A Carnot-efficiency engine operating between a reservoir of liquid mercury at its melting point and a colder reservoir extracts 15.0 J of heat from the mercury and does 4.0 J of work during each cycle.What is the temperature of the colder reservoir? Mercury melts at 233 K.
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 1 - (Tc/Th), where Tc is the temperature of the colder reservoir and Th is the temperature of the hot reservoir (233 K for mercury). The work done is 4.0 J, and the heat extracted is 15.0 J, so the efficiency is 4.0/15.0 = 0.267. Solving 1 - (Tc/233) = 0.267 gives Tc ≈ 171 K.

A Carnot-Efficiency Engine Operating Between a Reservoir of Liquid Mercury