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?
A) 2.93 K
B) 0.0500 K
C) 106 K
D) 0.0400 K

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by $\eta =1-\frac{T_C}{T_H}$, where $T_C$ is the temperature of the cold reservoir and $T_H$ is the temperature of the hot reservoir. We can rearrange this equation to solve for $T_H$: $T_H=\frac{T_C}{1-\eta}$.

Substituting the given values, we have $\eta = 0.40$ and $T_C = 1.76 	ext{ K}$. Therefore, $T_H = \frac{1.76}{1-0.40}= 2.93 	ext{ K}$.

So the answer is (A).

An Ideal Carnot Engine Operating Between a Warm Reservoir of Unknown