Further Considerations of Equilibrium

Recall the Gibbsian statements of equilibrium

$$\input{equations/17-1A}$$ (23-3)

``For equilibrium, any virtual change of the system at constant $P$ and $T$ must lead to an increase in the Gibbs free energy of the system.''

In other words, the Gibbs free energy must be a minimum:

$$\input{equations/17-1B}$$ (23-4)

Figure 23-2: Characterizing the extrema.

This is easier to see if we collect all the dependent variables in one coordinate:

Figure 23-3: One dimensional representation of a free energy curve, what conditions must apply for equilibrium?

Considering the local behavior of $G$:

$$\input{equations/17-2A}$$ (23-5)

The extrema can be characterized:

The points $A$ and $C$ are in local equilibrium.

$B$ is an unstable equilibrium.

$A$ is an absolute equilibrium.

$C$ is a local metastable equilibrium.

Question: What if the extensive variable is held fixed in state $B$ in Fig. 23-3.