Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at `27^@C`. (Density of air= 1.2 kg `m^-3` and R=0.083 bar `dm^3K^-1mol^-1`)

Explanation

formula :
` r= 10 m`
` m= 100 kg `
` T= 27^@ C = 300 K `
` d= 1.22 kg // m^3`
Volume of the ballon ` = 4/3 pi r^3`
` = 4/3 xx (22)/(7) xx 10^3`
` = 4190.5 m^3`
`p= 1.66 ` bar
` T= 300 K`
` V= 4190.5 m^3`
` R= 0.083 " bar" dm^3 k^(-1) mol^(-1)`
`PV = nRT `
` n= (PV) /(RT) = ( 1.66 xx 4190.5 )/( 0.083 xx 10^(-3)xx 300)`
=2793.70 moles
` = 0.083 xx 10^(-3) ` bar ` m^3 k^(-1) mol^(-1)`
` therefore ` weight of 279370 moles of He
` = 279390 xx (4)/(1000) `
` = 1117.48 kg `
total weight of ballon `= 100 + 1117.48`
`= 1217 .48 kg `
maximum wight of He ` = V xx d `
`= 4190 .5 xx 1.2`
`= 5028.6 kg `
` therefore ` pay load ` = 5028.6 - 1219.48`
`= 3811.12 kg `