A carnot engine operates with source at $227^{\circ} \mathrm{C}$ and sink at $27{ }^{\circ} \mathrm{C}$. If…
A carnot engine operates with source at $227^{\circ} \mathrm{C}$ and sink at $27{ }^{\circ} \mathrm{C}$. If the source supplies $50 \mathrm{~kJ}$ of heat energy, the work done by the engine is
$2 \mathrm{~kJ}$
$5 \mathrm{~kJ}$
$10 \mathrm{~kJ}$
$20 \mathrm{~kJ}$
Solution
Efficiency of engine:
$\therefore \quad \eta=1-\frac{T_2}{T_1}$
$\therefore \quad \eta=1-\frac{(273+27)}{(273+227)}$
$=1-\frac{300}{500}=\frac{2}{5}$
Also,
$\eta=\frac{\text { Work Done by Engine }}{\text { Heat Supplied }}$
$\therefore \quad \mathrm{W}=\frac{2}{5} \times 50=20 \mathrm{~kJ}$
.