Page 73 - Chemical equilibria Volume 4

Properties of States of Physico-Chemical Equilibrium 49
2.6.1. De Donder’s general stability condition
Consider a system S defined by the chosen values of the intensive
variables and by an extent ξ of the transformation envisaged (ξ can be null).
The values of the different physical intensive variables are kept constant. If,
at a given time, that system is at equilibrium, it is because its rate ℜ is null.
S
At the same time, imagine another system S’, identical to S except for its
extent, which is ξ’ = ξ + δξ. System S’ is said to be disturbed in relation to
system S. It is generally not at equilibrium, and thus its rate ℜ is different
' S
to zero. δξ is called the disturbance.

De Donder says that system S is stable in relation to the disturbance
δξ if the rate of system S’ has the sign which tends to bring S’ back to state
S.
Hence if δξ > 0, then ℜ must be negative in order for system S to be
' S
stable. Conversely, if δξ < 0, then ℜ must be positive. This gives us the
' S
stability condition of S according to de Donder:

ℜ ' S δξ < 0 [2.52]

2.6.2. Stability of a system with unilateral variations

System S will be said to be of unilateral variations if the disturbance
cannot take only a single positive or negative sign. Thus, we can take the
origin ξ = 0 for the extent.

0
Let us choose, for example, δξ > (we could also have made the opposite
choice and the conclusions drawn would have been the same). In view of the
inequality [2.52], system S will be stable if:

ℜ< 0 [2.53]
' S
Yet system S’ obeys de Donder’s inequality [1.50], so here:

A ' S ℜ> 0 [2.54]
' S