RICHARDS. CHANGING HEAT CAPACITY. 301 



9 U 

 The last inference drawn above is supported by this table. Clearly — — , 



d 1 

 3 A 

 is related to ^^-^f,. The two always bear opposite signs, and in general 



one is lariie when the other is larnre. The ratio of these two coefficients 

 varies from 1 : 0.13 to 1 : 1.70, neglecting the fifth cell, where the values 

 are too small to be significant. The average is 1 : 0.53 — that is to say, the 

 free energy of a given reaction changes on the average about twice as 

 fast as the total energy with change of temperature, but in the opposite 

 direction. When the total energy increases, the free energy diminishes. 



Expressed algebraically, -^^-^ — — M ,i-^, in which the value of J/aver- 



ages about 2. 



The relation of these two series of data is pointed out yet more clearly 

 by means of the accompanying diagram, in which several of the cells are 

 represented graphically. In this diagram energy is plotted vertically, and 

 temperature in the direction of the axis of abscissae. Tlie lines marked 

 f give the actual quantities of heat evolved in the chemical reactions, the 

 change with the temperature being calculated from Kirchhoff's equation, 

 while the lines marked A give the actual magnitude of the electromotive 

 enei'gy per gram molecule. (See next page.) 



On extrapolating the several lines, it is evident that each pair tends to 

 converge at a point not far from absolute zero. There is no reason for 

 surprise at this fact ; indeed, such a result is a necessary consequence of 

 the equation of Helmholtz, in which A — C7= when T° =0°. The 

 interest centres about the fact that the U always increases when A de- 

 creases with tlie temperature, and vice versa. 



It will be noticed that in order to converge at the absolute zero these 

 lines must be not exactly straight, but slightly curved, — at least the lines 

 for the free enei'gy must be. This is only natural ; for if 6'^ steadily in- 

 creases with the temperature when A is diminishing, U — A will grow 

 at a rate which is greater than that due to the change in A alone. 



U—A 9A ^ .... . ^ ^ . $A 



Hence — jp, — = — ^ „, also will nicrease as tlie temperature rises. - -, 



1 d J- a 1 



could be constant, or ^ .' T a linear relationsiiip only in the case of tlie 

 constancy of U. As a matter of fact IJugarzsky's results enable one to 

 conclude that the temperature coeilicient is on the average about 3 per 

 cent higher at 30"^ than it is at 10°. * Of course more accurate measure- 



* This calculation is based upon all except one of the cells for which Hugarzsky 

 jjives (lata. The mercuric sulpliitle cell is rejected because of known irregularity. 

 Zeitschr. anorg. Chcm., 14, 157 (1807). 



