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When looking at the 3D phase diagram of water I felt unsure whether the only physical points were the ones on the surface of the plot.

If it is unphysical to move outside the surface of the phase diagram ("on shell"?) the question might be moot, but I guess there are conditions for when the phase diagram applies/does not apply. I am not sure when thermodynamics applies and does not apply; is perhaps heating ice by whispering at it too fast a process, or using a frying pan too fast a process, or microwaving too fast a process, or exploding with a nuke too fast a process, is it the energy flow per unit time over some volume that decides whether the process is too fast, etc.

So the question is when is a phase diagram valid and what kinds of processes follow the phase diagram and does the process necessarily need to lie embedded as a curve in the surface of the phase diagram?

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I am not sure to understand your question.

A phase diagram typically describes the equilibrium state, in this case of water, depending on different thermodynamic parameters. So a phase exists for every point of the graph and typically a shell, as you describe, represents a phase transition, an interface between two phases.

You can connect two points of the phase space by changing the thermodynamic parameters and letting relax. You could describe non-equilibrium process, but should be very careful about what you define as your parameter.

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  • $\begingroup$ In for example commons.m.wikimedia.org/wiki/… does this mean that it is not the grey surface that is liquid, but it is rather the boundary of a region of possible states in which the phase is liquid? So one can increase the pressure and it is still a liquid? Seems odd that it is the surfaces that are given names and not the volumes in that case... $\endgroup$
    – Emil
    Commented Jun 27, 2017 at 10:40
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    $\begingroup$ This figure comes from this article, which I'm not sure you can access. The 3D plot is an intra/extra-polation of something you'd usually see in 2D, as is seen in the article. Basically, it's not the surface that is liquid but every point you would see above. The curves have something to do with constant parameters (like isobar, which is constant pressure) and allows to move adiabatically on this figure. $\endgroup$
    – gingras.ol
    Commented Jun 27, 2017 at 17:58
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The 3D phase diagram know also as thermodynamic phase diagram is associated to a binary system. 2 axis are composition of each component respectively. Then the third axis is for temperature. Therefore, phased are not limited to a state phase as liquid, solid or gas.

The diagrams show phase diagrams in the context of solutions. In all diary system. Some authors call these diagrams a crystallization diagram. Here is a good presentation on the subject here

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  • $\begingroup$ Sorry, do not understand your answer. $\endgroup$
    – Emil
    Commented Jun 27, 2017 at 21:12

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