ON OUH KNOWLEDGE OF THEBMODYNAMICS, 



111 



to take the angular velocity instead of the kinetic energy to represent 

 temperature. In this respect the model resembles the example (i.) given 

 in § 27, and the angular momentum takes the place of entropy. 



As in Boltzmann's models, I suppose the working substance repre- 

 sented by a hollow vertical revolving shaft C D, carrying a spoke on 

 which the mass E is free to slide. This shaft is terminated by circular 

 discs C, D ; while the source and refrigerator of the engine are repre- 

 sented by discs A, B, made to revolve with constant but unequal angular 

 velocities, to,, o).,. The discs C and A or D and B may be rigidly con- 

 nected together only when their angular velocities are equal, just as, in 

 Carnot's engine, the working substance and the source or refrigerator 

 are only placed in contact when their temperatures are equal. 



The string S passes down the interior of the shaft, and, instead of 

 hanging down freely, it may be passed over a fixed pulley R, its pull 

 being adjusted in any convenient manner. A frictionless swivel I 

 prevents torsion accumulating in the string. 



The four operations of Carnot's cycle will now be represented as 

 follows : — 



(i.) The angular velocity of the shaft C D being initially wj, work is 

 done on the system by pulling out the string S (and thus bringing the 

 mass E nearer to the axis of rotation) until the angular velocity has been 

 increased to w,. Since the angular momentum meanwhile remains con- 

 stant, this operation is isentropic. 



(ii.) The discs C and A may now be rigidly connected together, so 

 that during this operation the angular velocity must remain equal to wi, 



Ang. Vel. = w, 



An?. Vel. Variable 



Ang. Vel. = ( 



Fixed 



the change being isothermal. The mass E is then allowed to slide 

 further out, doing work on whatever contrivance maintains the pull in 

 the string. 



(iii.) The discs C and A are disconnected, and, the angular momentum 

 remaining constant, the mass E is allowed to slide still further out, again 

 doing work by means of the string. This operation must continue until 

 the angular velocity is reduced to wj. 



(iv.) The discs D and B are now rigidly connected, and work is done 

 on the system by pulling out the string until the mass E has regained its 

 original distance from the axis of rotation. 



The cycle is now complete, and is obviously reversible. If Q, is the 



