29 
1917-18.] 
Similarly, 
Thermodynamics of Adsorption. 
Neglecting as before the change in energy of the unadsorbed gas, we get 
dl] = (,v(p- + T 3 - a ) - —V ( + T— ] 
' • Vdp 0T / A- V dp 0T / 
/0E\ 
\dp/y,? 
\dp / s, T 
da rfi da \ as - 
dp 0T / A 2 
0A 
M\ 0E 
dp 
0T / 0s 
9 
0A 
019 
• =-(/V^rf^) _A qgVf T /3p\ _ 1/3A\ 1 
' \ 0 aA.T ” /V \ V0TA y J h A rWi P /\0aA + A 
"faking for simplicity </=l, we have 
0E\ 
da) (j. 
= - V T 
rJdp 
0T 
V, 
P I + \W A 
+ flYT 
,/0y\ 
\0T/ 
0E\ 
/0A\ 
0 ' 
0(7 A, t V da / t 
PUT 
1 (d A\ 
A \ 06« / T 
(15) 
The effect of a possible variation of A is represented by the second term 
on the right-hand side. We cannot easily directly estimate its value, since 
we cannot measure A. It is therefore necessary to compare the two sides 
of the equation (15) by means of other observed quantities. 
We may define the heat of adsorption as the ratio of the heat evolved 
to the gas adsorbed when only a very small quantity of gas is adsorbed. 
For our present purposes we will consider a and not a as the gas adsorbed 
per grm. As has been noted before, a and a differ in ordinary cases by a 
small quantity only. We will consider the following three cases* of 
adsorption at constant temperature : — 
(1) The gas is adsorbed very slowly, so that the vapour phase is con- 
stantly in equilibrium with the adsorbed phase. Work is done by pressure 
and surface forces. Let us denote this, the isothermal equilibrium heat of 
adsorption , by X T . Then 
diK = - X T da - pdv + crd A. 
The third term represents the work done by the gaseous phase in expand- 
ing, and may in general be ignored. 
(2) The gas is adsorbed at constant pressure. Consider first an equi- 
librium arrangement whereby a small portion da of the gas at pressure p 
* Following Donnan in an unpublished paper. 
