142 Physical Properties [OH. vi 



The following table, given by Berthelot*, gives the observed value for 



TINT 

 the ratio - - at the critical point. It will be seen that argon is the only 



gas in which this value approximates with any reasonable accuracy to the 

 value f given by equation (331) : 



Marsh gas 3'67, 



Carbon dioxide 3'61, 



Nitrogen 3*53, 



Oxygen 3'49, 



Argon 2-62. 



Other values of this quantity have been determined by Ramsay and 

 Young'f 1 ranging up to values as great as 5'00 for acetic acid. Young, 

 however, is of opinion that for all substances which can attain the critical 

 state without chemical change, the quantity is nearly constant, and has 

 a value of about 3'7|. 



Before leaving this question, it is of interest to examine the numerical 

 values at the critical point, given by the more general equation (303), 

 namely, 



m r 



Nm Nm . 



Let us write p = - and p& = - ^ , so that, as betore, we neglect 



squares of bfv. Then the equation becomes 



fy\ _ .~ 



P ~(v-b) 6 



The critical point is the point at which dp/dv and d*p/dv 2 both vanish. 

 If dp/dv = 0, we have by logarithmic differentiation, 



_ 

 ~ ' 



and if also d^p/di? = 0, the equation just obtained, regarded as an equation 

 for v, must have equal roots in v. The condition for this is that 



'' 



(0-fc) 2 RTtf 



From these two equations we obtain 



1 _2 



v b v ' 

 so that b = ^v, 



and 



* Soc. Frang. Phys. Bull. CLXVII. p. 4 (1901). 



t Phil. Mag. 1892, p. 503; 1894, p. 1. See also Weinstein, Thermodynamik, i. p. 469. 



Physikalische Revue, i. p. 385. 



