And that is indeed what is happening back in the gas station’s compressed-air tank as you allow some of its stored-up compressed air to expand into the outer world.
Why does expansion cool a gas? Well, if a collection of flying gas molecules is suddenly allowed to expand into a bigger space, the molecules have to push their way out against whatever happens to be occupying that space, usually, the atmosphere.
Doing that uses up some of the gas’s energy, and the gas molecules then move more slowly. (If the gas is expanding into a vacuum, all bets are off.) A gas whose molecules are moving more slowly is a gas that has a cooler temperature.
The next time you fly on a humid day, watch the airplanes wing during takeoff, which is the time of maximum lift. You may see a layer of fog just above the wings top surface. This is an example of expansion cooling. The air going over the top of the wing expanded, compared with the air underneath the wing. Bernoulli’s principle and all that; ask any pilot.
The expanded wing-top air may be cooled enough to condense water vapor out of the air, making a stream of visible fog.
