26 Mr. J. Kam on van der Waals* Equation and 



Making c = v 2 a, we could write equation (A) in the form 

 c v.U.T 



r +V 2 V-£ ' l 



in which equation v and /3 have the values given by (1) and 

 (2) and thus are variables. 



Equation (B) naturally leads to the equation 



P+^ = ^ r T , (C) 



a quadratic equation to be discussed later on. 



Equations (A) and (B) are cubic equations in V, having 

 three roots. With regard to the volume they thus are o£ 

 the third degree. 



With regard to the density, however, they are of the 



■p rp -i 



second degree, the density at the pressure-^- being „ , . 



Thus in equation (A), Y on the left only applies to the 

 volume, on the right to volume and inverse density, and 

 the meaning is not entirely identical, and we could not 

 write it in the form (making <£ = (V + &)) 



a _K 1 T 



as here we would have an equation of the third degree of 

 the density, instead of the quadratic which (A) is. 

 Neither could we write (A) in the form 



p+£= E - T 



V 2 V-6' 



as the volume of the molecules contained by V is not b but 

 only /3, which is a variable (vide equation 2). 



Still we can consider (A) of the third degree of V, the 

 volume, and its curve thus as cutting a horizontal pressure- 

 line in three points, denoting the three values of V. The 



two points of the curve for which -^-=0 approach more 



towards each other as the temperature rises, till at the 

 critical point they coincide. 

 For this point we then have 



2 » 



dp 2a _ R.T 



dv ~ u ' (v e +by- v, 



(Pp 6a _ 2.R.T C 



dv 2 _U ' (Y c + by" V c 3 



whence we obtain 



Vc=2b (5) 



