Question

An engine has an efficiency of 1/6. When the
temperature of sink is reduced by 62C, its
efficiency is doubled. Temperature of the source is-

• A. ${99}^{0}C$
• B. ${124}^{0}C$
• C. ${37}^{0}C$
• D. ${62}^{0}C$

Answer 1

The correct option is A ${99}^{0}C$

$\eta =1-\frac{T_2}{T_1}\Rightarrow \frac{1}{6}=1-\frac{T_2}{T_1}$
and $\frac{1}{3}=1-\frac{(T_2-62)}{T_1}\Rightarrow \frac{1}{3}=1-\frac{T_2}{T_1}+\frac{62}{T_1}$
$\Rightarrow \frac{1}{3}=\frac{1}{6}+\frac{62}{T_1}=\frac{1}{6}=\frac{62}{T_1}$