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  • A reversible engine has an efficiency of . If the temperature of the sink is reduced by <img alt="58^{\circ} \mathrm{C}" src="https://entrancecorner.codecog

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 sink:
 
Option: 1 180.4^{\circ} \mathrm{K}
Option: 2 382^{\circ} \mathrm{K}
Option: 3 174 K
Option: 4 280 \mathrm{K}

Answers (1)

best_answer

\eta = \frac{1}{4}= 1-\frac{T_{sink}}{T_{source}}
\frac{3}{4}= \frac{T_{sink}}{T_{source}}\rightarrow \left ( 1 \right )
\left ( \eta _{2} \right )= \frac{1}{2}= 1-\frac{\left ( T_{sink}-58 \right )}{T_{source}}
\frac{1}{2}= 1- \left ( \frac{T_{sink}}{T_{source}} \right )+\frac{58}{T_{source}}
\frac{1}{2}=\frac{1}{4}+\frac{58}{T_{source}}
\frac{1}{4}= \frac{58}{T_{source}}
T_{source}= 232
T_{sink}= \frac{3}{4}\left ( T_{source} \right )
          = \frac{3}{4}\times \left ( 232 \right )
\Rightarrow T_{sink}= 174 \, K
The correct option is (3)

Posted by

vishal kumar

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