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. 20%
• B. 40%
• C. 60%
• D. 80%

Hint:

Carnot Efficiency. The maximum possible efficiency for a heat engine operating between two temperatures \(T_H\) and \(T_C\) (absolute units, Kelvin). \(\eta_{Carnot = 1 - T_C / T_H\).

Answer 1

The Correct Option is B

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%.