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in Physics by (58.2k points)

Determine the size of a spherical balloon filled with hydrogen at 30°C and atmospheric pressure for lifting 400Kg payload. Atmospheric air is at temperature of 27°C and barometer reading is 75cm of mercury.

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Best answer

Given that:

Hydrogen temperature = 300C = 303K

Load lifting = 400Kg

Atmospheric pressure = 13.6 × 103 × 0.75 × 9.81 = 1.00 × 105 N/m2 = 1.00 bar

Atmospheric Temperature = 270C = 300K

The mass that can be lifted due to buoyancy force, 

So the mass of air displaced by balloon(ma ) = Mass of balloon hydrogen gas (mb) + load lifted ...(i)

Since PV = mRT; ma = Pa Va /RTa ; R = 8314/29 = 287 KJ/Kgk For Air; 29 = Mol. wt of air

= 1.00 × 105 × V/ 287 × 300 = 1.162V Kg ...(ii)

Mass of balloon with hydrogen

mb = PV/RT = 1.00 × 105 × V/ (8314/2 × 300) = 0.08V Kg ...(iii)

Putting the values of (ii) and (iii) in equation (i)

1.162V = 0.08V + 400

V = 369.67 m3

But we know that the volume of a balloon (sphere) = 4/3Πr3

322 = 4/3Πr

r = 4.45 m

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