What is Pressure?

Molecules of air are bumping into you all the time as they move about, and air pressure is simply a measure of the number and strength of these collisions. If there are lots of air molecules about, there will be many collisions and the pressure will be high, whereas if there are few molecules, there will be few collisions and the pressure will be low. However, temperature also has a role to play: if the temperature is high, the air molecules will be moving faster and will hit with more force, so the pressure can be high even if the amount of molecules is small, just so long as they are hot. If you imagine two identical containers with air in them, but one has half as much air in it as the other, the pressure in them will be the same if the one with only half as much gas in it has its gas at twice as high a temperature. It's important to understand that 20C is not twice as hot as 10C: bear in mind that true zero is -273C, so to double the temperature of something which is 10C you have to add 273 to it, double the result, then take 273 away again, and that gives you a very hot 293C.
You don't really notice all these molecules pushing against you, but the pressure around you is surprisingly high. Air pressure is caused by the weight of air above you, and by that I mean all the air right up to the top of the Earth's atmosphere: gravity is trying to pull the best part of a ton of this stuff down on top of your head all the time. Fortunately this massive weight of gas doesn't squash you flat: the molecules being pulled downwards will collide with other molecules at all manner of different angles, and the result is that they actually press against each other equally in all directions, including sideways and upwards, so pressure doesn't only press down on you, but it presses in from the sides and upwards from underneath you as well. You might still wonder why this pressure doesn't crush you inwards, but in fact you can't be crushed by it because you are made of solid and liquid material rather than gas, and it's only gas that can be compressed. Of course, it's perfectly possible for you to be crushed if a heavy force is applied to you from just one side, or even from two opposite sides, but that can only happen if bits of you are able to splat out in some other direction. When the air presses in on you, it does so from all possible directions with equal force and leaves no direction free for any part of you to splat out in: that is why you can never be crushed by it. The air even gets inside you, deep down into your lungs, and from inside there it presses outwards and prevents any part of you from being splatted into that internal space. So, however high it goes, air pressure can never crush you.
This is an important point to understand, because it is easy to be confused by things you see on television. A cup made of expanded polystyrene (foamy plastic - it's full of tiny air bubbles) can be crushed by pressure to a fraction of its original size just by being taken deep underwater where the pressure is extremely high, but it is only possible for such cups to be crushed because they contain lots of air bubbles: it is the air in the bubbles that can be crushed, and this allows the material of the cup to be crushed into the spaces where the bubbles were. Most submarines are not designed to be able to survive going deep underwater: like the cup, they have a lot of air space inside them and they can be crushed into that space if the pressure gets too high. Most submarines can only survive down to a few hundred metres below the surface, but that's far enough to hide from ships on the surface, so they don't need to go any deeper. The oceans can often be many miles deep, so you have to build very special submersibles to be able to go all the way to the bottom without being crushed. If you were able to swim down to the bottom of the deepest sea, you would not be crushed at all: the air in your lungs would be crushed, but that's as far as the process would go.
If you start at the edge of space and then travel down through the atmosphere, the pressure of the air increases as you go downwards because there is an increasing weight of air over your head the further you descend beneath it. You might wonder how the air knows what pressure it should be at different heights, because it can't know how high it is or how much air there is higher up. The answer's simply that there are more molecules of air in the same amount of space at low altitude: more molecules leads to more collisions, and more collisions means higher pressure. These collisions keep trying to push the molecules of air apart, but the only direction they can go in where the pressure is lower is up, and because air weighs something, gravity keeps trying to pull it all back down again. The net effect of this is that you get fewer molecules in a given amount of space the higher you go, and that results in fewer collisions and lower pressure. Most people don't realise that if all the air in the atmosphere was very cold, it would not have the energy to push itself high into the sky: it would just form a thin layer of dense gas over the sea, with all the hills and mountains on land sticking out through it into empty space: that is what would happen to the Earth if it was moved far away from the sun.
Pressure and temperature can be linked to each other. If you have a container filled with air and you heat the air inside it until it is twice as hot, the molecules will move with twice as much energy as before and so the pressure in the container will also double. This change in pressure happens without increasing the number of air molecules in the container at all. Another way to double the pressure is to put twice as much air into the same space without changing its temperature. This is not as easy to do as you might think, however, because whenever you pump air into a container you will accidentally warm up the air at the same time: the pressure will have doubled before you have managed to double the amount of air in the container because it will be warmer than it was when you started. Of course, if you leave the air to cool back down again, the pressure will fall a little, so you'll then have to pump a bit more air in to get it back up to double the original pressure, and if you keep doing this and leaving it to cool you will eventually reach the point where the pressure has doubled without any change from the original temperature. But why, you may ask, should pumping air to a higher pressure make it warmer?
The heating that happens when you pump up a bicycle tyre takes place inside the pump: the moving part of the pump hits the air as it squeezes it into a smaller space, and the collision energy speeds up the air molecules that hit it, thus making them a little hotter. When you've finished pumping up a tyre, the end of the pump will feel warm as a result of this heat generated by pushing the air to higher pressure, but it doesn't seem to double the temperature of the air by halving the volume: a bicycle pump can compress the air in the tyre to well over five times the pressure of the air outside, but you can put your finger over the end of the pump to block it and then compress the air in the pump without your finger being burnt, so it doesn't appear that the temperature of the air can be going up to over a thousand degrees (and indeed your finger won't even feel hot). Maybe the heat is generated, but is lost quickly to the material of the pump, tyre and wheel rim which all contain a lot more material than the air and can therefore hold massively more heat without feeling hot.
Imagine a container with only one single molecule of air in it. If you heat it up until it moves about with twice as much energy as before, it will hit the walls of the container with twice as much energy as before and thus make the pressure in the container twice as high. If instead of heating up that molecule of air we add a second molecule of air into the container at the same temperature as the first, the two molecules move about without getting any more energetic, but because there are now two of them there will be twice as many collisions with the walls of the container, so again the pressure is doubled. You could introduce the second molecule without changing the temperature of either of the two molecules, so in a case like this it is possible to double the pressure in an instant without warming anything up at all, but if you're dealing with large numbers of molecules you will have to compress them to get them in, and that's bound to cause some heating.
When you let a tyre down, the air cools down it loses pressure, but the coolness that you feel if you stick your finger in the way may be caused more by the air moving rapidy rather than by any real temperature difference. If we're talking about a bicycle tyre, the pressure and temperature of the air might drop to at least a fifth of their original values, so that could be -200C! It certainly doesn't feel that cold, so there's something strange going on here that doesn't add up. I've been trying to find a scientist who can explain this for quite some time, but no luck so far: I'll add more about this here if I ever get an explanation from anyone, but for now it's a bit of a puzzle. A spray can will certainly get quite cold during use, but the cooling effect may be caused mainly by the pressurised gas inside the can turning from liquid into gas as the pressure drops: if you remember the idea of latent energy (the heat soaked up or released by a material during a change of state while the material stays at the same temperature), the cooling occurs because heat energy is sucked into the evaporating material in order to convert it from liquid to gas, and the heat used to do this will cool down both the gas being sprayed out and the liquid left behind (and of course the cooling is also passed on to the container).
Some heaters work by radiating heat out in the form of infra-red photons, but other kinds of heaters heat up air instead and then blow it at you. This hot air feels hot because the molecules are moving about more energetically than unheated air: heating them simply makes them move faster, but this extra energy also makes the pressure of the hot air higher, so the hot air quickly pushes itself out to fill a greater volume of space until the pressure is back down to normal. It now weighs less for a given amount of space than unheated air and so it will try to travel upwards as a result: this is why hot air rises.
Pressure in liquids is not the same as with air because liquids don't compress in the way that gases do. You can fill a container with liquid and squeeze it as hard as you like, but it won't squash in very much at all. Molecules in a liquid are touching each other all the time, so the collisions between molecules caused by temperature are not so much collisions as temporary pressings: a molecule will press into an molecule on one side, then spring back out from it and press into one on the other side, and then it'll spring back out from there and press into the first one again, though it will remain in contact with both molecules the whole time. The strength of these temporary pressings will depend on the temperature of the molecule (or, to put it another way, how strongly it is vibrating about). Pressure in a liquid again involves molecules pressing against the other molecules around them, but this time these are constant pressings rather than the temporary, oscillating ones caused by temperature, and the higher the pressure, the stronger these constant pressings will be. An enormous increase in the pressing force will make a molecule press slightly further into another molecule, but this extra distance of travel will be extremely small, and so that is why there is no obvious compression in liquids. Warmer water will expand slightly and try to float on top of colder water, but the effect is not as strong as with hot and cold air.
Incidentally, when water freezes, it behaves in a very unusual way. Most materials become more dense when they freeze from liquids into solids, but solid water (ice) does the opposite: it expands and floats on top of liquid water. It takes up more space and is therefore lighter for a given volume. This is a good thing for fish, because it means that lakes freeze over at the surface and stay liquid underneath (the ice at the surface helps to insulate the water underneath against the freezing temperature of the outside air): if ice sank instead of floating, then lakes would freeze from the bottom upwards and they would gradually fill with solid ice all the way up to the top until there was nowhere left for the fish to live. The really interesting thing about this strange behaviour of water expanding as it turns into ice is that ice turns back into water when it is squeezed hard: if you put it under pressure, it tries to take up less space and it finds that easier to do if it turns back into a liquid, even if the temperature is below zero. Many scientists believe that this is what makes ice slippery: when you stand on it you squeeze and turn the surface into water, and it's actually the water that you slip on, though the latest idea is that it's simply that the molecules at the outside edge of ice vibrate more energetically than the rest and tend to turn to water on contact with other things. I suspect the old explanation is essentially right and that the new idea is merely an additional factor which amplifies the effect. Whatever the case, if ice didn't behave like this, skis and ice skates wouldn't work. If the temperature of ice is extremely low, its surface can't turn into water, and this explains why many Arctic explorers have reported encountering snow which their skis wouldn't slide on: it behaved more like sand.

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