[Drewch]

Okay ... someone help find the flaw in my reasoning:

According to multiple online calculators, to get 2.5 vol at 65F requires 26 psi, and at 40F requires 12 psi (rounding both to the nearest psi).

But according to the ideal gas law (P₁/T₁ = P₂/T₂), if I chill a fixed volume (for simplicity we'll assume the change in volume of the liquid in the keg is negligible) of CO2 at 26 psi from 65F to 40F, the pressure only drops by about 1 psi. Assuming my math isn't off.

So if naturally carb at 65F, do I need to manually lower the spunding valve to 12 psi after chilling to 40F? Or is there some other interaction that explains the rest of the pressure drop?

[Richard]

The solubility of CO2 in beer varies with temperature. It is more soluble at lower temperatures, so you need less pressure to drive the same amount of CO2 into solution than at higher temperatures. If  you carbonate to 2.5 volumes at 65 F in a closed system, then lower the temperature to 40F you would likely over-carbonate your beer because the pressure (as you calculated) would only drop a little bit. The thing unaccounted for is that as the CO2 goes into solution it leaves the head space, lowering the pressure as a result. P1/T1 = P2/T2 only holds if the volume and number of gas molecules are constant. If the  gas dissolves into the liquid then the number of molecules of gas drops. If you know the volume of your head space and the volume of beer you might be able to figure out how much of the gas would disappear and calculate the pressure drop. In any case, you would want the final pressure to be the 12 psi from the charts or you would end up with the wrong carbonation level.

[Drewch]

So if naturally carbing with a spunding valve (which would have to be done at room temp), do you set it for 13 psi so that you get 12 after chilling? Or set for 26 and then bleed it down to 12 after chilling?

[Richard]

Honestly, I don't know which would be better. I have never spunded. It seems to me that carbing at the higher pressure might be faster, since the beer would already be carbed before you cool it, but I don't know if the high pressure would have a negative impact on the yeast. Keeping the pressure low and then carbing at the low temperature would be more conservative, but slower.

[chinaski]

Okay ... someone help find the flaw in my reasoning:

According to multiple online calculators, to get 2.5 vol at 65F requires 26 psi, and at 40F requires 12 psi (rounding both to the nearest psi).

But according to the ideal gas law (P₁/T₁ = P₂/T₂), if I chill a fixed volume (for simplicity we'll assume the change in volume of the liquid in the keg is negligible) of CO2 at 26 psi from 65F to 40F, the pressure only drops by about 1 psi. Assuming my math isn't off.

So if naturally carb at 65F, do I need to manually lower the spunding valve to 12 psi after chilling to 40F? Or is there some other interaction that explains the rest of the pressure drop?

The ideal gas equations you present represent the change in pressure within the headspace above the beer as you change either pressure or temperature of the gas in that headspace.

You should assume that if you set your pressure to 26 psi as you spund (or otherwise create this pressure using CO2) that the pressure within the keg headspace will drop to 12 psi when you cool it to 40F.  The carbonation table tells you what the overlying headspace pressure needs to be to force a given volume of CO2 into the beer. 

[Drewch]

Ok. Thanks. I think my mistake was assuming that "2.5 vols" referred to a fixed number of molecules of CO₂ irrespective of T & P. If CO₂ will migrate from the ullage volume into the liquid as temp changes, then the ideal gas law no longer applies the way I was using it.

Knowing a little bit of physics is a dangerous thing.....

[Richard]

Describing carbonation level in "volumes" seems strange to me, but that is the way it is done.

[chinaski]

Ok. Thanks. I think my mistake was assuming that "2.5 vols" referred to a fixed number of molecules of CO₂ irrespective of T & P. If CO₂ will migrate from the ullage volume into the liquid as temp changes, then the ideal gas law no longer applies the way I was using it.

Knowing a little bit of physics is a dangerous thing.....

You are welcome.  There is all the solubility of gases stuff that has to be considered when considering the volumes into the beer.  Good thing the carbonation tables does that part for us.