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

We know
Weight of balloon ` =100 kg = 10 xx 10^(4) g`
Volume of balloon ` = (4)/(3) pir^(3) = (4)/(3) xx (22)/(7) xx ((20)/(2) xx 100)^(3)`
`=4190 xx 10^(6) cm^(3) = 4190 xx 10^(3) litre`
Weight of gas (He) in ballon ` =(PVm)/(RT)`
`( :' PV =(w)/(m) RT)`
` =(1 xx 4190 xx 10^(3) xx 4)/(0.082 xx 300) = 68.13 xx 10^(4) g`
`:.` Total weight of gas and ballon
` = 68.13 xx 10^(4) + 10 xx 10^(4) = 78.13 xx 10^(4) g`
Weight of air displaced
` = (1.2 xx 4190 xx 10^(6))/(10^(3)) = 502.8 xx 10^(4) g`
`:.` Pay load =wt of air displaced - (wt.of ballon + wt. of gas)
`:.` Pay -load ` =502.8 xx 10^(4) - 78.13 xx 10^(4)`
`=424.67 xx 10^(4) g` .