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 dm3 K–1 mol–1).
Payload of the ballon = mass of the displaced air – mass of the ballon
Radius of the ballon, r = 10 m
Mass of the ballon, m = 100kg
Therefore volume of the ballon = 4/3πr3 = 4/3 x 22/7 x (10)3 = 4190.5 m3
Now volume of the displaced air = 4190.5 m3
Given,
Density of air = 1.2 kg m–3
Therefore, the mass of the displaced air
= 4190.5 x 1.2 = 5028.6 kg
Let w be the mass of helium gas filled into the ballon,then
PV = (w/m)RT
OR w = PVM/RT
= (1.66 X 4190.5 X 103 X 4) / (0.083 X 300)
= 1117 kg (approx)
Total mass of the balloon filled with He = 1117 + 100 = 1217 kg
Therefore payload of the balloon = 5028.6 – 1217 = 3811.6 kg
Hence, the pay load of the balloon is 3811.6 kg.
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