A team designing a helium-filled balloon that will fly to analtitude of 80,000 f

Question

A team designing a helium-filled balloon that will fly to analtitude of 80,000 ft. As the balloon ascents, the upward forcewill need to exceed the total weight. Estimate the weight of thehelium inside the balloon. The balloon is inflated at a site wherethe atmospheric pressure is 0.89 bar and the temperature is 22 Cdegree. When inflated prior to launch, the balloon is spherical(radius 1.3m) and the inflation pressure equals the localatmosphere pressure.

I want to know where can I start this problem, and what formulascan be used, and the final answer? Thanks

Explanation / Answer

The upward force will need to exceed the total weight the upward force by atmosphere = weight of displaced air =air*V*g {force of buoyancy by air} we have V = (4/3)**1.33 (here r = 1.3 m)                  = 9.2 m3 from PV = mRT or, P = airRT or, air=P/RT =(0.89*105)/(0.287*103*295.15) {1bar=1*105 N/m2, R = 0.287 kJ/kg-K, T =22+273.15 = 295.15K}           = 1.05kg/m3 so, the weight of helium inside the balloon =air*V*g = 1.05*9.2*9.81 = 94.76 N

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