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 balloon (V) `= 4/ 3 pi r^3 = 4/3 xx (22)/(7) xx 10^3`
`=4190.50 m^3`
`=4190.5 xx 10^3 m^3`
Mass of displaced air = volume of air ` xx` density of air
` = 4190.5 xx 1.2 = 5028.6 kg`
Mass of He in balloon =`(PVM )/(RT ) = ( 1.66 xx 4190.5 xx 10^3 xx 4)/( 0.083 xx 300 )`
`=1117 xx 10^3 g= 1117 kg`
Mass of filled balloon `= 100 + 1117 = 1217 kg `
Pay load = mass of displaced air - mass of balloon
= 5028.6 - 1217 = 3811.6 kg