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 `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` bar `dm` 3 `K^(-1) mol^(-1)`) .

Answer

3811.1kg

Explanation

Given,
Radius of the balloon, r = 10 m
`therefore` Volume of the balloon `" "=4/3pir^(3)`
`=4/3xx22/7xx10^(3)`
= `4190.5m^(3)` (approx)
Thus, the volume of the displaced air is `4190.5m^(3).`
Given,
Density of air = 1.2 kg `m^(-3)`
Then, mass of displaced air `=4190.5xx1.2` kg
=5028.6 kg
Now mass of helium (m) inside the balloon is given by,
`m=(MpV)/(RT)`
Here,
`M=4xx10^(-3)kg mol^(-1)`
p= 1.66 bar
V= Volume of the balloon
= 4190.5 `m^(3)`
R= 0.083 bar `dm^(3) K^(-1)mol^(-1)`
T= `27^(@)C` = 300K
Then, m `=(4xx10^(-3)xx1.66xx4160.5xx10^(3))/(0.083xx300)`
=117.5 kg (approx)
Now, total mass of the balloon filled with helium = (100+1117.5) kg
= 1217.5 kg
Hence, pay load = (5028.6-1217.5) kg
=3811.1 kg
Hence, the pay load of the baloon is 3811.1 kg.