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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 $\sin k$ :
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)
$\frac{1}{2}=1-\frac{\mathrm{T}_{2}-58}{\mathrm{~T}_{1}}$
$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}-\frac{58}{\mathrm{~T}_{1}}=\frac{1}{2}$
$\frac{3}{4}=\frac{58}{T_{1}}+\frac{1}{2}$
$\frac{1}{4}=\frac{58}{\mathrm{~T}_{1}} \Rightarrow \mathrm{T}_{1}=232$
$\mathrm{T}_{2}=\frac{3}{4} \times 232$
$T_{2}=174 \mathrm{~K}$
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