In 1 st case, Carnot engine operates between temperatures 300 K and… | JEE Main 2022 (27 Jul, Shift 2)

Q33JEE Main 2022 · 27 JUL · SHIFT 2Medium

Heat Engines, Refrigerators & Second Law

In $1$ st case, Carnot engine operates between temperatures $300\text{ K}$ and $100\text{ K}$ . 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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Answer: (a)

1st case: $\eta = 1 - \frac{100}{300} = \frac{2}{3}$ .
2nd case: $Q_1 =$ heat from 300 K, $Q_3 =$ heat to 100 K; for reversible engines $\frac{Q_3}{Q_1} = \frac{Q_3}{Q_2}\cdot\frac{Q_2}{Q_1} = \frac{100}{200}\cdot\frac{200}{300} = \frac{1}{3}$ .
$\eta_{\text{comb}} = 1 - \frac{Q_3}{Q_1} = \frac{2}{3}$
So the answer is (a) same as the 1st case.

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