# Why does Triple point exist?

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.

Is the existence of Triple point a coincidence?

how does one explain existence of a three way junction?

Is it the junction of a part of the graph that is under the solid,liquid and gaseous phase?

• – Anubhav Goel Feb 18 '16 at 8:13
• Look at it this way: just try to draw a phase diagram where gas, liquid, and solid do not have a vertex in common. – Carl Witthoft Feb 18 '16 at 15:17
• What do you mean "why does it exist"? The lines have to meet somewhere (well, one could imagine a diagram that has those lines not meeting, but if you think about it, that substance would behave very strangely). – ACuriousMind Feb 18 '16 at 16:38

The three way junction is there because that is where the three phases (solid, liquid and vapour) of a substance can coexist in thermodynamic equilibrium with one another. At all other temperatures only two (or one) phases can co-exist together in equilibrium.

You might say that you can have ice in a beaker of water with the top of the beaker covered and eventually the ice and the water and the water vapour will all reach the same temperature. So here you have all three phases of water in equilibrium with one another and so it must be the triple point. That is not so because there is also air present which upsets the equilibrium.

Referring to the graph which you have provided which happens to be for water I think?

I imagine that you had a sample of pure water in a container and you could vary the pressure and the temperature within the container.

The phase diagram shows you for each value of pressure and temperature what will be happening to the water inside your container.

For example suppose you kept the temperature of the container at a fixed temperature which was above the triple point temperature but below the critical temperature and varied the pressure within the container starting from a very low pressure, every time waiting for the water to reach an equilibrium state.

Initially inside the container there would be just water vapour but as the pressure increased you would reach a pressure (actually called the saturated vapour pressure) when both water liquid and water vapour could coexist with one another.
The blue line is the saturated vapour pressure against temperature graph.

Increasing the pressure further you would have only water liquid in your container.

If you repeated the experiment at the triple point temperature, at low pressures you would first have water vapour but at a certain pressure you would find that all three phases of water, solid, liquid and vapour, are coexist together in equilibrium.

Increasing the pressure further would result in only water liquid being in your container.

The temperature at which the solid, liquid and vapour phases are in equilibrium is well defined enough to make triple point cells containing pure substance reference points for the calibration of thermometers.

You can gauge the extent to which purity is defined by reading the section Unit Of Thermodynamic Temperature (kelvin) p113-114. They even define the isotopic composition of the water.

I not know what you meant by the word coincidence. The triple point is not unique to water.

• I believe the OP asks why the point of common adjacency to all 3 phases exists. That's a simple topology question. – Carl Witthoft Feb 18 '16 at 15:18
• @CarlWitthoft If you think I am not answering what was asked i will delete my answer. I have tried to show the reason for there being a unique point on the graph where all three phases exist. "What is the explanation of existence of a three way junction?" was one of the questions – Farcher Feb 18 '16 at 15:51
• @Farcher By thermal equilibrium you mean thermodynamic equilibrium? Right? – SRS Feb 2 at 22:28
• @SRS Many thanks for pointing out my error (repeated many times) which I have now corrected. – Farcher Feb 3 at 8:10

The existence of a triple point is not a coincidence at all. It will be a necessary feature as soon as you have three different phases in your phase diagram that can all be reach from each other.

It's like when you have three countries that all share borders. By geometry alone there has to be a point were the borders intersect.

The position of the triple point, however, will of-course depend on the details of the substance at hand.

EDIT: Because thermodynamic phase diagrams can have critical points where phase boundaries terminate, the above rough explanation is not entirely true. One can think of situation where the third phase borders the critical region, as bellow:

However, I know myself of no such phase.

Apart from this I don't see how you can avoid the triple point. (I'm happy to be shown another (non-trivial) example where the triple point is avoided).

IN COMMENT: You may also be interested in looking at Gibbs' phase rule.

• i didn't downvote... but your geometric sense is wrong, for there can be 1. closed phase boundary curves 2. parallel phase boundary curves which can lead to no triple points... – Bruce Lee Feb 18 '16 at 8:34
• I don't understand why is this downvoted without even leaving a comment? It is clearly not universally true, but it is at least partially correct. However, I would have added a link to the Gibbs phase rule. – Yvan Velenik Feb 18 '16 at 8:38
• I accept you comments. One learns things every day. – Mikael Fremling Feb 18 '16 at 9:42
• @BruceLee Interesting - so do you know of any material which acts that way? The only possibilities I see are (1) requires nonzero pressure at 0Kelvin to solidify, (2) requires nonzero pressure at 0 Kelvin to liquify. I'm not sure this is possible under various laws of physics. – Carl Witthoft Feb 18 '16 at 16:44
• @CarlWitthoft: Helium is the only thing without a gas-liquid-solid triple point, simply because it doesn't really have a solid phase. – ACuriousMind Feb 18 '16 at 17:53