It is defined as ratio of net mechanical work done per cycle by the gas to the amount of heat energy absorbed per cycle from the source.
In isothermal process P1V1 = P2V2 …(1)
As B(V2, P2) and C(V3, P3) lie on same adiabatic
P2\(V_{2}^{\gamma}\) = P3\(V_{3}^{\gamma}\) …(2)
Again C and D lie on same isothermal
P3V3 = P4V4 …(3)
Finally D and A lie on same adiabatic
P4\(V_{4}^{\gamma}\) = P1\(V_{1}^{\gamma}\) …(4)
Multiplying (1), (2), (3), (4),
\(V_{2}^{\gamma-1}\)\(V_{4}^{\gamma-1}\)=\(V_{1}^{\gamma-1}\)\(V_{3}^{\gamma-1}\)
(V2V4) = (V1V3)
V2V4 = V1V3
\(\frac{V_2}{V_1}\)=\(\frac{V_3}{V_4}\)
Loge\(\frac{V_2}{V_1}\)=Loge\(\frac{V_3}{V_4}\)
Dividing (4) by (2),
\(\frac{Q_2}{Q_1}\)=\(\frac{KT_2log_e\frac{V_3}{V_4}}{KT_1log_e\frac{V_2}{V_1}}\)
=\(\frac{T_2}{T_1}\)
\(\frac{Q_2}{Q_1}\)=\(\frac{T_2}{T_1}\)
η=1-\(\frac{T_2}{T_1}\)
