An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts $15.0 \mathrm {~J}$ of heat from the warm reservoir and does $4.0 \mathrm {~J}$ of work. What is the temperature of the colder reservoir?
A)171 K
B)62 K
C)47 K
D)67 K

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by:$$e=\frac{W}{Q_H}=1-\frac{T_C}{T_H}$$where $W$ is the work done, $Q_H$ is the heat extracted from the warm reservoir, $T_C$ is the temperature of the colder reservoir, and $T_H$ is the temperature of the warm reservoir.We can rearrange this equation to solve for $T_C$:$$T_C=T_H(1-e)$$Substituting the given values, we get:$$T_C=233\mathrm{~K}(1-\frac{4.0\mathrm{~J}}{15.0\mathrm{~J}})=171\mathrm{~K}$$Therefore, the temperature of the colder reservoir is 171 K.

An Ideal Carnot Engine Operates Between a Warm Reservoir at 233