why do tanks of compressed air get cold, to the point of frosting over, when the gas is let out quickly?
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Pressure, volume and temperature are interlinked.
If you push more molecules closer together (more pressure), they will take up less room (volume) and get warmer.
If you heat molecules, they will try to move away from each other (they have more energy so they “hit each other harder”) – the gas will expand, or if it’s trapped, it will put more pressure on the container.
If you expand a container, the gas inside it will get colder (e.g. this is what we think is happening to the universe).
And if you release the pressure in a fixed container, the pressure *and* temperature will drop.
It helps to think of a gas as millions of “things” (molecules) which don’t want to sit close to each other. Heat makes them move faster. Volume is how much room they occupy. Pressure is how squished they are. The more you force them together, the more squished they are and the hotter they get. And the opposite
happens when you reverse it (they get less squished and cool).
In the specific case you’re talking about, when compressed into a container initially the pressure and temperature of the gas would have increased. Over time, the temperature will be lost to the environment (i.e. the container cooling in the factory / shop / forecourt). Thus when you let out the pressure after that, the temperature drops *lower* than ambient.
It’s got a really good use – freeze spray is very handy for fixing broken water pipes, for instance.
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