KCET · Physics · Thermodynamics
For which combination of working temperatures of source and sink, the efficiency of Carnot's heat engine is maximum?
- A \(600 \mathrm{~K}, 400 \mathrm{~K}\)
- B \(400 \mathrm{~K}, 200 \mathrm{~K}\)
- C \(500 \mathrm{~K}, 300 \mathrm{~K}\)
- D \(300 \mathrm{~K}, 100 \mathrm{~K}\)
Answer & Solution
Correct Answer
(D) \(300 \mathrm{~K}, 100 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
The efficiency of Carnot's heat engine, \(\eta=\frac{T_{1}-T_{2}}{T_{1}}\) For given combinations
\(\eta_{1}=\frac{1}{3}, \quad \eta_{2}=\frac{1}{2}, \eta_{3}=\frac{2}{5}, \quad \eta_{4}=\frac{2}{3}\)
So, it is maximum for
\(T_{1}=300 \mathrm{~K} \text { and } T_{2}=100 \mathrm{~K}\)
\(\eta_{1}=\frac{1}{3}, \quad \eta_{2}=\frac{1}{2}, \eta_{3}=\frac{2}{5}, \quad \eta_{4}=\frac{2}{3}\)
So, it is maximum for
\(T_{1}=300 \mathrm{~K} \text { and } T_{2}=100 \mathrm{~K}\)
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