Suppose that two heat engines are connected in series, such that the heat exhaust of the first engine is used as the heat input of the second engine as shown in figure. The efficiencies of the engines are $\eta_1$ and $\eta_2$, respectively. The net efficiency of the combination is given by
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$ \eta_{net} $$=\frac{\omega_1+\omega_2}{\theta_1}$
$ \eta_1=$$ \frac{w_1}{\theta_1} \eta_2=\frac{w_2}{\theta_2} $
$ \eta_{\eta_{e t}}$$=\frac{\eta_1 q_1+\eta_2 q_2}{\theta_1} $
Now, $=1-\frac{\theta_2}{\theta_1} $
$ \frac{\theta_2}{\theta_1} $$=1-\eta_1 $
$ \eta_{net} $$=n_1+\left(1-\eta_1\right) \eta_2 $
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