Payload is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload, when a balloon of radius 10 m of mass 100 kg is filled with helium at 1.66 bar at 27 ∘C. (Density of air = 1.2 kg m3 and R = 0.083 bar dm 3 K−1 mol−1)
Solution: The volume of the balloon is V=34πr3. The radius of balloon is 10 m. Hence, the volume of the balloon is V=34×3.1416×(10)3=4186.7m3. 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=RTPV=0.083×3001.666×4186.7×103=279.11×103.
Note: Here, the unit of volume is changed from m3 to dm3.
Mass of helium present is obtained by multiplying the number of moles with molar mass. It is 279.11×103×4=1116.44×103g=1116.4 kg. The mass of filled balloon is the sum of the mass of the empty ballon 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