*THE POPULAR SCIENCE MONTHLY.*

required to drive the feed water pump), and the quantity of heat *H*_{2} is delivered to the condenser.

According to the first law of thermodynamics, the work *W* must be equal to *H*_{1} — *H*_{2}, both quantities of heat being expressed in energy units. Therefore

W = H_{1} — H_{2} |
(9) |

As far as the net result is concerned the operation of the steam engine may be thought of as (a) the conversion into work of the whole of the heat H_{1} from temperature T_{1}, and (*b*) the reconversion of a

portion *H*_{2} of this work into heat at temperature *T*_{2}. The regeneration^{[1]} associated with process (*a*) is equal to *H*_{1}/*T*_{1} according to equation (8), and the degeneration associated with process (*b*) is equal to *H*_{2}/*T*_{2} according to equation (8). If the operation of the engine involves sweeping processes, then the degeneration *H*_{2}/*T*_{2} must exceed the regeneration *H*_{1}/*T*_{1}, that is, we must have

H_{2}/T_{2} > H_{1}/T_{1} |
(10) |

or, substituting the value of *H*_{2} from equation (9) and solving for *W,* we have

W < T_{1} - T_{2}T_{1} H_{1} |
(11) |

The fractional part [(*T*_{1} — *T*_{2})/*T*_{1}] of the heat *H*_{1} which is converted into work by the engine is called the efficiency of the engine, and the inequality (11) shows that the efficiency of any engine working between temperatures *T*_{1} and *T*_{2} must be less than [(T1 — T2)/T1] whatever the nature of the working fluid and whatever the design of the engine.

*The Perfect Engine.* — An engine involving no irreversible or sweep-

- ↑ To convert an amount of work W into heat at a given temperature involves an amount of degeneration, and to convert the heat into work involves the same amount of what may be called thermodynamic regeneration.