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Subsections

# Geometric Interpretation and Phase Diagrams

## Tangents and Minimization

Suppose we have a system at constant . We minimize .

This means we make a line and the curve A(N). We want to minimize the distance between the line and curve we make a tangent. If the curve is above tangent, the point is locally stable, otherwise--unstable.

• One phase--one minimum

• Binodal--two equal minima

• Metastable point and stable point--two unequal minima (we changed and do not have a bitangent anymore!)

• Unstable point and stable point--minimum and maximum (even greater change in )

Spinodal divides metastable points from stable points!

## Phase Diagrams

In -T space we have a coexistence curve:

In N-T space we have a coexistence region

Why the difference? Because is intensive, and N is extensive variable!

## Critical Point

Is there an ending point for coexistence curve?

Two possibilities:

1.
Free energies of two phases A1 and A2 are different curves--ending point! Liquid-solid phase transition.

2.
A1 and A2 are parts of same curve--ending point is possible! it is called critical point. Liquid-gas phase transition.

Next: Gibbs Phase Rule Up: Phase Equilibria Previous: Free Energy Minima and

© 1997 Boris Veytsman and Michael Kotelyanskii
Thu Oct 2 21:02:12 EDT 1997