A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts 10.0 J of heat from the mercury and does 8.0 J of work during each cycle. What is the temperature of the colder reservoir?
A) 47 K
B) 186 K
C) 163 K
D) 207 K

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by:$$e = 1 - \frac{T_c}{T_h}$$where $T_c$ is the temperature of the colder reservoir and $T_h$ is the temperature of the hotter reservoir.We are given that the efficiency of the engine is 80%, so we can write:$$0.8 = 1 - \frac{T_c}{233 K}$$Solving for $T_c$, we get:$$T_c = 233 K - 0.8 * 233 K = 46.6 K$$Therefore, the temperature of the colder reservoir is 46.6 K, which is closest to choice A, 47 K.

A Carnot Engine Operating Between a Reservoir of Liquid Mercury