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)`)

Options

A. 4952.42 kg
B. 4932.42 kg
C. 493.242 kg
D. none of these

Answer

b

Explanation

(b) Mass of balloon `=100kg=10xx10^(4)g`
Volume of balloon `=(4)/(3)pi r^(3)`
`=(4)/(3)xx(22)/(7)xx((21)/(2))^(3)`
`=4851m^(3)=4851xx10^(3)L`
Mass of gas (He in balloon `=(PVM)/(RT)`
`=(1xx4851xx10^(3)xx4)/(0.082xx300)`
`=78.878xx10^(4)`
`:.` Total mass of gas and balloon
` =78.878xx10^(4)+10xx10^(4)`
`=88.878xx10^(4) g " or " 888.78 kg`
Mass of air displaced `=1.2xx4851`
`=5821.2kg`
`:.` Pay load =mass of air displaced - mass of (balloon +gas)
`:.` Pay load `=5821.2-888.78=4932.42kg`