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What is the cause behind a gas being difficult to liquify above its critical temperature no matter how much pressure is applied on it?

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No, it is compressible. Liquids aren't compressible. You are misunderstanding something. – peterh Jun 22 '14 at 17:23
That's a good question and anyone can give an intuitive explanation of why the liquid gas transition disappears above the critical temperature I would be interested to read it. "Intuitive" is the key word here! – John Rennie Jun 22 '14 at 19:37

Consider a fixed mass of, say 10g water in a 100ml container at low temperature. Attractive forces cause most of the water to condense into liquid form, with a density of about 1g/cm3. A tiny amount is in the vapour form, at a very low pressure with an extremely low density.

As we raise the temperature of the water, the molecules begin to move about more, and two things happen: The density of the liquid goes down, and the vapour pressure goes up (therefore the density of the vapour goes up!)

At a certain temperature, the vapour pressure is so high that the density of the vapour is equal to the density of the liquid. At this point the vapour and liquid become indistinguishable. The meniscus (interface. between liquid and vapour) disappears. This is of course the critical temperature.

So that, for me at least, is the best way to think of it. The critical temperature is the temperature at which the density (and all other properties) of the liquid and the vapour become the same.

The molecules are moving about so much that the attractive forces are insufficient to cause them to condense into a liquid form.

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As the substance approaches critical temperature, the properties of its gas and liquid phases converge, resulting in only one phase at the critical point: a homogeneous supercritical fluid. The heat of vaporization is zero at and beyond this critical point, and so no distinction exists between the two phases.

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Yes, but why? (Or at least: how?) – peterh Jun 22 '14 at 18:08

How's this for simple and intuitive?

A gas is separate particles moving around at great distances from each other. As you compress the gas, the particles get closer together.

The particles of a liquid are in contact with each other, but as you heat it, there is more and more space between them as they zip and jiggle more and more.

The combination of heat and pressure cause both gas and liquid to reach an intermediate point where the distances between the particles are the same. If there's no difference, there IS no difference. Gas and liquid merge.

Or how about a simple drawing? It shows up in an interesting way on the Phase Diagram. If you were to draw the liquid/vapor line from an angle so you can see the heat of vaporization as the height of a cliff, the cliff gets shorter and shorter and ends at the critical point.

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To have a picture of the critical temperature, let us consider the 3d or 2d Ising model.

It is known that in the absence of an external magnetic field, there is a critical temperature $T_c$. Below $T_c$, the system can either point up or down on average. The up-pointing state can be labelled as the gaseous phase, while the down-pointing state can be labelled as the liquid phase. These two phases are essentially the same phase. The only difference lies in the value of some physical quantity. Here, in the Ising model, it is the magnetization. In the gas-liquid phase transition, it is the density per volume. Like the gas phase and the liquid phase, the up-pointing and down-pointing states can be continuously linked.

For the Ising model, we need to go below some critical temperature to enter the spontaneously magnetized phase; for a cloud of molecules, we also need to go below some critical temperature to have the gas-liquid phase transition.

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The ising modeled particles above the critical temperature would be in which state according to you? Are you saying that an ordered phase transition is only possible at subcritical temperatures, without discussing what happena above it? – Kurtovic Jun 25 '14 at 13:19

There are not many difference between liquid and gas (vapour):

  1. Liquid is more dense than gas (also has greater viscosity, refraction coefficient, etc)
  2. Liquid is "not compressible"
  3. Liquid has surface tension

The first one is vague (one cannot define a threshold above which the stuff can be called liquid).

The second one is a small lie: any liquid can be compressed, it's just usually too hard to do it.

So what about surface tension? It's caused by the molecules on the liquid-gas boundary being "sucked" into the liquid phase.

When the temperature of the liquid rises, the density decreases, so there are fewer neighboring molecules that suck it inside the liquid. In addition, each molecule has a greater chance to escape, because it has more energy. At some point (critical temperature), pressure is just not enough. The energy of each molecule becomes greater than attraction force from its neighbors (at that temperature and density).

Here you can see the experiment on CO₂.

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Simply put, a liquid stays where it is but a gas fills the space available because the attraction between the molecules in a liquid is usually great enough. Not always, though. The energy of molecules is randomly distributed, and therefore even in a liquid there will be a few molecules with high energies. If they're near the surface, their high energy will allow them to escape - that's why fluids evaporate even if not boiling.

Still, that leaves the question why there's a critical point. Basically, if you increase pressure, you push the molecules closer together, which increases attraction and raises the boiling temperature. But if the temperature is sufficiently high, no amount of pressure will bring them close enough together; energies flat out exceed the possible attraction.

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Does this explain how you can go smoothly from a liquid (below the critical temperature) to a gas (below the critical temperature) without a phase transition by taking a path in the pressure-temperature plane which goes above the critical temperature? – Peter Shor Jun 22 '14 at 23:48

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