A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines – engine E₁ works between 473K to 373K and engine E₂ works between 373K to 273K. If $η_{12}$ , $η_{1}$ and $η_{2}$ are the efficiencies of the engines E, E₁ and E₂, respectively, then

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$η_{12} \geq η_{1} + η_{2}$

$η_{12} = η_{1} + η_{2}$

$η_{12} < η_{1} + η_{2}$

$η_{12} = η_{1} η_{2}$

answer is A.

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Detailed Solution

$\begin{aligned} η_{12} = 1 - \frac{273}{473} = \frac{200}{473} = 0.423 \\ η_{1} = 1 - \frac{373}{473} = \frac{100}{473} = 0.211 \\ η_{2} = 1 - \frac{273}{373} = \frac{100}{373} = 0.268 \end{aligned}$

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