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
  1. $2 \mathrm{~kJ}$
  2. $5 \mathrm{~kJ}$
  3. $10 \mathrm{~kJ}$
  4. $20 \mathrm{~kJ}$

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, $\eta=\frac{\text { Work Done by Engine }}{\text { Heat Supplied }}$ $\therefore \quad \mathrm{W}=\frac{2}{5} \times 50=20 \mathrm{~kJ}$ .

Asked in: MHT CET 2023 (13 May Shift 2)

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