Suppose that two heat engines are connected in series, such that the heat released by the first engine is used as the heat absorbed by the second engine, as shown in figure. The efficiencies of the engines are $\epsilon_1$ and $\epsilon_2$, respectively. The net efficiency of the combination is given by :
Diffcult
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$e_{1}=\frac{\omega_{1}}{\theta_{\mathrm{req}}}$ $...(1)$
$\mathrm{e}_{2}=\frac{\omega_{2}}{\theta_{1}}$ $...(2)$
$e_{\text {net }}=\frac{\omega_{1}+\omega_{2}}{\theta_{\text {req }}}$
substituting $e_{1}$ and $e_{2}$ from equation
$(1)$ and $( 2)$
$e_{\mathrm{net}}=\frac{\theta_{\mathrm{req}} \mathrm{e}_{1}+\theta_{\mathrm{req}} \mathrm{e}_{2}-\omega_{1} \mathrm{e}_{2}}{\theta_{\mathrm{req}}}$
$e_{n e t}=e_{1}+e_{2}-e_{1} e_{2}$
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