An engine operates by taking a monatomic ideal gas through the...

$W = 2{P}_{0}{v}_{0}$

${Q}_{+} = {W}_{AB} + {W}_{BC}$

$= n . {c}_{v}{\Delta T}_{AB} + {nC}_{P}{\Delta T}_{B}C$

$= \dfrac{3}{2} \times \left[3{P}_{0}{v}_{0} - {P}_{0}{v}_{0}\right] + \dfrac{5}{2}\left[6{P}_{0}{V}_{0} - 3{P}_{0}{V}_{0}\right]$

$= 3{P}_{0}{V}_{0} + \dfrac{15}{2}{P}_{0}{V}_{0}$

$= \dfrac{21}{2}{P}_{0}{V}_{0}$

$η = \dfrac{W}{{Q}_{+}} = \dfrac{2{P}_{0}{V}_{0}}{\dfrac{21}{2}{P}_{0}{V}_{0}} = \dfrac{4}{21}$

$η$