LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 269 



dlni = 



m/'<^)/'' 



Equating the second members of these equations and substituting for 

 the partial differential coefficient their values from equations V and 

 VIII, 



Y — Pr V Y' — Pi' r< 



Y-Pv-Y' + Pi' v'-v .J. 

 RT^ ^^=-EF'^^- 



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- H ' 



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 A^alue 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 wTite, for the influence of pressure on the activity, at constant 

 temperature, 



v • 



d\\\.i = syhdP. 

 Ill 



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

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

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

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



P = 1I- « 



v-b 



2 



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

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

 equation, 



