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Question

A ballon of diameter 21 m weighs 100 kg. Calculate its payload if it is filled with helium at 1.0 atm and 27 C. Density of air is 1.2 kg m3
(R=0.08 dm3atm K1mol1)
 
  1. 4912.7 kg
  2. 3520.14 kg
  3. 5250.25 kg
  4. 3888.12 kg


Solution

The correct option is A 4912.7 kg
Volume of the balloon =43πr3=43×227×(10.5)3=4851 m3
Mass of the air displaced =4851×1.2=5821.20 kg
Number of moles of helium in the balloon = PVRT
=1×4851×1030.08×300=202125 mol
So, mass of helium = 4×202125 g=808500 g=808.5 kg
Mass of filled balloon = 808.5+100=908.5 kg
Payload = Mass of air displaced - Mass of filled balloon
=5821.2908.5=4912.7 kg

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