Q 11-11-128JEE MainJEE Main 2021 (25 Jul, Shift 2)Medium
A heat engine has an efficiency of $\frac{1}{6}$. When the temperature of sink is reduced by $62^\circ$C, its efficiency gets doubled. The temperature of the source is:
Answer: (D) $99^\circ$C
$1 - \dfrac{T_2}{T_1} = \dfrac{1}{6} \Rightarrow T_2 = \dfrac{5}{6}T_1$
$1 - \dfrac{T_2 - 62}{T_1} = \dfrac{1}{3} \Rightarrow T_2 - 62 = \dfrac{2}{3}T_1$
$\dfrac{5}{6}T_1 - 62 = \dfrac{2}{3}T_1 \Rightarrow T_1 = 372$ K $= 99^\circ$C.
Solution by Sreeraj P, M.Sc Physics