Question

A Carnot engine operates with sources at ${127}^{\circ }C$ and sink at ${27}^{\circ }C$. If the source supplies $40kJ$ of heat energy, the work done by the engine is

• A. $30kJ$
• B. $10kJ$
• C. $4kJ$
• D. $1kJ$

Answer 1

Answer: (B)

$10kJ$

Efficiency, $\eta =1-\frac{T_2}{T_1}$
$\therefore \eta =1-\frac{(273+27)}{(273+127)}=1-\frac{300}{400}=1-\frac{3}{4}=\frac{1}{4}$
Also $\eta =\frac{\text{Work done by engine}}{\text{Heat supplied by source}}=\frac{W}{40kJ}$
$\therefore W=40\eta =40\times \frac{1}{4}=10kJ$.