Pay load is defined as the difference between the mass of displaced air and the mass of the ballon Calculate the pay-load when a balloon of radius `10m` 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` nar `dm^(-3) K^(-1) mo1^(-1)`) .

Explanation

Radius of the balloon =10 m
`:.` Volume of the balloon`=(4)/(3)pir^(3)=(4)/(3)xx(22)/(7)xx(10 m)^(3)=4190.5" m"^(3)`
Volume of He filled at 1.66 bar and `27^(@)C=4190.5" m"^(3)`
Calculation of mass of He :
PV=nRT`=(w)/(M)RT`
or `" " w=("MPV")/("RT")=((4xx10^(-3)" kg mol"^(-1))(1.66"bar")(4190.5xx10^(3)"dm"^(3)))/((0.083" bar dm"^(3)" K "^(-1)"mol"^(-1))(300K))=1117.5" kg"`
Total mass of the balloon along with He `=100+1117.5=1217.5" kg"`
Maximum mass of the air that can be displaced by balloon to go up =Volume xxDensity
`=1490.5" m"^(3)xx1.2" kg "m^(-3)=5028.6" kg"`
`:. " Pay load" =5028.6-1217.5" kg" =3811.1" kg"`