Page:Popular Science Monthly Volume 76.djvu/246

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242
THE POPULAR SCIENCE MONTHLY.

required to drive the feed water pump), and the quantity of heat H2 is delivered to the condenser.

According to the first law of thermodynamics, the work W must be equal to H1H2, both quantities of heat being expressed in energy units. Therefore

W = H1H2 (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

 

PSM V76 D246 Demonstration of the second law of thermodynamics.png

Fig. 1.

 

portion H2 of this work into heat at temperature T2. The regeneration[1] associated with process (a) is equal to H1/T1 according to equation (8), and the degeneration associated with process (b) is equal to H2/T2 according to equation (8). If the operation of the engine involves sweeping processes, then the degeneration H2/T2 must exceed the regeneration H1/T1, that is, we must have

H2/T2 > H1/T1 (10)

or, substituting the value of H2 from equation (9) and solving for W, we have

W < T1 - T2T1 H1 (11)

The fractional part [(T1T2)/T1] of the heat H1 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 T1 and T2 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-

  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.