Q 11-11-103JEE MainJEE Main 2022 (26 Jun, Shift 2)Medium
A heat engine operates with the cold reservoir at temperature $324\ \text{K}$. The minimum temperature of the hot reservoir, if the heat engine takes $300\ \text{J}$ heat from the hot reservoir and delivers $180\ \text{J}$ heat to the cold reservoir per cycle, is ______ K.
Numerical value type. Enter your answer.
Answer: 540
Efficiency $\eta = 1 - \dfrac{180}{300} = 0.4$. No engine can beat a Carnot engine, so $1 - \dfrac{324}{T_H}\ge0.4$:
$$T_H\ge\frac{324}{0.6} = 540\ \text{K}$$
Solution by Sreeraj P, M.Sc Physics