Question

A scientist says that the efficiency of his heat engine which works at source temperature ${127}^{\circ }\text{C}$ and sink temperature ${27}^{\circ }\text{C}$ is $26\%$, then

• A. It is possible but less probable
• B. Data are incomplete
• C. It is quite probable
• D. It is impossible

Answer 1

The correct option is D It is impossible

Given:
$T_{\text{sink}}={27}^{\circ }\text{C}=300\text{K}$
$T_{\text{source}}={127}^{\circ }\text{C}=400\text{K}$
Efficiency of heat engine is given by
$\eta =\frac{T_1-T_2}{T_1}=1-\frac{300}{400}=\frac{1}{4}=25\%$
Since maximum possible efficiency is less than the efficiency given in question.
So, it is impossible.
Hence, option $\left(A\right)$ is correct.