In 1^st case, Carnot engine operates between temperatures 300 K and 100 K. In 2^nd case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2^nd case) will be :

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may increase or decrease with respect to the 1^st case

always greater than the 1^st case

same as the 1^st case

always less than the 1^st case

answer is A.

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Detailed Solution

First case : $η = 1 - \frac{100}{300} = \frac{2}{3}$

Second case : $η_{net} = η_{1} + η_{2} - η_{1} η_{2}$

$\begin{array}{l} η_{1} = 1 - \frac{200}{300} = \frac{1}{3} \\ η_{2} = 1 - \frac{100}{200} = \frac{1}{2} \\ η_{net} = \frac{1}{3} + \frac{1}{2} - \frac{1}{6} = \frac{2}{3} \end{array}$

$η$ (first case) = $η$ (second case)

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