1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Liquid-gas phase transition: metastable mixed states?

  1. Jan 2, 2018 #1
    Hello everybody.

    I am trying to understand better what happens at a liquid-gas phase transition for the Van Der Waals model.

    From what I have understood, from the Van Der Waals model we are able to plot the curve P(V) and to calculate the free energy F. Here are such curves :

    Then, we remark that the free energy doesn't have the good convexity property between a and b. For a system to be stable the Free energy must be concav.

    In fact this "mistake" on the free energy is from what I have understood an inaccuracy of the van der waals model (this one assume that the density is uniform and it is no longer the case when we have a phase transition).

    The maxwell construction thus "correct" the model.

    My question are :

    Between a and b, I am in an unstable states, what does that mean ? Usually we work in the (N,P,T) ensembles for gas-liquid transition. I take the temperature and pressure associated to the curve plotted in the P(V) graph above.

    • Does that mean that if I wait long enough, my volume will never reach a value between V_1 and V_2 ? It can only be V_1 or V_2 (where we are stable).

    Between the points 1 and a, I have read that the liquid-gas mixture is metastable. But I don't understand why as the derivative of the Gibbs Energy is not 0 in this zone (The Gibbs function is not plotted above but it is clearly not 0 in this whole zone). Thus we are not in an minimum of G.

    • Can this metastability be understood from the thermodynamic variable we compute ? Or it can't because as we said, the van der waals model is innacurate when having the phase transition. And then I can't focus on the derivative of G to know if I am stable, unstable, metastable...
    • What does that physically mean to have a metastable equilibrium between two phases ? A stable equilibrium I totally get it (if I let the system like this it will last forever in this state). But for a metastable thermodynamic equilibrium ? What would change if the equilibrium would be stable for example ?
    Thank you a lot for your help.
  2. jcsd
  3. Jan 5, 2018 #2
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted