An engine operates by taking \(n\,moles\) of an ideal gas through the cycle \(ABCDA\) shown in figure. The thermal efficiency of the engine is : (Take \(C_v =1 .5\, R\), where \(R\) is gas constant)

According to principle of calorimetry

Heat given\( = {Q_{AB}} = {Q_{BC}}\)

\( = n{C_V}d{T_{AB}} + n{C_p}d{T_{BC}}\)

\( = \frac{3}{2}\left( {nR{T_B} - nR{T_A}} \right) + \frac{5}{2}\left( {nR{T_C} - nR{T_B}} \right)\)

\( = \frac{3}{2}\left( {2{P_0}{V_0} - {P_0}{V_0}} \right) + \frac{5}{2}\left( {4{P_0}{V_0} - 2{P_{.0}}{V_0}} \right)\)

\( = \frac{{13}}{2}{P_0}{V_0}\)

Thermal efficiency of engine \(\left( \eta  \right)\)

\( = \frac{W}{{{Q_{given}}}} = \frac{2}{{13}} = 0.15\)