Q170 / 180 · KCET 2007 · Physics
A Carnot's engine operates with source at $127^{\circ} \mathrm{C}$ and sink at $27^{\circ} \mathrm{C}$. If the source supplies $40 \mathrm{~kJ}$ of heat energy, the work done by the engine is
- A$30 \mathrm{~kJ}$
- Correct answerB$10 \mathrm{~kJ}$
- C$4 \mathrm{~kJ}$
- D$1 \mathrm{~kJ}$
Solution
Efficiency $\eta=1-\frac{T_{2}}{T_{1}}$
$$
=1-\frac{(273+27)}{(273+127)}=1-\frac{300}{400}=\frac{1}{4}
$$
$$
\begin{aligned}
\eta &=\frac{\text { Work done }}{\text { Heat supplied }} \\
\frac{1}{4} &=\frac{W}{40} \Rightarrow W=10 \mathrm{~kJ}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.