Section III, 1918 [47] Trans. R.S.C. 



Air and the Law of Corresponding StatesT 

 By Dr. A. L. Clark, F.R.S.C. 



(Read May Meeting, 1918.) 



The equation of van der Waals, ( P +~ ) (v — b) = R T, contains 



only three constants; consequently, it leads at once to the values of 

 the critical constants. We may derive these by writing the equation in 

 the form (v — Vc)^ = O at the critical point and equating the coeffi- 

 cients of like powers of v in the two equations. We may arrive at 

 the same results by taking account of the fact that there is a hori- 

 zontal inflexional tangent at the critical point which requires that 



dP , d^P , , . . , 



— - = O and -r-, = O. These derived equations and the origmal 

 dv dv- 



equation lead to the values 



a 8a 



Vc = 3 b, Pc = ^y-j^ and R Tc = ^y-j^ . 



v P T 



Substitution oi v = —,P = ~ and T = —, the reduced values of 



Vc Pc i c 



V, P and T, in van der Waals' equation leads to 



p + - j (3 Î' - 1) = 8 r. 



the reduced equation of state, which is independent of the nature of 

 the substance. In this equation, the units employed for any sub- 

 stance are the critical values of v, P and T. Two substances are in 

 corresponding states when the reduced pressures, volumes and tem- 

 peratures have the same values. Their properties are then similar. 

 The great advantage of van der Waals' equation, besides its simplicity 

 and applicability to representation of a great variety of substances, 

 is the fact that it leads to a reduced equation of state, and hence the 

 law of corresponding states. 



RTc 8 . ' 



Further, the ratio — = rr ^^ a constant for all gases obeying the 



r^cVc «J 



equation of van der Waals. The departure of this critical coefficient 



for any substance from the theoretical value ma}'^ be taken as a measure 



of the degree of approximation with which it is represented by the 



equation of van der Waals. We may group substances according 



