Helium gas goes through a cycle ABCDA (consisting of two isochoric...

Helium is mono atomic gas, for which
${C}_{V} = \dfrac{3}{2}R . {C}_{p} = \dfrac{5}{2}R$

Work done by the gas in one complete cycle $W =$ area $ABCDA = {p}_{0}{V}_{0}$

From $A$ to $B$, Heat given to gas $= n{C}_{V}\DeltaT$

$= 1 \times \left(\dfrac{3}{2}R\right) \times \DeltaT = \dfrac{3}{2}{V}_{0}\left(\Deltap\right) = \dfrac{3}{2}{V}_{0}{p}_{0}$

From $B$ to $C$, heat given to gas $= n{C}_{p}\DeltaT$

$= 1 \times \left(\dfrac{5}{2}R\right) \times \DeltaT = \dfrac{5}{2}\left(2{p}_{0}\right)\DeltaV = 5{p}_{0}{V}_{0}$

Efficiency of cycle $= \dfrac{Workdonebythegas / cycle}{Totalheatgiventogas / cycle}$

$= \dfrac{{p}_{0}{V}_{0}}{\dfrac{3}{2}{p}_{0}{V}_{0} + 5{p}_{0}{V}_{0}} = \dfrac{2}{13}$

Efficiency \left(%\right) = \dfrac{2}{13} \times 100 = 15 . 4 %