31 
1917-18.] Thermodynamics of Adsorption. 
(3) The gas is adsorbed at constant volume. Consider first an equi- 
librium arrangement as before, whereby a small portion da is isothermally 
expanded to the equilibrium pressure p of the isolated adsorption chamber. 
The remaining gas is expanded to occupy the initial volume, while da is 
adsorbed. The total change in energy is, as before, 
da + da 
oa Jq, T 
, fV8E\ 
J V' \dV J T 
dV + 
n 0 - da )( 
© 
) Y 'da = I 
da/q, t 
da approx. 
In the non-equilibrium adsorption the work done is nil. The energy change 
is the same as in the equilibrium adsorption. (We are again assuming the 
gas phase in the adsorption chamber negligibly small.) Hence, if \ v T denote 
the isothermal heat of adsorption at constant volume, 
X 
v, T = 
In practice the heat effect measured in any case will not be X, but 
\da. 
Ja, 
Freundlich, who has dealt with heats of adsorption in his Kapillar- 
chemief considers an “ isosteric ” heat of adsorption where a is constant , 
p and T variables, and gives the heat of adsorption per mol. under these 
conditions in terms of the Clapeyron equation X = RT 2 ^^— . The formula 
corresponds to the value for \ p> T above. But it is difficult to see how we 
can have an isosteric heat of adsorption per mol. adsorbed, for under the 
defined conditions nothing is adsorbed. We have merely a readjustment 
of p and T. 
The energy change is, in fact, 
Hence the heat change is 
) d T, and the work done 
9 , a 
where the quantity in brackets is evidently the specific heat of the 
system at constant a. 
The only published measurements connecting the heat of adsorption 
with p, a, T are those of TitofF.j* He compares his measured heat of 
adsorption with that calculated from Freundlich’s empirical formula, 
which is based on the substitution of a = a 0 pn in the Clapeyron equation. 
It seems more desirable to compare the observed heat with that calculated 
directly from the thermodynamical formula. As Titoff carried out his 
observations under none of the arrangements (1), (2), (3) studied above, 
* P. 108 et sequitur. See also Partington, Thermodynamics , p. 444. 
t Zeits. f. physik. Them., lxxiv, p. 641 (1910). 
