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JEE Main 2022 (26 Jun, Shift 2) · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from JEE Main 2022 (26 Jun, Shift 2)

Q39JEE Main 2022 · 26 JUN · SHIFT 2Medium

Heat Engines, Refrigerators & Second Law

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ____________ K.

Numerical answer type. Work it out, then open the answer.

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Answer: 540

Actual efficiency $\eta = 1 - \frac{180}{300} = 0.4$ .
It cannot exceed Carnot: $0.4 \le 1 - \frac{324}{T_1} \Rightarrow T_1 \ge \frac{324}{0.6}$ .
Minimum $T_1 = 540\text{ K}$

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