A reversible engine has an efficiency of
Question:

A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ} \mathrm{C}$, its efficiency becomes double. Calculate the temperature of the $\sin k$ :

1. $174^{\circ} \mathrm{C}$

2. $280^{\circ} \mathrm{C}$

3. $180.4^{\circ} \mathrm{C}$

4. $382^{\circ} \mathrm{C}$

Correct Option: 1

Solution:

$T_{2}=\operatorname{sink}$ temperature

$\eta=1-\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}$

$\frac{1}{4}=1-\frac{T_{2}}{T_{1}}$

$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{3}{4} \ldots$ (i)

$\frac{1}{2}=1-\frac{\mathrm{T}_{2}-58}{\mathrm{~T}_{1}}$

$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}-\frac{58}{\mathrm{~T}_{1}}=\frac{1}{2}$

$\frac{3}{4}=\frac{58}{T_{1}}+\frac{1}{2}$

$\frac{1}{4}=\frac{58}{\mathrm{~T}_{1}} \Rightarrow \mathrm{T}_{1}=232$

$\mathrm{T}_{2}=\frac{3}{4} \times 232$

$T_{2}=174 \mathrm{~K}$