# Stability, unstability (and metastability) in liquid-gas phase transition: unstable in regards to what?

Physics Asked on February 26, 2021

I have a question about the stability, unstability (and extra questin about metastability, between the spinodal lines if you have time), when we are having a liquid gas phase transition.

Here, a curve including the spinodal lines. The main thing to look at is in fact the red line obtained by Maxwell construction.

My question is mainly: What do we precisely mean by “unstability” in the phase transition, and how will the system move when I prepare the system in given states.

The volumes $$V=a$$ and $$V=b$$ represent the spinodal lines. Between those two curves the system is said unstable.

Between $$V_1$$ and $$a$$, $$b$$ and $$V_2$$, the state is metastable.

But I want to make things really clear: what do we precisely mean by “stable” and “unstable” zones of the diagram?

Does it mean that if I take an initial state such that:

• the temperature corresponds to this curve $$P(V)$$ (because it is isothermal curves here)

• the volume is such that $$a leq Vleq b$$

And then from this initial state, I fix $$(T,P)$$ and I let the volume change.

The system will be unstable in this $$(T,P)$$ ensemble (the volume will change until reaching the equilibrium). And in practice this zone also corresponds to the phase transition liquid-gas. Thus when the talk about stability, unstability here, they implicitly assume we are in $$(T,P)$$.

Am I right?

I advise to take a look at the beginning of page 64 of this document for further info if you want a more detailed context https://www.uam.es/personal_pdi/ciencias/evelasco/master/tema_III.pdf

Extra question: If I am right with my previous explanation, what happens if I initialize my system in the metastable zone : $$V_1 leq V leq a$$? How do I know if the system stays here, go to do a phase transition to reach the stable state in the “other direction”, go to the stable state just at $$V=V_1$$?