﻿[ 1020 ] 



XCII. On a Revised Equation of State. By Alfred 

 W, Porter, D.Sc, F.R.S., F.lnst.P* 



["YEETERICFS characteristic equation of gases in the 



reduced form is <x = . ^ /£ /_i ex P- I 2(1 «) , which 



can be modified by putting <y n instead of 7 in the exponential 

 term. This equation is very fairly satisfactory, when 

 w = 3/2, in the region of low pressures; but it breaks down 

 for pressures above the critical value. 



Bertbelot also developed an equation in which the 

 respective terms are based directly on experiment instead of 

 theory. It is explicitly applicable to low pressures only, and 

 is very much used for that region. This equation is 



16 32y 



*+^{T$$1 .;.' , ';■-., 



It will be observed that it does not pass through the critical 

 point (a — /3 = y=1). On fig. 1 are shown experimental 

 values of a(3 plotted against ex. for isopentane, and on this 

 same figure values calculated from Berthelot's equation are 

 represented by a. dotted curve. Values from van der Waals' 

 equation are indicated by small squares. 



The chief fault of Dieterici's equation is that it makes the 

 critical volume only twice the least volume of the liquid, 

 whereas experiment shows that it is in most cases very 

 nearly four times. To get over this, Dieterici treats the 

 volume of the molecules themselves as being a function of 

 the pressure. 



The first object of this paper is to point out that there is a 

 way of testing the equation which shows that this last-stated 

 modification (even if it should be necessary) cannot be the 

 only change required, and that it is no use making it until 

 other changes are made. 



If the equation be written 



« = 7 F(/?)exp.(J^), 

 where F(/3) is a function of the volume alone, the value of 



* Communicated by the Author. 



