Chemistry Reference
In-Depth Information
The phase rule criterion of single substancehood is subject to restrictions, and
even within its range of application, it conflicts with other criteria. It is restricted,
first and foremost, to equilibrium conditions. Thermodynamics, and the phase rule
deduced from it, applies to systems at equilibrium—that is, equilibrium under
prevailing constraints (there is no unqualified notion of equilibrium). If a rigidly
fixed wall of a vessel is somehow unlocked and allowed to move, for example, the
system comprising the material in the vessel will readjust to the new equilibrium
conditions, perhaps by reducing its internal pressure or changing the amounts of
matter in two or more phases. The question of how to recognise equilibrium is a
notorious issue. Duhem was led to introduce the notion of false equilibrium for
apparently unchanging states which don
t comply with thermodynamic conditions.
Clearly, it is not a simple matter of observation, as Callen puts it in his well-known
textbook:
'
quiescence is not sufficient. As the state is assumed to be characterised completely by the
extensive parameters,
U, V, N
1
,
...
,
N
r
, it follows that the properties of the system must be
independent of the past history. This is hardly an operational prescription for the recogni-
tion of an equilibrium state
...
In practice the criterion for equilibrium is circular.
Operationally, a system is in an equilibrium state if its properties are consistently described
by thermodynamic theory!
(Callen
1985
, pp. 13-5)
Callen illustrates the point by pointing out that “failure of H
2
to satisfy certain
thermodynamic equations motivated the investigations of the ortho- and
para-forms of H
2
” (loc. cit.). Whether concepts applicable under equilibrium
conditions continue to apply under non-equilibrium conditions calls for careful
consideration. Temperature, for example, is a thermodynamic concept not appli-
cable to a body which is not at equilibrium. But an extension of thermodynamics
to irreversible thermodynamics allows that, under not too radical non-equilibrium
conditions, thermodynamic concepts such as temperature can be applied to points
at instants of time, varying smoothly from one point and time to another.
4
In that
case, even though a body not at equilibrium doesn
t have a temperature, it may
well be possible to assign a temperature gradient over the body. A similar
distribution of substances may be possible throughout a body subject to diffusion
and chemical reactions.
A related constraint concerns the time scale of the intervals during which
two quantities stand in the same substance relation. Thermodynamic equilibrium
corresponds on the microscale to a dynamic balance between constantly ongoing
processes, which is achieved for times long enough for fluctuations to be ironed out
by statistical averaging. It can therefore only provide criteria for sameness and
distinctness of substances holding for sufficiently long times. This covers intervals
'
4
It is apposite to note that in his final chapter, Denbigh (
1981
) emphasises the importance of the
concept of equilibrium even in kinetics: “There is no theory of rates which stands
on its own
feet; all existing theories depend, in one form or another, on ideas carried over from the study of
matter at equilibrium” (p. 439).
...
