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

Radius of ballon `(r) = (20 m)/(2) = 10 m`
Volume of balloon `(V) = 4/3p pir^(3) = 4/3 xx 22/7 xx (10 m)^(3) = 4190.5 m^(3)`
Mass of air displaced `= "Volume of air" xx "Density of air"`
`= (4190.5 m^(2)) xx (1.2 kg m^(-3)) = 5028.6 kg`
Moles of He present `(n) = (PV)/(RT) = ((1.0 atm) xx (4190.5 m^(3)))/((0.082 xx 10^(-3) m^(3) atm K^(-1) mol^(-1)) xx (300 K))`
`= 170.346 xx 10^(3)` mol
Mass of He present `= "Moles of He" xx "Molar mass of He"`
`= (170.346 xx 10^(3) mol) xx (4g mol^(-1))`
`= 681.38 xx 10^(3) g = 681.38 kg`
Mass of filled ballon `= 100 + 681.38 = 781.38 kg`
Pay load = Mass of air displaced - Mass of filled balloon
`= 5028.6 -781.38 = 4247.22` kg.