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I remember there being something misleading about the "temperature" in pV=nRT, but yeah, I think I was getting confused because I was thinking about it purely formulaicly.
But if the pressure drops and the volume of the gas increases, in order for it to cool, that would mean the drop in pressure is much less significant than the rise in volume?
But yeah, I should've remembered that expanding gasses cool, because I know how aerosol cans work. It's time to touch up on this stuff lol.
I had a similar conversation with my wife a few weeks ago. We were watching the hydraulic press channel, where they were compressing water to very high pressures. When the water inevitably squirted out of the chamber, it turned to steam. My wife said yeah that makes sense, applying that much energy to compress the water would increase its temperature, so it wants to expand to become steam. Then I thought about it a while, and said wait, according to first principles of thermodynamics, shouldn't compressing water lower it's temperature?! The turns out the real world is correct, I was wrong.
You're mixing cause and effect.
The effect of lowering temperature is shrinking gases. If you force a gas to shrink it will increase temperature.