A reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by 62^° C , the efficiency of the engine is doubled. The temperatures of the source and sink are

Correct answer: (A) 99^° C, 37^° C. The efficiency of engine, η=(T_1-T_2)/T_1 According to question, 2 η=(T_1- (T_2-62 ))/T_1 or 1/2=(T_1-T_2)/((T_1-T_2 )+62) or 62= (T_1-T_2 ) Only option (a) satisfies the condition.

Q142 / 160 · TS EAMCET 2011 · Physics

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

Correct answer
A
$99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
B
$80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
C
$95^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
D
$90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

Solution

The efficiency of engine, $\eta=\frac{T_1-T_2}{T_1}$ According to question, $2 \eta=\frac{T_1-\left(T_2-62\right)}{T_1}$ or $\quad \frac{1}{2}=\frac{T_1-T_2}{\left(T_1-T_2\right)+62}$ or $62=\left(T_1-T_2\right)$ Only option (a) satisfies the condition.

Hence, the correct answer is option: 'A'.

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