Question

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by ${62}^{o}C$. The efficiency of the engine is doubled. The temperatures of the source and sink are:

• A. ${99}^{o}C,{37}^{o}C$
• B. ${80}^{o}C,{37}^{o}C$
• C. ${95}^{o}C,{37}^{o}C$
• D. ${90}^{o}C,{37}^{o}C$

Answer 1

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

Given,
$\eta =\frac{1}{6}$
$\eta =1-\frac{T_L}{T_H}$

${\eta }^{\prime }=1-\frac{T_L-62}{T_H}$ = 2 $\eta$
Solving the 2 eqns for $T_{H}and{T}_L$,
$T_H={99}^{o}Cand{T}_L={37}^{o}C$