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# Size of a hydrogen spherical balloon for lifting a payload

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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 75 cm of mercury.

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Qn. 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 75 cm of mercury.

Given :
Hydrogen temperature = 30°C = 303K
Load lifting = 400Kg
Atmospheric pressure = 1.00 bar
Atmospheric Temperature = 27°C = 300K

Solution:

Mass of air displaced by balloon(ma) = Mass of balloon hydrogen gas (mb) + load lifted........(i)
Since PV = mRT;
ma= PaVa /RTa;
where R = 8314/29 = 287 KJ/KgK (Mol. wt of air=29)

ma = (1 x 105 x V)/ 287 x 300
= 1.162Vkg................................................(ii)

Mass of balloon with hydrogen, mb = PV/RT
= (1 x 105 x V)/ {(8314/2) x 300}
= 0.08Vkg.......................(iii)
Putting the values of (ii) and (iii) in equation (i)
1.168V = 0.08V + 400
V = 369.67m3.
But we know that the volume of a balloon (sphere) V= 4/3Πr3
Substituting for V we get, r = 4.45m. (ANS)

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