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Question -

Pay load is defined as the difference between themass of displaced air and the mass of the balloon. Calculate the pay load whena balloon of radius 10 m and mass 100 kg is filled with helium at 1.66 bar at27°C. (Density of air = 1.2 kg m-3 andR = 0.083 bar dm3K-1mol-1).



Answer -

Step I Calculation of the mass of displaced air
Radius of balloon (r) = 10 m
Volume of balloon (V) = 4 πr3 = 4 × 22 ×(10 m)3 = 4190.5 m3
Mass of the displaced air = Volume of air (balloon) × Density of air
= (4190.5 m3) × (1.2 kg m-3) = 5028.6 kg
Step II Calculation of the mass of the filled balloon.

=279.37 × 103 mol.
Mass of He present = Moles of He × Molar mass of He
= (279.37 × 103 mol) × (4 g mol-1)
= 1117.48 × 103g = 1117.48 kg
Mass of filled balloon = 100 + 1117.48 = 1217.48 kg
Step III. Calcu lation of the pay load
Pay load = Mass of displaced air – Mass of filled balloon
= 5028.6 – 1217.48 =3811.12 kg.

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