TMonter,
What you posted here is only partially correct.
While I am not going to dispute your numbers, I'd like to point out that air density and volume have nothing to do with your calculated results. In the formula you provided, we deal with degrees, pounds and BTUs.
...it takes 0.2401 btu/lb*F to heat that air up. Each pound of air consumes ~9.21 Btu, much more if temperatures are colder.
So 105.2*9.21 = 968.892 Btu for each pound of wood burned...
In the above you used 105.2 cu. ft, while you should have used 8 lbs instead.
Thus, to heat that 8 lbs of air from 30 to 70 °F it would take
(70 - 30) degrees * 8 lbs * 0.2401 btu/lb*F = ~76.832 BTU and _NOT_ 968.892 BTU as you posted.
There is a significant difference between 77 and 969 BTU to heat 8 lbs of air, right?
On the other hand, this is the heat to be spent on heating the _DRY_ air. Extra heat would be spent to evaporate the moisture from 8 lbs of air, but in no way would the total come close to 969 BTU.
OAK’s save heat, no doubt about it.
This would depend on lots of things, including prevailing winds (frequency, speed and direction) and their effects on the internal house pressure. This debate is ongoing, and I would spend more time researching this, but for now the heat savings from OAKs are highly questionable.
What is not questionable is that OAK does not rob Peter to pay Paul, namely it ensures the oxygen for the stove without having all the oxygen-consuming appliances in the house fighting each other.
Cheers!