I know this isn't the answer either. Charles law essentially says that at a constant pressure as absolute temperature increases, the volume of the gas also increases in proportion. We aren't looking at constant pressure and I'm trying to understand why some of the gas gets hot as it expands while other parts of the gas get colder. I'm pretty sure it has to do with the fact that this is an irreversible process in which entropy increases and the fact that the scuba tank is not thermally connected to the fill tank.
It's not Charles's Law, Dalton's Law, Boyle's Law, Henry's law or even the Ideal Gas Law. I'm becoming more confident that it has to do with the path the second 1cc parcel of air follows through P, V and T as it moves from the fill tank to the scuba tank.
---------- Post added February 21st, 2013 at 02:56 PM ----------
Well that's the whole point of my question. The gas in the scuba tank doesn't go from low pressure to high pressure. It starts at high pressure in the fill tank and room temperature. It ends up in a larger volume, at a lower pressure and a higher temperature. Just focus on the gas. It's at a high pressure in the fill tank and ends up at a lower pressure in the scuba tank. There's no way to avoid that and any explanation has to take that into account.