Question

An engine has an efficiency of $1/6$. When the temperature of sink is reduced by ${62}^{\circ }C$, its efficiency is doubled. The temperature of source will be

• A. ${37}^{\circ }C$
• B. ${62}^{\circ }C$
• C. ${99}^{\circ }C$
• D. ${124}^{\circ }C$

Answer 1

The correct option is C ${99}^{\circ }C$

The efficiency of heat engine is given by:

$\eta =1-\frac{T_2}{T_1}$.

from the given data, we have:

${\eta }_1=1-\frac{T_{2,1}}{T_1}=\frac{1}{6}⟹\frac{T_{2,1}}{T_1}=\frac{5}{6}{\eta }_2=2{\eta }_1=\frac{1}{3}⟹\frac{T_{2,2}}{T_1}=\frac{2}{3}{T}_{2,1}-T_{2,2}=\frac{T_1}{6}=62⟹T_1=372K=99°C$.