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

Explanation

Volume of ballon `=4/3 pi r^3=4/3 pi(10)^3=4190.47cm^3`
Weight of air=5028.5 kg
Moles of `He=(pV)/(RT)`
`=(1.66ba r times4190.47 times10^3)/(0.083 b ar LK^-1 mol^-1)=279364.6 mol.`
Weight of He= `279364.6 times 4=1117450 g =1117.45 kg`
Pay load= Weight of air - Weight of He-Weight of balloon
=5028.5-1117.45-100=3811.1 kg