Well...density is mass divided by volume, so in an evacuated barrel, where the mass (apart from that of the barrel) is theoretically zero, I'd say that would be more bouyant.

But consider this....the mass of the barrel is going to be orders of magnitude greater than that of the mass of the gas inside, barring lots and lots of compression. The mass difference between a barrel filled with air that is at atmoshperic pressure and a barrel that contains a vacuum is going to be negligible. 50 gallons of air at 1 atm. pressure..let's see, approximating with ideal gas laws, n=PV/RT and n=m/MM. The average molar mass of the atmosphere is about 29 g/mol (70% N2, 20% O2, 5% Ar, 5% misc, averaged together by %) So m=(MM*P*V)/(R*T) 50 gal is approximately 12 L (very rough estimate), R is 0.0820575 L atm/mol K, and we'll assume 298 K for temp. (about 25 deg Celcius) the mass of the air is about 14 grams. Compare that to the mass of the barrel, which is probably about 15 kg, (45-50 lbs) and you'll see that removing the air doesn't change the total mass very much. (15000 g vs. 15014 g)

Now, if you're really bored, given that the density of water at 25 deg C is about 0.9917 g/mL and the rest of the assumptions I made above, calculate the pressure of air inside that would increase the total density of the barrel + air to that of the water so that it no longer floats.

Back to my phys. chem. lab report now. See what this class is doing to me? =P

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