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A ballon of diameter 20 meter weights 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 kgm^(-3) [R=0.082 dm^(3)" atm k"^(-1)" mol"^(-1)]

Answer»

Solution :Weight ballon `=100 KG =10xx10^(4)g`
VOLUME of ballon `=(4)/(3) pi r^(3)`
`(4)/(3)xx(22)/(7)xx((20)/(2)xx100)^(3)`
`=4190xx10^(6) cm^(3)`
`=4190xx10^(3)` LITRE
Weight of gas (He) in balloon `=(PV)/(RT)`
`=(1xx4190xx10^(3)xx4)/(0.082xx300)`
`=68.13xx10^(4)g`
`:.` Total weight of gas and balloon
`=68.13xx10^(4)+10xx10^(4)=78.13x10^(4)g`
Weight of air displaced `=(1.2x4190xx10^(4))/(10^(3))`
`=502.x10^(4)g`
`:.` Pay load =wt of air displaced -(wt)of baloon +wt of gas)
`:.` Pay load `=502.xx110^(4)-78.13xx10^(4)`
`=424.67xx10^(4)g`


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