Question

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27^o C

(Density of air = 1.2 kg m^-3 and R = 0.083 bar dm³ K^-1 mol^-1).

Answer 1

Weight of balloon = 100 kg = 100 x 10³ g = 10⁵ g  

Volume of balloon

Weight of the gas filled in balloon = PVm/RT = 1.66 x 4190 x 10³ x 4/ 0.083 x 300

= 1.117 x 10⁶ g

Total weight of (gas + balloon) = 11.17 x 10⁵ + 10⁵ = 12.17 x 10⁵ g

Weight of air displaced (Volume x density) by balloon 

= 1.2 x 4190 x 10⁶/10³ = 5.028 x 10⁶ g

Pay load =50.25 x 10⁵ - 12.17 x 10⁵ = 38.11 x 10⁵ g

= 3811 kg