In $1^{\text {st }}$ case, Carnot engine operates between temperatures $300\,K$ and $100\,K$. In $2^{\text {nd }}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\text {ad }}$ case) will be.
JEE MAIN 2022, Medium
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First case : $\eta=1-\frac{100}{300}=\frac{2}{3}$
Second case : $\eta_{\text {net }}=\eta_{1}+\eta_{2}-\eta_{1} \eta_{2}$
$\eta_{1}=1-\frac{200}{300}=\frac{1}{3}$
$\eta_{2}=1-\frac{100}{200}=\frac{1}{2}$
$\eta_{\text {net }}=\frac{1}{3}+\frac{1}{2}-\frac{1}{6}=\frac{2}{3}$
$\eta$ (first case) $=\eta$ (second case)
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