Question

A Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by ${62}^{o}C$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

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

Answer 1

The correct option is D ${99}^{o}C,{37}^{o}C$

Given,
$\frac{1}{6}=1-\frac{T_{sink}}{T_{source}}\Rightarrow \frac{T_{sink}}{T_{source}}=\frac{5}{6}...\left(1\right)$

Also,
$\frac{2}{6}=1-\frac{T_{sink}-62}{T_{source}}\Rightarrow \frac{62}{T_{source}}=\frac{1}{6}...\left(2\right)$

$\therefore T_{source}=372K={99}^{o}C$

Also, $T_{sink}=\frac{5}{6}\times 372=310K={37}^{o}C$
(Note :- Temperature of source is more than temperature of sink)