How much does a cubic mile (1x1x1) of air at sea level weigh? Go big. Very, very big.
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A cubic mile of air (1x1x1) weighs ~5 million tons!
Here are the calculations:
The weight of a cubic mile of air at sea level is 5,280 x 12 squared times the air pressure at sea level minus the air pressure at 5,280 feet.
This is (5,280 x 12) 2 x (14.7 – 12.26) = 9,795,354,624 pounds or 4.898 million tons.
Earth’s atmosphere has been measured to extend to 621 miles up. The square root of 621 is 24.920.
The inverse of 24.920 is .04013. So to total 1 cubic mile of air up to the maximum height, the column will have to be .0413 x 5,280 feet on a side = 211.88 feet
211.88 feet x 12 inches per foot x 211.88 feet x 12 inches per foot = 6,464,556.5 square inches
Times 14.7 PSI = 95,028,980 pounds or only 47,514 tons, less than one percent of the volume of 1 x 1 x 1.
This is the minimum weight of a cubic mile of air at sea level assuming STP (standard temperature and pressure).
The maximum weight would be a one inch thickness instead of one mile or 621 miles thick.
5,280 feet cubed = 147,197,952 cubic feet x 12 inches cubed = 254,358,061,056,000 cubic inches in one cubic mile.
254,358,061,056,000 x 14.7 psi = 3,739,063,497,523,200 pounds or 1,869,531,748,761.6 tons which equals 934,765,874.38 million tons, 190,846,442 times as much as one mile square of air one mile in height.