Question:
A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. Calculate the efficiency of the engine.
A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. Calculate the efficiency of the engine.
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Carnot Efficiency. The maximum possible efficiency for a heat engine operating between two temperatures \(T_H\) and \(T_C\) (absolute units, Kelvin). \(\eta_{Carnot = 1 - T_C / T_H\).
Updated On: May 7, 2025
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The Correct Option is B
Solution and Explanation
The thermal efficiency (\(\eta\)) of a Carnot engine operating between a hot reservoir at absolute temperature \(T_H\) and a cold reservoir at absolute temperature \(T_C\) is given by:
$$ \eta_{Carnot} = 1 - \frac{T_C}{T_H} $$
Given:
Hot reservoir temperature \(T_H = 500\) K
Cold reservoir temperature \(T_C = 300\) K
Substitute the values:
$$ \eta = 1 - \frac{300 \, \text{K}}{500 \, \text{K}} $$
$$ \eta = 1 - \frac{3}{5} = 1 - 0.
6 = 0.
4 $$ To express the efficiency as a percentage, multiply by 100%: $$ \text{Efficiency} = 0.
4 \times 100\% = 40\% $$ The efficiency of the Carnot engine is 40%.
6 = 0.
4 $$ To express the efficiency as a percentage, multiply by 100%: $$ \text{Efficiency} = 0.
4 \times 100\% = 40\% $$ The efficiency of the Carnot engine is 40%.
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