Pay load is defined as the difference between the mass of displaced air and the mass of the ballon 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` nar `dm^(-3) K^(-1) mo1^(-1)`) .

Explanation

Pay load is the difference between the mass of displaced air and the mass of the balloon.
`"Volume of balloon "=(4)/(3)pir^(3)`
`"Radius of balloon, r"=10m`
`V=(4)/(3)xx3.14xx(10)^(3)=4186.7m^(3)`
`"Mass of displaced air"=4186.7m^(3)xx"1.2 kg m"^(-3)`
`=5024.04kg`
`"Moles of gas present "=(pV)/(RT)`
`=(1.66xx4186.7xx10^(3))/(0.083xx300)`
`=279.11xx10^(3)" mol"`
`"Mass of helium present"=279.11xx10^(3)xx4`
`=1116.44xx10^(3)g`
`=1116.4kg`
`"Mass of filled balloon "=100+1116.4=1216.4kg`
`"Pay load"="mass of displaced air"-"Mass of balloon"`
`=5024.04-1216.44=3807.6kg.`