A plastic bag is filled with hydrogen at atmospheric pressure and 19.0 o C. Assu

Question

A plastic bag is filled with hydrogen at atmospheric pressure and 19.0 oC. Assume that the mass of the bag is negligible and take the temperature of the outside air to be 0 oC. With the help of this balloon we want to lift a 57.0 kg girl off of her feet. Part A: How large a volume of hydrogen (in m3) is required? Part B: If hot air is used instead of hydrogen, what is the required volume of the balloon if the air inside can be maintained at 38.0 oC? Part A was found to have a volume of 47.5 m3 using a density of 1.2 kg/m^3, Can anyone explain how to find the density for Part A & how to solve Part B if the answer is 362 m^3?

Explanation / Answer

P = 1 atm
Tin = 19 degC = 292 K
Tout = 0 degC = 273 K
m = 57 kg
Let volume of air displaced = V
from , PV = nRT
We have ,
PM = d RT,
Thus, density of H2 at 19 degC is
d = (101.325 kPa x 2)/(8.315 x 292) =0.083485
Thus the buoyancy force must be greater than mxg = 57 x 9.8 = 558.6 N
B = (Density of air at 0 degC - density of H2 at 18 degC)xVxg
=> 558.6 = (1.32 kg/m3 - 0.083485 kg/m3) x V x 9.8
=> V = 46.097 m3

For air,
d at 0 degC = (101.325 x 28.964)/(8.315 x 273) = 1.29285 kg/m3
For air at 38 degC
d = (101.325 x 28.964)/(8.315 x 311) = 1.13488 kg/m3

B = (1.29285-1.13488) x V x 9.8 = 57 x 9.8
=> V = 360.828 m3

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