Heat engine examples

The master-equations for generic heat-engine problems are the conservation of energy and the heat-temperature relation for a Carnot engine:

$\mbox{\large\colorbox{yellow}{\rule[-3mm]{0mm}{10mm} \ $\displaystyle W=Q_H-Q_C \qquad\hbox{and}\qquad {Q_C\over Q_H}={T_C\over T_H}$ }}$

The question will give you one of $Q_H$, $Q_C$ and $W$, and the master-equations give you the other two.

Try these problems for yourself before checking the detailed answers!

• Ex. 1 A power station contains a heat engine operating between two heat reservoirs, one consisting of steam at $100^{\rm o}$C and the other consisting of water at $20^{\rm o}$C. What is the maximum amount of electrical energy which can be produced for every Joule of heat extracted from the steam?

  Answer: $0.21$J. Details here.

• Ex. 2 When a fridge stands in a room at $20^{\rm o}$C, the motor has to extract 500W of heat from the cabinet, at $4^{\rm o}$C, to compensate for less than perfect insulation. How much power must be supplied to the motor if its efficiency is 80% of the maximium achievable?

  Answer: $2.9$J. Details here.