The thing that burns my biscuits is the myth that 'most' of the CO2 is in the headspace after all of the priming sugar has fermented.
But where have you ever seen this said? Your post was the first time I'd ever heard anyone mention a claim that most of the CO2
was in the headspace. I'm pretty sure a significant amount of the CO2
is in the headspace of a warm beer, though.
The example of the keg is quite different than a bottle. In the keg, you're talking about gas at constant pressure, and you're exactly right about the undercarbonation. With the bottle, you're talking about a constant volume of CO2, where the pressure in the bottle will increase with temperature.
Temperature is why the carbonation is lower in a warm bottle of beer, since the pressure at temperature and the solubility at temperature curves don't mirror each other.
If you take as an example a beer that you want to serve at 2.5 volumes of CO2
at 40ºF, the final pressure in the bottle will have to be about 12.3 psi at 40ºF. Then, if you solve PV = mRT for constant volume and mass, you find that the pressure would increase about 1.06-fold for a rise in temperature from 40ºF to 70ºF:
1xRx294ºK / 1xRx278ºK = 1.06
12.3 psi (at 40ºF) x 1.06 = 13.0 psi. (at 70ºF)
However, the solubility of CO2 decreases at warmer temperatures. If the bottle is at 13.5 psi and 70ºF, then the beer will have 1.52 volumes of CO2
, instead of the 2.5 volumes it would have had at 12.3 psi and 40ºF, despite the slightly higher temperature.
So, most of the CO2
isn't in the headspace in a warm beer, but 39% of the CO2
that you want in the beer is still in the headspace. That's going to take some amount of time to get into the beer when you chill it, just as it would if you had a keg at 1.52 volumes and you increased the pressure to get it to 2.5 volumes.
Edit: Fixed some sloppy math. I'm pretty sure the logic is sound, but I'm not much of a physicist, so I could be missing something that makes the actual values wrong.