A Carnot engine $(\mathrm{E})$ is working between two temperatures 473 K and 273 K. In a new system two engines - engine $E_1$ works between 473 K to 373 K and engine $E_2$ works between 373 K to 273 K.
If $\eta_{12}, \eta_1$ and $\eta_2$ are the efficiencies of the engines $E, E_1$ and $E_2$, respectively, then

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Aicharya · Accepted Answer

Efficiencies of a carnot engine $\eta=1-\frac{T_{\text {sink }}}{T_{\text {source }}}$
$\begin{aligned}
\Rightarrow & \eta_1=1-\frac{373 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\ & \eta_2=1-\frac{273 \mathrm{~K}}{373 \mathrm{~K}}=\frac{100}{373} \\ & \eta_{12}=1-\frac{273 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\ & \eta_{12}-\eta_1=\frac{200}{473}-\frac{100}{473}=\frac{100}{473} < \frac{100}{373} \\ \Rightarrow & \eta_{12}-\eta_1 < \eta_2 \\ \text { or } & \eta_{12} < \eta_1+\eta_2
\end{aligned}$

A Carnot engine $(\mathrm{E})$ is working between two temperatures 473 K and 273 K. In a new system two…

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