242 



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 X -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 x from temperature T 1} and (&) the reconversion of a 



steam 



engine 

 cylinder 



steam 



valve 



1 condensing 

 water 



feed-water 

 pump 



water 



water 



Fig. 1. 



portion H 2 of this work into heat at temperature T 2 . The regenera- 

 tion 8 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 HJT 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 HJT X) that is, we must have 



H 2 /T 2 > HJT, 



(10) 



or, substituting the value of H 2 from equation (9) and solving for 

 W, we have 



W < 



Z\ 



— -H 

 T x x 



(11) 



The fractional part [(T 1 — T 2 )/T 1 ] of the heat H x 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 x and T 2 must be less than [(7\ — 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- 



8 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. 



