November 20, 1903.] 



SCIENCE. 



651 



The reader iinist not imagine, however, 

 that thermodynamic degeneration has any- 

 thing to do with structural degeneration 

 or dissolution, which is the most prominent 

 feature of the calamity which befell 

 Ilumpty Dumpty, but, to put the case con- 

 cretely, if one shakes up a quantity of pure 

 and homogeneous water in a bottle, one 

 plays that irreparable havoc which consti- 

 tutes therjuodynamic degeneration. 



9. ENGINES. 



The further development of the subject 

 of thermodjTiamies depends upon the es- 

 tablishment of the exact relation between 

 the degeneration which is represented by 

 the transfer of heat from a high to a low 

 temperature and the degeneration which is 

 represented by the conversion of work into 

 heat. To establish this relation it is neces- 

 sary to consider a reversible process in 

 which the degeneration of heat from high 

 to low temperature is compensated by the 

 regeneration of heat into work, or vice 

 versa. 



The engine is a machine which deter- 

 mines such a process. The ordinary en- 

 gine, indeed, is subject to friction, and the 

 steam as it passes through the engine does 

 not undergo a reversible process; but if 

 the engine were frictionless, if it were 

 driven slowly, if the cylinder were pre- 

 vented from cooling the steam, if the steam 

 were expanded sufficiently to prevent puff- 

 ing and if the feed water were heated, in 

 a ' regenerative ' feed water heater, to boiler 

 temperature before entering the boiler, 

 then the processes involved in the operation 

 of the engine would be reversible. Such 

 an ideal engine w'e will call a reversible 

 engine or a perfect engine. 



During a given interval of time the en- 

 gine takes an amount of heat H, from the 

 boiler at temperature T,. it converts into 

 work W a certain fractional part of 77, 



and delivers the remainder Ho to the con- 

 denser at temperature T^- 



The work W done by the engine is equal 

 to the difference 77, — 77, according to the 

 first law of thermodvnamics. That is. 



: u, — //,. 



(1) 



Now, all the heat used in the engine 

 comes from the region at temperature T„ 

 and the net result of the operation of the 

 engine is: (a) to convert the quantity 

 W{^Hi — n„) of heat from tempera- 

 ture T, into work, and (6) to transfer the 

 quantity 77o of heat from temperature Ti 

 to temperature T,- The result (a) in- 

 volves an amount of regeneration which is 

 proportional to W, temperature being 

 given; this regeneration may, therefore, 

 be represented by mW where m is a con- 

 stant depending only on the temperature 

 T,. The result (b) involves an amount 

 of degeneration which is proportional to 

 77„, temperatures being given; this degen- 

 eration may, therefore, be represented by 

 nil., where ?i is a constant depending only 

 on the temperatures T^ and T„. If the 

 engine is reversible we must have 



mW = iiII,, (-2) a 



or, using the value (77, — W) for 77., and 

 solving for TF we have 



{•2)b 



in wliich n/{ni -\- «) depends on T, and 

 T., only, irrespective of the kind of engine 

 and of the physical properties of the fluid 

 employed in the engine, provided, only, 

 that the engine is reversible. The frac- 

 tional part n/{m -f- n) of the heat TTj 

 which the engine converts into work is 

 called the efficiency of the engine, and from 

 equation (2)6 it follows that the efficiency 

 of all reversible engines is the same for 

 given values of the temperatures T, a7id 

 T,. 



