>} . . . . (., 



Molecular Thermodynamics. 607 



to make possible an extension of Planck's method to the 

 general ease, is that F 1 and ¥ 2 shall permit of expansion in 

 the forms 



F 1 = tu x f x (c^gCg . . . .) 



F 2 =tv x f x (c 1 c 2 c l 



where f l9 f 2 , . . . are functions independent of temperature 

 and pressure, while m 1s u 2 . . ., v { , v 2 . . . are parameters 

 dependent only on temperature and pressure. 



Some of these parameters may of course be zero, since we 

 use the same series of functions, f x f 2 . , ., for both F 1 

 and F 2 . 



This minimum assumption is clearly a very wide one which 

 will probably always be, at least very approximately, 

 applicable. 



Now as there can be little doubt that the linear form 

 treated by Planck is the limiting form at the most extreme 

 dilution, we may conveniently separate the simple linear terms 

 from the rest which we shall call the "General terms" : 



F 1 = %u 1 e l + %uJ f x (dC2 . . . .) 



¥ 2 = %ViC 1 + l f Vx f x {cic 2 . • . •)• 



.The general terms must be of degree higher than the first 

 in c±c 2 ...., in order that the linear may be the limiting- 

 form. 



For general treatment we may best express the concentra- 

 tions as molecular ratios referred to the total number, v t or 

 %n, of molecules, as denominator 



n x ni g 



c 1 =~=^ L &c. 

 n t Zn 



For special applications, as we shall see later, other "con- 

 centrations " may be preferable. 



Taking the mean molecular weight in grams as the unit 

 quantity of solution, and writing U and V for the Total- 

 Energy and Volume of the whole solution, 



— = %u l c J +2,u x 'f x (c 1 c 2 ....), 

 V 



that is 



=2t>ici+2tfc'>i(c 1 ci ....), 



JJ—'Zn l u i +n t tu x 'f x {c 1 e 2 . • . .) 1 



Y = %n 1 v 1 + n f Xv x %(c 1 c 2 ....)i ' ' ' U 



