Lynne Wong's PhD thesis

6.4 HEATS OF SORPTION OF THE MONOLAYER AND MULTILAYER
In the GAB model, m o is the monolayer moisture content, and b and c are constants related
to monolayer and multilayer properties. The temperature dependence of the GAB
constants b and c may be described with an Arrhenius form of equation (Sanni et al.,
1997):
[ ( H1 − Hm
) / RT]
= b e
b
o (1)
[ ( HL − Hm
) / RT]
= c e
c
o (2)
where b o , c o are adjusted constants for the temperature effect, H 1 and H m (kJ mol -1 ) are the
heat of sorption of the monolayer and multilayer respectively, H L (kJ mol -1 ) is the heat of
condensation of pure water vapour (43.53 kJ mol -1 at 35 °C), R is the universal gas
constant (8.314 J mol -1 K -1 ) and T is the Kelvin temperature (K).
The terms (H 1 -H m ) and (H L -H m ) represent the difference in enthalpy between monolayer
and multilayer sorption and the difference between the heat of condensation of water and
the heat of sorption of the multilayer respectively (van den Berg, 1984).
Arslan and Toğrul (2005) evaluated b o , c o , H 1 and H m for the sorption isotherms of
macaroni by using non-linear regression analysis after inserting b and c in equations (1)
and (2) into the GAB equation.
An alternative way of solving for the constants b o , c o , H 1 and H m is as follows:
( ) m
From equation (1), ln b = ln b o +
R T
( ) m
and from equation (2), ln c = ln c o +
R T
1
By plotting ln b against , the intercept is ln bo and the slope is ( H H ) m
T
1
similarly plotting ln c against , the intercept is ln co and the slope is ( H H ) m
T
H
H
1 −
L −
H
H
1
1
1 − and by
R
L − .
R
The heat of vaporisation for the temperature range studied (30 to 60 °C) was taken as the
value at 45 °C. This value was found by interpolation from data in Table 5.3 and was
found to be 44.62 kJ mol -1 .
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