SECOND LAW OF THERMODYNAMICS 243 



ing processes in its operation would be called a perfect engine. In 

 such an engine the degeneration H 2 /T 2 above mentioned would be 

 equal to the regeneration H 1 /T 1 so that for a perfect engine we should 

 have 



H 2 /T 2 = H 1 /T 1 (12) 



or 



TJT 2 = HJE 2 (13) 



Substituting the value of H 2 from equation (9) in equation (12) or 

 (13), and solving for W, we have 



T T 



w^-^-^n, (li) 



This equation shows that the efficiency of any perfect engine working 

 between the temperatures T x and T 2 would be equal to [(T 1 — T 2 )/T 1 ]. 



Lord Kelvin's definition of the ratio of two temperatures may be 

 understood with the help of equation (13) in which H l and H 2 are 

 the amounts of heat taken in and given out by a perfect engine during 

 a given time, and T x and T 2 are the temperatures between which the 

 engine is working. 



Efficiencies of Engines in Practise. — A fraction of the heat which is 

 delivered to an engine with the steam which drives the engine is con- 

 verted into work. In order that this fraction may be large, the ratio 

 TJT 2 must be as large as possible, and sweeping processes must be 

 obviated as much as possible in the operation of the engine; T t being 

 the temperature of the steam supplied to the engine, and T 2 being the 

 temperature of the exhaust. The ratio of the initial temperature to 

 the final temperature of the expansion steam or gas in an engine 

 depends upon the ratio of the initial volume to the final volume of 

 the steam or gas. 



In order that moderately small cylinders 9 may be used for the 

 development of a given amount of power, the initial pressure of the 

 steam or gas must be high; and in order that the final temperature 

 may not be lower than atmospheric or available condenser water tem- 

 peratures, the initial temperature must be high. The first point con- 

 cerning high initial pressures is exemplified in the operation of the 

 ordinary gas or gasoline engine in which the mixed charge of gas and 

 air is highly compressed before it is exploded. 



In the gas engine the initial temperature is the temperature of the 



8 The objections to large cylinders are: (a) their great cost, (&) the great 

 amount of heat radiated by them, (c) the great amount of cylinder condensa- 

 tion in a large cylinder as explained later, and (d) the great amount of piston 

 friction and cost of lubrication. 



