A reversible engine converts one-sixth of the heat input into wor… - Vidyadip

MCQ

A reversible engine converts one-sixth of the heat input 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

A
$80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
B
$95^{\circ} \mathrm{C}, 28^{\circ} \mathrm{C}$
C
$90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
✓
$99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

✓

Answer

Correct option: D.

$99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

Initially $\eta=\left(1-\frac{T_2}{T_1}\right)=\frac{W}{Q}=\frac{1}{6}$
Finally $(\eta^\prime)=(1-\frac{T_2^\prime}{T-1}) =\left(1\frac{(T_2)-62}{T_1}\right)=1\frac{T_2}{T_1}+\frac{62}{T_1}$
$=\eta+\frac{62}{T_1}$It is given that $\eta^{\prime}=2 \eta$.
Hence solving equation (i) and (ii)
$\Rightarrow T_1=372 \mathrm{~K}=99^{\circ} \mathrm{C}$ and $T_2=310 \mathrm{~K}=37^{\circ} \mathrm{C}$

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