A Carnot engine operates between a hot reservoir at $T_1 = 500$ K and a cold reservoir at $T_2 = 300$ K. The efficiency of the engine is:
A$20\%$
B$40\%$
C$60\%$
D$100\%$
Answer & Solution
Correct answer: B. $40\%$
Carnot efficiency $\eta = 1 - \dfrac{T_2}{T_1}$ (temperatures in Kelvin, always).
$\eta = 1 - \dfrac{300}{500} = 1 - 0.6 = 0.4 = 40\%$.
No real heat engine can exceed this for the same two reservoirs. Option D would require $T_2 = 0$ K, which the third law forbids.
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