-- The density of air at 1 atm pressure and 0°C is 1.2922 kg/m3.
The density of hydrogen under the same conditions is 89 gm/m3.
The difference is 1.2032 kg/m3.
-- On or near the surface of the Earth, that 1.2032 kg weighs 2.6526 pounds.
-- For 50 pounds of buoyancy, you need 50/2.6526 = 18.85 m3 of buoyancy.
-- That's 665.7 cubic feet.
-- That's a weightless, spherical balloon 10.8 feet in diameter.
-- All of that just exactly lifts your 50-lbs off the ground in sea-level air.
If your balloon is not weightless, and if you want to keep rising as the
air gets thinner, you'll need some more.
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