B}}{\text{V}}_{\text{B}}{\text{-P}}_{\text{A}}{\text{V}}_{\text{A}}\right)\text{\hspace{0.17em}+\hspace{0.17em}}\frac{\text{5}}{\text{2}}\left({\text{P}}_{\text{C}}{\text{V}}_{\text{C}}{\text{-P}}_{\text{B}}{\text{V}}_{\text{B}}\right)$

$\text{=}\frac{\text{3}}{\text{2}}\times \left[{\text{3P}}_0{\text{V}}_0{\text{-P}}_0{\text{V}}_0\right]\text{\hspace{0.17em}+\hspace{0.17em}}\frac{\text{5}}{\text{2}}\left({\text{6P}}_{\text{0}}{\text{V}}_{\text{0}}{\text{-3P}}_{\text{0}}{\text{V}}_{\text{0}}\right)$

${\text{=\hspace{0.17em}3P}}_{\text{0}}{\text{V}}_{\text{0}}\text{+}\frac{\text{15}}{\text{2}}{\text{P}}_{\text{0}}{\text{V}}_{\text{0}}\text{=}\frac{\text{21}}{\text{2}}{\text{P}}_{\text{0}}{\text{V}}_{\text{0}}$

Efficiency$\text{η\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}}\frac{\text{W}}{{\text{Q}}_{\text{in}}}\text{=}\frac{{\text{2P}}_{\text{0}}{\text{V}}_{\text{0}}}{\frac{\text{21}}{\text{2}}{\text{P}}_{\text{0}}{\text{V}}_{\text{0}}}\text{=}\frac{\text{4}}{\text{21}}\Rightarrow \text{η\%=}\frac{\text{400}}{\text{21}}\approx \text{19}$