A reversible heat engine converts one-fourth of the heat input into… | JEE Main 2021 (25 Feb, Shift 2)

Q47JEE Main 2021 · 25 FEB · SHIFT 2Medium

Heat Engines, Refrigerators & Second Law

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.

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

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Answer: 208

Reversible engine: $\eta = 1 - \frac{T_2}{T_1}$ .
$\frac{1}{4} = 1 - \frac{T_2}{T_1} \Rightarrow T_2 = \frac{3}{4}T_1$
After cooling the sink: $\frac{1}{2} = 1 - \frac{T_2 - 52}{T_1} \Rightarrow T_2 - 52 = \frac{T_1}{2}$
$\frac{3}{4}T_1 - \frac{1}{2}T_1 = 52 \Rightarrow T_1 = 208$ K
So the source temperature is $208$ K.

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