A heat engine has an efficiency of $\frac{1}{6}$. When the temperature of sink is reduced by $62^{\circ} \mathrm{C}$, its efficiency get doubled. The temperature of the source is :

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Heat & Thermodynamics

A heat engine has an efficiency of

\frac{1}{6}

. When the temperature of sink is reduced by

6 2^{\circ} C

, its efficiency get doubled. The temperature of the source is :

(A) $12 4^{\circ} C$
(B) $9 9^{\circ} C$ ✓ Correct
(C) $3 7^{\circ} C$
(D) $6 2^{\circ} C$

Answer: (B)

Solution

Efficiency

η = 1 - \frac{T _{2}}{T _{1}} = \frac{1}{6}

. When sink temperature is reduced by 62°C, the new efficiency is

\frac{1}{3} = 1 - \frac{T _{2} - 62}{T _{1}}

. From the first equation:

\frac{T _{2}}{T _{1}} = \frac{5}{6}

. From the second:

\frac{T _{2} - 62}{T _{1}} = \frac{2}{3}

. Subtracting:

\frac{62}{T _{1}} = \frac{5}{6} - \frac{2}{3} = \frac{1}{6}

, giving

T_{1} = 372

= 9 9^{\circ}

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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