# Size of a hydrogen spherical balloon for lifting a payload

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

Given :

Hydrogen temperature = 30Â°C = 303K

Load lifting = 400Kg

Atmospheric pressure = 1.00 bar

Atmospheric Temperature = 27Â°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= 4/3Î r3

Substituting for V we get, r = 4.45m. (ANS)

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