26 Proceedings of the Royal Society of Edinburgh. [Sess. 
If we are dealing with a gas below its critical temperature, we may 
regard or as a function not of p and T but of p/P and T, where P is the 
saturated vapour pressure at T. 
Then 
0(7 
0T A 
0<x\ 
dl'Jp/F + [Sp/pJt ' V *0T 
So- \ fdp/P 
= (t) +?( S p 
0TA 
Pi P 
dpj t 
p (IP 
F ' dT 
= + r yP . 
V0TA/P P cT r 
dp 
0E\ 
ds / p, t 
CT 
- T SLrl’a- p 
Jd<r\ f 
_pV 
T 
r 
( 10 ') 
Let us consider the case when p = P, and denote o-(P, T) by o- P . Then 
0E\ 
= ; <t 
0S / P,T 
'T' tcr p I I r| 
0T ' " 
frp^P 
\ [ dT 
p y.r 
( 10 ") 
T dP _ p 
dT 
Now the change in energy when one mol. vapour condenses into liquid 
is given by 
AE = — ^V G — V L 
Hence, since 
TV = a(V G — V a ) approximately, 
= a(Y G -Y L ) 
the energy change when the adsorbent is exposed to liquid instead of 
vapour is given by 
0E'\ 
=(rp 
OS / P, T 
■\( T(X p 
dT 
(ii) 
an equation similar to that originally given by Kelvin for the stretching 
of a film. <7 P evidently corresponds to the surface tension between two 
liquids. 
When a powder is immersed in a liquid no external work is done, 
hence the heat of immersion emitted per grm. adsorbent is given by 
V 
'0E /N 
\ 
- b/ ' 
' P. T 
0E ,N 
) ‘ A 
. 0S / 
'P,T 
V 
rpd'Tp\ 
dT ) 
when the powder is free from any adsorbate before immersion. It must, 
however, be noticed that in the equations above we have considered the 
development of the surface to proceed from the interior of the adsorbent 
amidst the gas. In the case of immersion a surface has already been 
