Page:Popular Science Monthly Volume 76.djvu/246

242 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

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

portion $$H_{2}$$ of this work into heat at temperature $$T_{2}$$. The regeneration 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

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

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