Page:Popular Science Monthly Volume 76.djvu/246

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 H₁ from temperature T₁, and (b) the reconversion of a

Fig. 1.

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

style="text-align:center;"|$H_{2}/T_{2}>H_{1}/T_{1}$

(10)

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

$W<{\frac {T_{1}-T_{2}}{T_{1}}}H_{1}$

(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 $[(T_{1}-T_{2})/T_{1}]$ whatever the nature of the working fluid and whatever the design of the engine.

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

1. 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.