An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $40.0 \%$ What is the temperature of the warm reservoir?

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by 
$$\eta = 1-\frac{T_C}{T_H}$$
where $T_C$ and $T_H$ are the temperatures of the cold and hot reservoirs, respectively. We are given that the efficiency of the engine is $40\%$, so we can write
$$0.40 = 1-\frac{T_C}{T_H}$$
Solving for $T_H$, we get
$$T_H = \frac{T_C}{1-\eta} = \frac{(1.76\mathrm{~K})}{1-0.40} = 2.93 \mathrm{~K}$$
Therefore, the answer is (A).

An Ideal Carnot Engine Operating Between a Warm Reservoir of Unknown