MHT CET · Physics · Thermodynamics
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
- A \(2 \mathrm{~kJ}\)
- B \(5 \mathrm{~kJ}\)
- C \(10 \mathrm{~kJ}\)
- D \(20 \mathrm{~kJ}\)
Answer & Solution
Correct Answer
(D) \(20 \mathrm{~kJ}\)
Step-by-step Solution
Detailed explanation
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,
\(\eta=\frac{\text { Work Done by Engine }}{\text { Heat Supplied }}\)
\(\therefore \quad \mathrm{W}=\frac{2}{5} \times 50=20 \mathrm{~kJ}\)
\(\therefore \quad \eta=1-\frac{T_2}{T_1}\)
\(\therefore \quad \eta=1-\frac{(273+27)}{(273+227)}\)
\(=1-\frac{300}{500}=\frac{2}{5}\)
Also,
\(\eta=\frac{\text { Work Done by Engine }}{\text { Heat Supplied }}\)
\(\therefore \quad \mathrm{W}=\frac{2}{5} \times 50=20 \mathrm{~kJ}\)
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