# B Critical temperature, or: Is the supercritical liquid a phase?

1. Feb 22, 2017

### Staff: Mentor

Somehow I am worried it is a can of worms, but I will still try.

This started with a student confused with statements describing critical temperature for the gas/liquid equilibrium. Some books and sources state it is the highest temperature AT which it is possible to liquefy the gas just by applying higher pressure, some state gas can be liquefied only BELOW the critical temperature, I have also seen a statement that the critical point is the first point where only one phase (supercritical fluid) exists. While it doesn't matter much for practical purposes, I can see how it is confusing.

So, which one it is? At, or below?

My thought was - critical point is the end point of a phase equilibrium curve. In other words - as long as the curve exists there are two phases, liquid and gas. But, if we think about the supercritical liquid as a third phase, critical point becomes something like a triple point, where three phases - gas/liquid/supercritical liquid - coexist (yes, I know - it is a moot, as at critical point these three phases become indistinguishable). This makes whole discussion much easier and less confusing IMHO, and it also makes the answer "at" the correct one. But is it?

2. Feb 22, 2017

### hilbert2

There should be some kind of a discontinuity in heat capacity and molar volume when going from one phase to another. When approaching the critical point, this discontinuity becomes "smaller" and at the critical point the discontinuity disappears.

3. Feb 22, 2017

### Staff: Mentor

Good point (and that's more or less what I meant stating that these phases become indistinguishable). But it still doesn't help to address the original problem - is the critical point the first one at which the liquid no longer exists, or is it the last point at which liquid does exist?

4. Feb 22, 2017

### hilbert2

When you approach the critical point temperature, the discontinuous jumps in the molar quantities eventually become so small that it's impossible to notice a phase change happening, so I'd say that the critical point is the first point where liquid doesn't exist. It's not very useful to talk about mathematically exact values of temperatures, when it's about thermodynamical variables that in a rigorous sense are defined only at the thermodynamical limit (infinitely large system).

5. Feb 22, 2017

Staff Emeritus
Both are sets of measure zero.

6. Feb 22, 2017

### Staff: Mentor

Perhaps I am missing something, but if so, I don't see how to define the critical point in a way that produces any number.

7. Feb 22, 2017

Staff Emeritus
Think about a phase diagram - the critical point is a point on this diagram. Not an area.

8. Feb 22, 2017

### Staff: Mentor

Definitely, but the same can be said about triple point, or - for constant pressure - about boiling point and melting point. These are points, but it doesn't stop us from defining them in an unambiguous way.

9. Feb 22, 2017

### Khashishi

It sounds like you are asking, is 0 the largest negative number or the smallest positive number? Neither. As for which side of the boundary the critical point lies, don't worry about it. It's not important.

10. Feb 22, 2017

### Staff: Mentor

Sure. Still, measure of the set containing just zero is not zero (to use nomenclature suggested by V 50).

I am not worried about it I am looking for a best way of helping someone confused.

Apparently the best approach is to wave hands and say "you see, critical point is different from other specific points on the phase diagram".

11. Feb 22, 2017

### zbikraw

Supercritical fluid is simply a fluid, i.e. belongs to the same category as liquid and gas. It simply has no shape and moves in characteristic fluid manner. The differences between liquid and gas are about their surface. Gases have not surfaces, only borders to another phases. Next to it is compessible-expansible behavior. Supercritical fluids have not surfaces, so behaves like gases. Their densities, viscous behaviour and elastic properties are more liquid-similar. In a phase diagram they occupy high-pressure regions, so observation of their surface properties is only possible when they do not mix with other fluid (mainly there is surface of this other fluid). This surface-less behaviour means they nearly perfectly wet any body in contact with. This property is exploited in machine washing and live matter extraction (exploiting essential oils and grasses).

12. Feb 23, 2017

### 256bits

Perhaps the PV diagram can give another aspect that the PT diagram does not.
The point on the PT becomes a curve of the phase lines of saturated liquid and saturated vapour.
The point of maxima is where the 2 curves meet.
And one can follow the critical temperature line also.

http://www.learnthermo.com/T1-tutorial/ch02/lesson-B/pg06.php

Or, maybe the Pρ( density) diagram where the critical temperature isothermal has a point of inflection at the critical pressure.
http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture_25/node1.html

13. Feb 24, 2017

### zbikraw

For the sake of systematics: give names to things and phenomenas only when they cannot be descripted in categories of other things or phenomena. Supercritical fluids match some properties of gases and liquids we know from everyday observations. Some other properties are between gases and liquids. This is mainly because they are high pressure phases. In terms of thermodynamics there is nothing unusual, they are simply high pressure gases. From our atmospheric pressure point of view they are marvelous, have unique properties, etc. There are many strange properties of high pressure phases, for example 15 (as I well remember) different phases of ice, most accesible from other high prassure phases through specific and uncommon paths realized in diamond-anvil apparatus.
Quoted phase diagrams have some rules of making and reading them. Lines (in genereal surfaces, but it is not easy to visualise them on 2D diagram) are paths of 2 or more phases coexistence in equilibrium. When changing parameters, points of equilibrium shifts to other value and curve arrives. Worthy noting that even simple changes demand at least 3D to dynamically visualise them and 2D curves are oversimplification, mainly for didactic purposes. In reality they are surfaces. Lines are discontinuities in physical properies of materials which constitute phase changes. Their classification is also simple: first order phase change is discontinuity of first derivative of thermodynamic potential, second order is discontinuity of second derivative, etc. Note that most thermodynamic potential are not measured directly and theis numerical values bears errors from measurement of all necessary properies.
There may be infinite numbers of phase changes of pure substances but measurement errors and difficulties in obtaining a real thermodynamic equilibria (there are metastable phases, etc., and any change should go through "excited state" characterized by activation energy or volume) make most of them worthless. Quite other situation is met in a many-component mixtures, frequently important in economy or non-physical sciences. In metallurgy and ceramics simplest way to investigate phases is diffraction of X-rays, electrons, neutrons, etc. We must remember that really measured crystal lattice parameters are of "statistical" precision, and textbook diagrams may be false.
Nota bene: "suerheated vapor" in PV diagram is technical decsription born in steam-boiler technology. It is simply gas. Such high-temperature water is non-polar and dissolves fats, which in technology is name-worthy.
Best regards,
zbikraw