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Explanation:
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Answer: The volume of the balloon is V= 4/ 3 πr³.
The radius of balloon is 10 m.
Hence, the volume of the balloon is V=4 / 3 ×3.1416×(10) ³ =4186.7m ³.
The mass of displaced air is obtained from the product of volume and density. It is 4186.7 × 1.2=5024.04kg.
The number of moles of gas present are n= PV/RT = 1.666×4186.7×10³
0.083×300
= 279.11×10³.
Note: Here, the unit of volume is changed from m³ to dm³ .
1m³ =1000dm³.
Mass of helium present is obtained by multiplying the number of moles with molar mass. It is 279.11×10³×4=1116.44×10 ³ g=1116.4 kg.
The mass of filled balloon is the sum of the mass of the empty balloon and the mass of He. It is 100+1116.4=1216.4 kg.
Pay load = mass of displaced air − mass of balloon
=5024.04−1216.44=3807.6 kg
=5024.04−1216.44=3807.6 kg
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