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Subsections

# Phase Transitions in Van der Waals Gas

## General Theory

We know from previous lectures :

Stability condition:

Is this always true for VdW gas?
 (4)

1.
If T is large enough, the first term in (4) dominates--system is always stable
2.
If T is small, first term wins only for and --system is unstable at intermediate V!
3.
Borderline case: just in one point (critical point K)

Phases:

1.
At T>Tc one phase (fluid)--no phase transitions
2.
At T<Tc two phases (liquid & gas)--first order phase transition
3.
At T=Tc--second order phase transition

Equation for Tc:

or

Result:

## Law of Corresponding States

Let us measure everything in critical units:

Van der Waals law:

This is same for all van der Waals gases! All PVT data lie on same master curve. This is called law of corresponding states.

## Maxwell Construction

Let us determine binodal for van der Waals gas. In coexisting phases or

If , we have , or

It means that dashed areas below are equal!

Next: Quiz Up: Thermodynamics of Phase Transitions Previous: Phase Transitions

© 1997 Boris Veytsman and Michael Kotelyanskii
Tue Oct 7 22:16:36 EDT 1997