Worth noting the gas in your canister isn’t necessarily just expanding, it may also be evaporating. The pressure in the bottle holds it in liquid form at room temp, and a reduction of pressure as it exits causes the liquid to vaporise.
This furthers the cooling effect as vaporisation is highly endothermic (absorbs a bunch of heat).
Your AC unit works on the same principle – by releasing compressed liquid into a very cold gas, using it to cool the room then compressing it back into a liquid (the liquid will be hotter than at the start). The compressor is the noisy and power hungry bit in your AC.
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