74 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



one. If this increment is greater than the accompanying decre- 

 ment, then the final outcome of this direct passage from hot to 

 cold is an increase in the total number of complexions of the 

 two gases. There will then, by our precise definition, be a con- 

 responding increase in the total entropy of the two systems. It 

 is foreign to our present purpose to prove in an independent, 

 purely mechanical way, that such excess does finally exist and 

 will here content ourselves with the well-known and simple 

 thermodynamic expression for this excess, 



(32) 



where Q is the heat energy thus directly transferred from the 

 hot to the cold body, T\ the absolute temperature of the hot body 

 and jT 2 that of the cold body. 



THE WORK OF FRICTION is CONVERTED INTO HEAT 



The group under head (b) contains a class of events which 

 usually attends, in one form or another, most natural phenomena. 



We will here consider an interesting (but perhaps too special) 

 case, namely, the experiment performed by W. THOMSON and 

 JOULE on the flow of gas through a porous plug. The plug 

 obstructed the uniform, non-conducting, passage through which 

 the gas was forced without sensibly changing its velocity of flow: 

 (See LORENZ' Technische Warmelehre, p. 275). It can easily be 

 shown (in L., p. 274) that with an ideally perfect gas, 



Final temperature T 1 2=-Ti= initial temperature. 



As a matter of fact, there was an actual though slight drop in 

 temperature found to exist with the most perfect gases available. 

 Evidently the process was a throttling one, reducing the larger 

 initial pressure to the smaller final one, which reduction was of 

 course accompanied by a corresponding increase in volume. 



