Question

A spherical balloon is made from a material whose mass is 2.60 kg. The thickness of the material is negligible compared to the 1.30 m radius of the balloon. The balloon is filled with helium (He) at a temperature of 280 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m³ and the molar mass of helium is 4.0026×10-3 kg/mol. Find the absolute pressure of the helium gas.

Answer 1

V sub Ball = ( 4/3 ) ( pi ) ( r^3 )

V sub Ball = ( 4/3 ) ( pi ) ( 1.3^3 ) = 9.20 cu m

m sub He = ( P ) ( V ) ( M ) / ( R ) ( T )

m sub He = ( 9.20 cu m ) ( 1000 L/cu m ) ( 4.0026 ) ( P ) / ( 0.08205 ) ( 280 )

m sub He = ( 1602.85 ) ( P in atm )

W sub He = ( m sub He ) ( g )

W sub He = ( 1602.85 ) ( 9.807 ) ( P in atm )

W sub air = ( V sub BALL )( d sub AIR ) ( g )

W sub AIR = ( 9. 20) ( 1.19 )(1000 g/kg ) ( 9.807 ) = 107367 N

W sub AIR displaced = F sub Buoyant = W sub He + W sub BALL

W sub He = 107367- ( 2.60 ) ( 9.807 ) = 107341.5 N

1602.85 ) ( 9.807 ) ( P in atm )  ( P ) = 107341.5 N

P=6.83atm