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 `10m` 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` 3 `K^(-1) mol^(-1)`) .

Explanation

Volume of balloon, `V=4/3pi r^(3)`
`r=10 m`
`V=4/3xx3.14xx(10)^(3)=4186.6 m^(3)=4186.6xx10^(3) dm^(3)`
Mass of displaced air is
`4186.6 m^(3)xx1.2 kg m^(-3)=5024 kg`
`T=27+273=300 K`
Moles of gas present,
`n=(PV)/(RT)`
`=(1.66xx4186.6xx10^(3) dm^(3))/(0.083xx300)=279.1xx10^(3) mol`
Mass of He present `=279.1xx4xx10^(3) mol`
`=1116.4xx10^(3) g`
`=1116.4 kg`
Mass of filled ballon `=100+1116.4=1216.4 kg`
Pay load=Mass of displaced air- Mass of ballon
`=5024-1216.4=3807.6 kg`