Discussion
In a Carnot engine if the ratio of the heat rejected to the sink to the heat absorbed from the source is 1 : 4, then the efficiency of the engine is
Answer: A
The efficiency is 75 %.
The efficiency of a heat engine is the fraction of absorbed heat converted to work:
\[ \begin{aligned} \eta &= 1 - \frac{Q_{2}}{Q_{1}} \\ &= 1 - \frac{1}{4} \\ &= \frac{3}{4} \\ &= 75\% \end{aligned} \]
Here \(Q_{2}\) is the heat rejected to the sink and \(Q_{1}\) the heat absorbed from the source. 25 % is the fraction rejected, not converted. 50 % and 60 % do not follow from a 1 : 4 ratio.
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