Answer to Question #2688 in Molecular Physics | Thermodynamics for Eman Faniin

Question

& A hot-air balloon must support its own weight plus a person for a total weight of 1200 N Ambient air is at 20C and 1 atm . The hot air inside the balloon is at 65C and 1 atm. What diameter of spherical balloon just will support the total weight ? neglect the size of the hot-air inlet vent .

Answer 1

Archimedes' theorem: the ball will support the total weight in the air, if the density of the ball with air + cargo equal to the density of air at 20 degrees.

1200 N = 120 kg
ρ_sys = (120 +V* ρ ₆₅)/V = ρ₂₀
ρ₆₅ = 1.045 kg/m³ - density at 65 degrees
ρ₂₀ = 1.204 kg/m³ - density at 20 degrees

thus
V = 755 m³ => r = (3V/ 4 π)1/3 = (180) 1/3 = 5.65 m
Hence diameter D = 2r = 11.3m