A balloon of diameter 21 meter weight 100 kg. Calculate its pay-load, if it is filled with He at 1.0 atm and `27^(@)C`. Density of air is 1.2 kg `m^(-3)` . (Given : R=0.082 L atm `K^(-1)mol^(-1)`)

Explanation

Weight balloon = 100 kg =`10 xx 10^(4)g`
Volume of balloon `=(4)/(3) pi r^(3) , (4)/(3) xx (22)/(7) xx ((20)/(2) xx 100)^(3) = 4190 xx 10^(6) cm^(3) =4190 xx 10^(6) cm^(2) = 4190 xx 10^(3)` litre
Weight of gas (He) in balloon `= (PV)/(RT) = (1 xx 4190 xx 10^(3) xx 4)/(0.082 xx 300) = 68.13 xx 10^(4) g`
`:.` Total weight of gas and balloon `=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 balloon + wt. of gas)
`:.` Pay load `= 502.9 xx 10^(4) - 78.13 xx 10^(4) = 424.67 xx 10^(4) g`