Given,Radius of the balloon = r = 10 m
Volume of the balloon = = 43 πr3
= 43 × 227 × 103
= 4190.5 m3 ( approx )
Thus, the volume of the displaced air is 4190.5 m3
Given,
Density of air = 1.2 kg m-3
Then, mass of displaced air = 4190.5 × 1.2 kg
= 5028.6 kg
Now, mass of the helium (m) inside the balloon is given by,
m = MpVRT
Here,
M = 4 × 10-3 kgmol-1
p = 1.66 bar
V = Volume of the balloon
= 4190.5 m3
R = 0.083 bar dm3 K-1mol-1
T = 27°C = 300 K
Then, m = 4×10-3×1.66×4190.5×1030.083×300
= 1117.5kg (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 balloon is 3811.1 kg.