444 Dr. F. G. Donnan on the Relative Rates of 



If we were dealing with an ideal gas 3 we should have 



U+^ = CT. and ^(U+/w)=C, 



where C = specific heat at constant pressure. This is not 

 strictly applicable to the present case, but we may introduce 

 it into [I) and obtain an approximation. From (1) and (2) 

 we therefore obtain 



which on integration gives 



U+pv= =^ H-/(T) (3) 



Employing (3 | and the fundamental equation given above, 

 we obtain an expression for the velocity of effusion which 

 involves the constant of the Joule-Thomson equation : — 



./ = 2[/.T ) -/(T.,: + 2KC(£-.g). . . (4) 



For an ideal gas K=0 and f(T) = CT. We may therefore 

 write approximately: — 



jS=2C(T.-T) +2KC(£-0). 



r rhe first term on the right-hand side was given by Saint- 

 Venant and WantzeL The second term appear-, therefore, 

 as a correction-term in a form involving the Joule-Thomson 

 constant. The equation may also be written in the form 



<-£i(g-j) + ««i(fr-e) 



It is important to determine the sign of the correction-term. 

 To do this it appears justifiable to assume the ideal gas laws, 

 and so one has 



2KC #-S)= 3KCB (t-|) 



= 2KcB ?Kr-4 



Consider first the region where 2>— > 1. Since 

 £L— r&V it is clear that the expression in square brackets 



