1st and 2d order phase transitions

[paweld]

What's the difference between first and second
order phase transitions. Could anyone give me some simple
examples of both?
Thanks.

 

[Mapes]

For homework-type questions, we ask you to show your own reasoning first, then you'll likely get comments on your proposed answers.

 

[paweld]

OK, I'm looking for a simple example of second order phase transition.
Is "melting" of glass a good example? First derivatives of Gibbs potential
are continuous but what about higher. Second derivatives need to be
discontinous. Are they?

 

[paweld]

What in case of van der Waals gas. On the p-V-T plot all transitions are continous.
How about entropy?

 

[Mapes]

OK, I'm looking for a simple example of second order phase transition.
Is "melting" of glass a good example? First derivatives of Gibbs potential
are continuous but what about higher. Second derivatives need to be
discontinous. Are they?

I'm not sure a glass is the best example. Glasses aren't at equilibrium (they would generally crystallize except for kinetic limitations), so some object to applying equilibrium concepts like phase transitions to them.

Keep searching; there are one or two transitions that are always used as examples of second-order transitions.

 

[paweld]

Of course there are some examples which are alway used but they are not simple.
I don't have any idea why ferromangetic, superconductor or superfluid phase
transition are second order (how to prove it or at least intuitivly understand?).

How to prove that van der Waals gas transition are first order.

 

[Hypersphere]

The general idea is to take the first (n-th) derivative of the free energy and to see that it is discontinuous. The van der Waals transition is a bit complicated given its coexistence region though. I'm sure the proof is available in some lecture notes online or you can find the details in some book on statistical mechanics.

The Fossheim, Sudbo book gives a very clear idea in its first chapter on the second order transition for superconductors. Quite generally second order transitions are linked to symmetry changes. It's quite intuitively easy to see one in superconductors when the Cooper pairs form and break. You get a similar phenomenon in ferromagnets where domains of aligned magnetic momenta are formed.

 

[Mute]

A first order transition (or discontinuous) will give off latent heat during the transition. A second order transition (or continuous transition) will not give off any heat during the transition.

Classification of transitions based on continuity of the derivatives of the free energy is outdated, as it fails to account for cases in which a derivative of the free energy diverges at the transition.

http://en.wikipedia.org/wiki/First-order_phase_transition#Classifications