A ballon of diameter 20 metre weighs `100 kg` Calculate its pay-load if its is filled with He at 1.0 atm and `27^(@)C` Density of air is `1.2 kg,^(-3)`
`[ R =0.082 dm^(3)` atm `K^(-1) mo1^(-1)]` .

Explanation

Volume of balloon,
`V=(4)/(3)pir^(3)`
`r=10m`
`therefore" "V=(4)/(3)xx3.14xx(10)^(3)=4187m^(3)`
Mass of displaced air `=4187m^(3)xx1.2kgm^(-3)`
`=5024.4kg`
`"Moles of gas present, n"=(pV)/(RT)`
`=(1xx4187xx10^(3))/(0.082xx298)`
`=170.2xx10^(3)" mol"`
`"Mass of He present"=170.2xx10^(3)xx4`
`=680.8xx10^(3)g`
`=680.8kg`
`"Mass of filled balloon "=100+680.8=780.8kg`
`"Pay load "="Mass of displaced air"-"Mass of balloon"`
`=5024.4-780.8=4243.6kg`