An engine has an efficiency of 1 / 6 . When the temperature of sink...

Efficiency of an engine, (\quad \eta=1-$\frac{T_2}{T_1}where$T_1$is the$temperature of the source and $T_2$ is the temperature of the sink. (\therefore \quad\frac{1}{6}=1-\frac{T_2}{T_1} \quad$or, (\quad$\frac{T_2}{T_1}=\frac{5}{6} (\therefore \quad 2 $\times$\frac{1}{6}=1-$\frac{\left(T_2-62\right)}{T_1}$ or, ($\frac{1}{3}=1-$\frac{\left(T_2-62\right)}{T_1}$or, ($\frac{2}{3}=\frac{T_2-62}{T_1} or, $2 T_1=3 T_2-186$ or, (2 T_1=3 \left[\frac{5}{6}\right]T_1-186 \quad) [using (i)] (\therefore \quad \left[\frac{5}{2}-2\right] T_1=186 \quad) or, (\quad $\frac{T_1}{2}=186) or, (T_1=372$\mathrm{~K}=99^{{}^{\circ}} \mathrm{C}.