Heat Engines, Refrigerators & Second Law question from NEET 2007 (AIPMT)

Answer: (c)

1. $\eta = 1 - \frac{T_2}{T_1}$: $T_2 = \frac{5}{6}T_1$; after reduction $\eta = \frac{1}{3}$, so $T_2 - 62 = \frac{2}{3}T_1$.
2. A change of $62^\circ\text{C}$ equals 62 K. Subtract: $\frac{T_1}{6} = 62 \Rightarrow T_1 = 372\text{ K}$.
3. $T_1 = 372 - 273 = 99^\circ\text{C}$
4. So the answer is (c) $99^\circ\text{C}$.