1917 — 18 .] 
Thermodynamics of Adsorption. 
23 
y — Thermodynamics of Adsorption. By A. M. Williams, M.A., B.Sc., 
1851 Exhibition Scholar of the University of Edinburgh, 1911-14. 
Communicated by Professor James Walker, F.R.S. 
(MS. received July 10, 1917. Read December 9, 1917.) 
Some calorimetric work on adsorption * led the author to a closer con- 
sideration of the thermodynamical aspects of the problem, and the ensuing 
paper is the result. 
Let us consider an adsorbent whose surface of contact with a gas we 
can reversibly change. 
Let v = volume of the system ; 
T = absolute temperature of the system ; 
p — equilibrium pressure of the gas ; 
n = number of mols. of gas in the system ; 
m— „ grins, adsorbent; 
g = , „ „ „ , adsorbing at p, T ; 
a = „ mols. of gas adsorbed per grm. adsorbent, adsorbing 
at p, T ; 
V = volume of one mol. gas at p, T ; 
V tt = „ „ adsorbed gas at p, T ; 
v Q — „ one grm. adsorbent, not adsorbing; 
Va= „ „ „ adsorbing; 
s = surface area adsorbing ; 
A = „ „ per grm. adsorbing ; 
cr = surface tension ; 
H = heat taken in by system from without ; 
, W — work done by system ; 
E = change in energy of system ; 
<p= „ entropy of system. 
We have the two following relations among the variables : — 
s = Ag . . . . . . . . (1 ) 
v = (n- ga)Y + gaV a + (m - g)v 0 + gv a . . . (2) 
We will assume that we cannot arbitrarily alter the dispersivity of 
the system which is measured by A. When n and m are given p and T 
* Proc. Roy. Soc. Edin vol. xxxvii, p. 161 (1917). Before this, Professor F. G. Donnan, 
E.R.S., and the author projected a thermodynamical paper on somewhat different lines 
from the present. The author acknowledges with pleasure his indebtedness to Professor 
Donnan. 
