# P-T Phase diagram. Density of material at critical point

One of the questions I had while reading through some material was:

Why is the density of a given volume of gas uniquely defined at the critical point, but not at the triple point?

Is it because at the critical point, a substance will flow like a liquid but retains properties of gas? While at the triple point, any small fluctuation will drive the substance into one of the other well defined phases.

Many thanks

• This is consistent with the Gibbs Phase Rule for one component systems, which is a rule of thermodynamics. I'm not sure how to answer 'why' thermodynamics is obeyed but it often is. Above the critical point there is one fluid phase, and below that two, you gain a phase and lose a degree of freedom. Below the triple point you gain another phase, and lose another degree of freedom. – Mark Rovetta Jan 28 '13 at 18:26
• Many thanks for your answer. I have another question: A P-T phase diagram is a diagram of constant volume. (or more precisely, it is a projection of the 3D graph by a slice at some volume). I read in places that speak of volume changes on this graph. E.g when water is heated from the solid phase, it's density increases and so its volume decreases. This makes sense as a human being, but how does it conform with the fact that the P-T diagram is a projection of the 3D diagram sliced at constant volume? – CAF Jan 30 '13 at 22:54
• Systems can have more degrees of freedom than three (each component is another degree of freedom) and they can be represented in a 2D diagram various ways. See Phase Diagram for an example of a 3D p-V-T diagram for a pure system of a fixed amount of material, but more complex systems and diagrams are possible. – Mark Rovetta Jan 30 '13 at 23:54

This really doesn't have to do with whether the fluids flow or not. Given the limited amount of information, it might be best understood in terms of macroscopic thermodynamics theory, critical-state fluid properties, and phase equilibrium.

For a system of one component (a pure substance) there is an inflection point in the critical isotherm on a PV diagram. The first and second partial derivatives of the pressure with respect to pressure (at constant temperature) approach zero approaching the critical point. This relationship can then be used to evaluate two parameters of an equation of state which is applicable near the critical point. This is the reason that the theorem of corresponding states can be used to model the equation of state of the fluid near the critical point.

The corresponding states approximation becomes more inaccurate away from the critical state conditions, and would not be applicable far away from the critical point at the triple point. There are zero degrees of freedom in a one component system at the triple point (three phases.) So if a any state variable is changed in a system at the triple point, a phase will disappear (Gibbs Phase Rule.)

Although macroscopic thermodynamics theory can not explain what is actually happening at the molecular level. That might be possible using molecular dynamics modeling but you would also need to specify information about the actual composition of the system.

If one looks at a $p-T$ diagram for a single phase system one notes that there is a line that separates the liquid and gaseous states. That line starts at the triple point, where three phases coexist, all at different densities and runs up to the critical point. This terminates at the critical point.

Note that in this set up, the volume is constant.

As you move up this line from the triple point by slowly heating the system, you find that the pressure of the gas phase rises because more and more liquid evaporates and the volume is fixed. Thus its density increases. The liquid phase, on the other hand, becomes less dense as the system is heated.

At the critical point the densities of the two phases vanishes and thereafter there is only one phase present, conventionally called the "fluid phase". The density at this point is clearly defined.

Very very near this critical point microscopic fluctuations in density become both macroscopic and visible with different small regions entering the gas state and then rejoining the liquid state. There are slight differences in density between the two because the system isn't quite at the critical point. Because of this light is strongly scattered by the system which now looks "opalescent" to the naked eye. Once the critical point is passed, in either direction, the "critical opalescence" vanishes.

Critical opalescence is one of those rare cases in which microscopic phenomena become macroscopic and detectable by our senses.