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 `= (4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx (10)^(3) = 4190.47 m^(3)`
Mass of the air displaced `= 4190.47 xx 1.2 = 5028.56 kg`
No. of moles of helium in the balloon `= (PV)/(RT)`
`= (1 xx 4190.47 xx 10^(3))/(0.082 xx 300) = 170344`
Mass of helium `= 4 xx 170.344 xx 10^(3) g = 681.376 kg`
Mass of filled balloon `= 681.376 + 100 = 781.376 kg`
Payload = Mass of air displaced - Mass of filled ballon
`= 5028.56 - 781.376 = 4247.184 kg`