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?

The maximum efficiency comes from using a Carnot (reversible) engine, for which $Q_H/Q_C=T_H/T_C$, and so

$$W=Q_H-Q_C=Q_H\left(1-{T_C\over T_H}\right)$$

With $T_H=373$K and $T_C=293$K, for every Joule of heat extracted from the hot reservoir ($Q_H=1$J), $W_{\rm max}=0.21$J.