Solids can be thought of as the lowest energy state for ordinary matter. The molecules of the substance don't move very much and only vibrate back and forth. There is no large scale translation of position. As a result, the kinetic energy of the molecules is relatively very low.

The molecules of a liquid have more energy than in a solid. They may slide past each other and move around, but are still bound to each other somewhat. Liquids occur at higher temperatures than solids and thus contain more energy.

Gas molecules have more energy still. The kinetic energy of the molecules is so great that the gas molecules break their cohesive bond to their fellow molecules and are free to propagate. Of course this should all be relatively familiar.

This transition does not come free however. There is an energy cost which we must pay in order to change phases. This energy is known as the latent heat of the phase change. The amount of latent heat is the amount of energy that one must put into the substance in order to change the state, and this energy does not go into raising the temperature at all. During a phase change, the temperature of the substance remains constant as energy is put in. Of course, this is only for phase changes associated with heating up the substance. When cooling, the latent heat instead come out of the substance and into the environment.

Okay, but what's so important about it? When a system is in equilibrium we can say that there is no heat flow into or out of the system. All forces are balanced and nothing is accelerating. As we will see, this does not mean that the temperature or forces acting on a system have to be zero, just balanced. There are plenty of examples of equilibrium around you all the time. The pencil that might be sitting on your desk is in thermal equilibrium with the desk and the air; they are all at the same temperature whether you like it to be a cool 15 Celsius in your room or a balmy 25. It is also in mechanical equilibrium. The force of gravity pulling it downwards is not gone; it's still quite there. It is just being balanced out by the force of the desk acting upwards. Neither of these forces are zero, but they are balanced, hence the pencil is in mechanical equilibrium with its surroundings.

With all of this nothing going on, it may surprise you to find out that there are actually two kinds of equilibrium that are quite different. Yes, a system doing nothing can be doing it in two different ways. The first is called stable equilibrium and is the one most of us are familiar with. When a system is in stable equilibrium it is in its lowest energy state given the current conditions. Think of that pencil sitting on your desk again. Or perhaps a ball in a hole. There is nowhere for it to go, you can knock it around the hole a little bit and it will sit there.

The second type of equilibrium is called meta-stable equilibrium. Think of 'meta-stable' to mean 'sort-of stable'. Think of that pencil again, but this time, imagine you balanced it carefully on its eraser end. It is still at the same temperature, so it's in thermal equilibrium, and it's just sitting there on your desk, not accelerating, so again it's in mechanical equilibrium. There is one key difference though. If you disturb the pencil a little bit, it will fall over. This is the difference between stable and meta-stable states. In a stable equilibrium, the system will return back to its original state when disturbed, in a meta-stable state the system does not return to its orginal state.

Meta-stable states are usually the result of a careful change of the environment around an object or system. Again, think of your pencil. When you stood it on its eraser you used your hands to stabilize it while you stood it up. With your hand still around it, the pencil is in a stable equilibrium. You then have to carefully remove your hands to set up the meta-stable state.

In general matter is physically in stable equilibrium. Water at 20 degrees Celsius is usually a liquid. Iron is usually a solid at room temperature. Nitrogen is usually a liquid at -200 Celsius. But can we set up a meta-stable state of matter? Can we have liquid water at -5 Celsius at standard pressure? What about 105 Celsius? Water vapour at 95 Celsius?

Let's start with supercooling. Supercooling is the process of cooling a fluid below its normal freezing or condensation point without the fluid undergoing a phase change. This might not sound possible but in fact it is possible to have liquid water at standard pressure at -42 Celsius. Supercooled water exists naturally in the form of supercooled water droplets in stratiform and cumulus clouds at high altitudes. In these clouds, liquid water droplets are cold enough to be solid ice. They will stay liquid until a disturbance, such as the wingtips of an airplane, disturbs the meta-stable equilibrium. Once this happens, the liquid solidifies rapidly.

It is also possible to superheat liquids to temperatures above their normal boiling point. This is something that you may have experienced by accident. Microwaves have the ability to heat a cup of water rapidly and evenly, a process which can often lead to superheating. If you have ever put a cup of water in the microwave on high power for a long time, taken it out, and put your tea bag in it only to find it rapidly bubble as soon as you do, then you have experienced superheated water. That water was actually sitting at over 100 degrees Celsius in a meta-stable state until you put your teabag/spoon/hot chocolate mix/etc in.

You can super-saturate solutions as well. Normally, sodium acetate will dissolve readily in water. We can add more sodium acetate and dissolve that as well, but eventually there will be a point where the water can't hold any more and whatever extra we continue to add will sit at the bottom of the glass as a solid. We can heat up the water and it will dissolve more sodium acetate as hot water is able to hold more solute than cool water. By carefully cooling the solution, all of the sodium acetate will remain dissolved, even when the temperature of the water would not normally permit all of the solute to be dissolved. This state is known as super-saturation.

Why don't supersaturated solutions precipitate out? Why don't supercooled fluids condense or freeze? Why don't superheated liquids boil? The answer to these questions is simliar to the reason why a tabletop of set-up dominoes doesn't fall over. They are in an equilibrium state and will remain there until disturbed.

To disturb a tabletop of dominoes one simply has to push the first one over. Through a chain-reaction, the other dominoes fall until they are all laying in a stable equilibrium state. The key is to get the first domino to fall over. This is quite similar to what happens in a supersaturated state. In a substance, the area where the first molecules undergo a phase change is called a nucleation site. These are quite easy to observe. If you have ever boiled a pot of water, you might notice that there are a few spots on the bottom of the pot where bubbles seem to stream from. Or perhaps you have noticed the stream of carbon dioxide molecules coming from a spot along the side of a glass of a carbonated drink. These are nucleation sites and are generally the site of a small impurity in the container or substance.

One can introduce impurities to induce a phase change. In sodium acetate heating bags a button is pressed which releases a small amount of crystalline sodium acetate into a supersaturated solution. The injected crystals provide an impurity around which a chain reaction starts. As the dissolved sodium acetate precipitates out, the latent heat of dissociation is released and the bag heats up.

Perhaps one of the most ingenious uses of this is that of the cloud chamber, or its more recent incarnation, the bubble chamber. In a cloud chamber a cooled metallic plate cools down a pool of isopropyl alcohol at the bottom of the chamber. A source of warm alcohol vapour is provided near the top of the chamber. A temperature gradient is set up such that near the top of the chamber the alcohol is at a temperature and pressure such that it exists as a gas whereas near the bottom of the chamber the temeperature is such that the alcohol is a liquid. Just above the pool of liquid alcohol, there exists a layer of alcohol vapour that is at a temperature such that it should be a liquid. The vapour is supercooled and just needs a nucleation site for it to condense around. The sun and other astronomical phenomena stream radiation at the earth constantly, and many of these particles make it to the surface where they pass through walls, cars, people, and lab experiments. These particles can enter the chamber and ionize the alcohol vapour along its path, knocking electrons off of the molecules and leaving them with a net charge. These molecules can then be attracted or repelled from each other, knocking into one another, and providing enough of an impurity that a nucleation site is formed and the vapour condenses. The net effect is a thin condensation track becoming visible in the alcohol vapour and then raining down on the alcohol pool. It is really a beautiful invention as it provides macroscopic visual evidense of the subatomic world. Magnetic fields can be applied to the chamber and the tracks of charged particles can be seen to bend. In the bubble chamber, hydrogen gas is cooled until it liquifies, and then is re-heated slowly to just above its boiling temperature. The superheated hydrogen liquid will boil and bubble along the track of an ionizing particle.