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developed vector analysis. Gibbs’ life was uneventful; he never married and lived in his
Chapter 4
Material Equilibrium family’s house until his death. Ostwald wrote of Gibbs: “To physical chemistry he gave
form and content for a hundred years.” Planck wrote that Gibbs “will ever be reckoned
among the most renowned theoretical physicists of all times....”

4.2 ENTROPY AND EQUILIBRIUM

Consider an isolated system that is not at material equilibrium. The spontaneous chem-
ical reactions or transport of matter between phases that are occurring in this system
are irreversible processes that increase the entropy. These processes continue until the
system’s entropy is maximized. Once S is maximized, any further processes can only
decrease S, which would violate the second law. The criterion for equilibrium in an
isolated system is maximization of the system’s entropy S.
When we deal with material equilibrium in a closed system, the system is ordinar-
ily not isolated. Instead, it can exchange heat and work with its surroundings. Under
these conditions, we can take the system itself plus the surroundings with which it in-
teracts to constitute an isolated system, and the condition for material equilibrium in the
system is then maximization of the total entropy of the system plus its surroundings:

S syst S a maximum at equilib. (4.1)*
surr
Chemical reactions and transport of matter between phases continue in a system until
S S has been maximized.
syst surr
It is usually most convenient to deal with properties of the system and not have to
worry about changes in the thermodynamic properties of the surroundings as well.
Thus, although the criterion (4.1) for material equilibrium is perfectly valid and gen-
eral, it will be more useful to have a criterion for material equilibrium that refers only
to thermodynamic properties of the system itself. Since S is a maximum at equilib-
syst
rium only for an isolated system, consideration of the entropy of the system does not
furnish us with an equilibrium criterion. We must look for another system state func-
tion to find the equilibrium criterion.
Reaction equilibrium is ordinarily studied under one of two conditions. For reac-
tions that involve gases, the chemicals are usually put in a container of fixed volume,
and the system is allowed to reach equilibrium at constant T and V in a constant-
temperature bath. For reactions in liquid solutions, the system is usually held at atmo-
spheric pressure and allowed to reach equilibrium at constant T and P.
To find equilibrium criteria for these conditions, consider Fig. 4.1. The closed
system at temperature T is placed in a bath also at T. The system and surroundings are
isolated from the rest of the world. The system is not in material equilibrium but is in
mechanical and thermal equilibrium. The surroundings are in material, mechanical,

Surroundings at T

System at T
Figure 4.1
Impermeable wall
A closed system that is in
mechanical and thermal
equilibrium but not in material
equilibrium. Rigid, adiabatic, impermeable wall