30 Proceedings of the Boyal Society of Edinburgh. [Sess. 
is isothermally expanded to the equilibrium pressure p of the adsorption 
chamber, which is isolated from the gas to be adsorbed. The change of 
energy on expansion will be 
da 
( ( d F) dV . 
'v- \3 V / t 
The change of energy on equilibrium adsorption of da, the adsorption 
chamber being brought back to its original volume, will be 
(— ) da. 
\da Jg, T 
Hence the total change in energy of the system will be 
/0E\ j 7 , 
— - da + da 
\daJ 
g, t 
70E\ 
Jv- \dVA 
where the second term is in general negligible. 
In the non-equilibrium adsorption of da, the work done by the gas will 
be —p'Y'da. The change of energy will be the same as in the equilibrium 
adsorption. Hence, if \ p ,t denote the isothermal heat of adsorption at 
constant pressure , 
— X p ^da + p'V'da' 
— ) da 
da J g, T 
or 
da . 
,fda'\ 
\daj 
( 17 ) 
^ ^ is the ratio of the gas entering the adsorption chamber to the gas 
actually absorbed, and will in general (i.e. at low pressure, etc.) be approxi- 
mately unity. Thus we have, equating volumes, 
In - a)Y = (n 4- da — a — da) { Y + da ) t . 
I \0a/T J 
da 
da 
)I 
V 
( d X\ . 
\dp J t 
\daJ' 
The second term is usually negligible. For example, taking y>V = RT, 
we have 
1 0Y 
dp 
n — a 0 logy 
a 
— (n — a) 
Y 
da p da 
0 log a 
By taking the gaseous phase in the adsorption chamber n — a sufficiently 
small relative to a, we can make the expression as small as we please, since 
0 logy 
, although never less than unity, is finite. 
0 log y . - 
° ^ =n when a = a n p n 
o log a 01 
0 log a 
and n is usually greater than unity.) The third term in case (1) may be 
similarly treated. 
