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 = 4/3Πr3
r = 4.45 m