A 650 kg weather balloon is designed to lift a 4600 kg package. What volume should the balloon have after being inflated with helium at 0 degrees celcius and 1 atm pressure to lift the total load?

The buoyancy force must equal the weight lifted. Let V be the volume.

g*[(He density)* V + 650 kg] = (Air density)*V*g
Cancel out the g's. Assume the outside air density correesponds to the same 1 atm and 0 C. He density is 4 kg/22.4 m^3 and the air density is 29/22.4 kg/m^3
0.179 V + 650 = 1.295 V
Solve for V (in cubic meters)

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  1. Lifted weight= Bouyant force

    g*[(He density)*V+650+4600]=Air density *V*g

    g= gravity= 9.8 N/Kg
    Air Density= 1.29 Kg/m^3
    He Density= 0.179 Kg/ m^3
    Ballon Voulme= Gas Volume= Air volume approximately
    Solving the equation
    V= 4227 m^3

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