I know the difference between first and second order phase transition in terms of the discontinuity of the derivatives of free energy.

I am curious to know what happens as the system is viewed. Suppose a liquid is heated in a container. For a first order phase transition, a liquid, which has a finite volume (but takes the shape of the container), will consume the volume of the whole container when it turns into gas.

What happens in case of a second order phase transition?

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Suppose I take a system in state P ($T>T_c, P > P_c$) or Q ($T > T_c, P < P_C$) in the phase diagram. Will it have a finite volume, or will it consume the whole volume of the container? In a second order transition, can a fluid "continuously" transit between a state with finite volume and a state consuming all volume of the container (in other words, infinite volume when allowed to grow)?

It seems to me that the property of whether the fluid will have finite volume or not, cannot change continuously.

  • $\begingroup$ Please note that I am not asking about what happens to the thermodynamic quantities during a second order phase transition. I am asking how it is different (as seen by the experimenter) compared to the usual boiling of water. I could not find any similar question in Physics Stack exchange. $\endgroup$ Commented Oct 17, 2020 at 16:59
  • $\begingroup$ It would be great if someone can suggest a better title. $\endgroup$ Commented Oct 17, 2020 at 17:24

1 Answer 1


To hit the critical point precisely, you must have exactly the right amount of fluid (and nothing else but the liquid and its vapour in equilibrium with it-- no air for example) in a sealed container with fixed volume. Too little and the mensicus separating the liquid from the gas phase will go down as the temperature rises, and all the fluid will change to gas before the critical temperature. Too much and the meniscus will go up and all the fluid will change to liquid before you get to $T_c$. Above $T_c$ the resulting liquid or gas phases will become indistinguishable.

If you have exactly the right amount (i.e. the amount in the sealed vessel such that at $T=T_c$ you have $P$ exactly equal to $P_c$) the meniscus will stay in the same place as you heat. As you approach $T_c$, the fluid will get cloudy (critical point opalescence) and then clear again and meniscus separating the liquid and gas will have disappeared. On cooling there usually little opalescence and droplets of liquid will suddenly appear in the gas as $T$ falls below $T_c$. Initially the liquid has the same density as the gas, but soon the liquid will become denser and fall to the bottom of the vessel so a mensicus will appear and separate the two phases.

It's a rather dramatic thing to watch. Physics apparatus vendors used sell sealed glass vials for demonstrating these effects in classrooms. I think the fluids were fluorocarbons, so I don't know if they still sell them.

  • $\begingroup$ Suppose I take water in a sealed container at room temperature, but $P>P_C$. The whole container is filled by water, and there is no meniscus. Then I heat it, so that the temperature keeps increasing, and I don't stop heating until $T > T_C$. What changes will I see? $\endgroup$ Commented Oct 18, 2020 at 10:53
  • $\begingroup$ Thanks for mentioning the demonstration. I found this youtube.com/watch?v=yBRdBrnIlTQ . Due to the pandemic, I cannot return to our university to try it out myself. $\endgroup$ Commented Oct 18, 2020 at 10:55

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