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What is the weight of one gallon of air?

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βˆ™ 2007-04-13 17:44:09

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Air at sea level weighs about 1.2 kg per cubic meter. You can find that using the ideal gas law pV=mRT where p is pressure V is volume m is mass of gas R is the gas constant for air = universal gas constant/average molecular mass of air T is the temperature in absolute units. All of those are better in metric units, so p is in pascals, V is in cubic meters, m is in kilograms, T is in kelvins, and R is 8314/28.8 = 288 N-m/kg-K. At sea level, standard pressure is 101325 Pa, temperature is about 20 deg C or 293 K. For a volume of 1 cubic meter, m/V = p/RT = 101325 / (288 * 293) = 1.201 kilograms per cubic meter. Since you wanted to know gallons, 264.2 gallons is 1 cubic meter, and 2.204 lb in one kg, so 1.201 kg/m^3 * (1 m^3/264.2 gal) * (2.204 lb/kg) = 0.0100 lb/gal. Not a heckuva lot, but not zero. One thing to notice is that if you put a gallon of air on a scale, (in a wieghtless container, of course) you would measure zero, exactly. That's because the buoyancy caused by the surrounding air exactly counteracts the weight of the air in the container. If you pressurized the air in your gallon container to, say ten times the outside pressure (or 147.0 psi absolute, or 132.3 psi gauge) it would now weigh nine times 0.01, or 0.09 lb. Of course, the container that held all that pressure would have to weigh a lot more than 0.09 lb, so measuring the change would require a very good scale.

2007-04-13 17:44:09
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