LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 269 



Equating the second members of these equations and substituting for 

 the partial differential coefficient their values from equations V and 



Y — /V r v Y' — Pc' r' 



- m ^ r dT+ -j^dP = RT2 clT+jj^dP, 



Y-Pv-V + Pc' ._ r'-v 7D 

 or ~RT*~ ~11T~ 



The numerator of the first fraction is obviously equal to the heat of 

 fusion of one mol of ice. Calling this Q, we have 



dT (V - v) T 

 dP ~ ' Q ' 



which is the familiar equation of Thomson for the change of freezing 

 point with the pressure. 



As a third illustration of the application of these equations we will 

 consider a general method for determining the numerical value of the 

 activity of a substance. Let us first consider a gas which is at such 

 a pressure as no longer to obey the gas law. According to equation V 

 we may write, for the influence of pressure on the activity, at constant 

 temperature, 



v 

 d\n$ = -jvfdP. 



From this equation we may find the activity at one pressure when it is 

 known at any other, if we know the molecular volume, v, as a function 

 of the pressure, P. For this purpose we may use any empirical 

 equation, such as that of van der Waals, namely, 



RT a 



v — b vr 



Differentiating this equation, substituting the value of dP in the pre- 

 ceding equation, and integrating between v and v', we obtain the 

 equation, 



