﻿JL 



4' 



Revised Equation of State. 1023 



The values of a, 6, and c will be functions of the tempera- 

 ture. 



Now ±%*§1 = =i_ + £L + ?* + l« 



*p d/3 W-i) & P 3 P 



At a = 0, /3=oo, this becomes zero (and because ^- does 



OP 



not do so, so also does 'd(a/3)/'du) when 



a = 

 It we write a = -' , 



this occurs when 



7 » = 4a 1 = 6'04 = (2-455) 2 . 



Now the u(3 against a. curve for nitrogen starts out 

 horizontally when 7 = 2*54 ; hence n — 2 nearly. Inserting 

 these values, which are obtained solely by making the 

 equation suit the critical state, it is interesting to see how 

 nearly the equation becomes Berthelot's equation when the 

 pressure is small. It can be written 



«=-fe ( 



/3-iV 



or 





(a+ —J™) = o for large values of fi. 



In Berthodot's equation the numbers are 5*33 and 3*55 

 respectively. 



If b be written bjy™, the value of m is found from the 

 curves of isopentane to be a high one — about 12 to 15. It 



can be obtained also by considering the value of =— at the 



critical point. We have in general 



7d« _ i , ^i , j^i , 32i 

 «^7 ~ 7 n /3 7 w /3 2 ' y?/3 3 ' 



or at the critical point the right side is 



1 + nai+mbi + gcx, 



or 1 + 3 + -267m- -237g. 



There are not data enough to find m and q with certainty. 

 But since this critical slope is for all substances nearly 

 equal to 1, it follows that m must be at least 10, which 

 agrees with what we find from the experimental curves. 



