For
N2 vapor adsorbing on a nanopowder at 77 K, we use
a multicomponent canonical ensemble to determine the conditions for
equilibrium between a contacting vapor phase and the adsorbed molecular
clusters. Provided the substrate variations (heterogeneities) do not
cause a phase transition, such as wetting or capillary condensation,
we show that the equilibrium conditions allow an expression for an
adsorption isotherm to be formed. The isotherm expression contains
four constants that are to be obtained empirically from mass-specific
adsorption measurements. The specific surface area of a substrate
is expressed in terms of the specific number of adsorption sites and
the cross-sectional area of an adsorbed N2 molecule on
materials. This procedure is investigated by using the respective
specific surface areas of different samples of a given material to
transform the data into an area-specific basis. We pooled data sets
from multiple samples with possibly different specific surface areas
to form a single data set. The thermodynamic (zeta adsorption) isotherm
is formulated after a regression analysis is performed on the pooled
data set. This isotherm is used with the Gibbs adsorption equation
to obtain the solid surface energy of a material as a function of
the amount adsorbed. Five materials are examined: silica, α-alumina,
γ-alumina, carbon black, and graphitized carbon. Their respective
solid surface energies are each shown to be a material property.