a) The molecular weight of air may be taken as 28.6 g/mole. At the surface of th

Question

a) The molecular weight of air may be taken as 28.6 g/mole. At the surface of the earth, with a temperature of 20° C, what volume of air will be occupied by one mole? You may then compute the density of air at this temperature and
pressure.

b) A spherical helium balloon has a radius of 10 m. What buoyant force (mass) is available to lift the balloon at an air temperature of 20° C?

c) Assume that the mass of balloon, helium and cargo is 90% of the mass computed in part (b). When the tethers are released the balloon will begin to
rise.. Will this rise continue indefinitely? Explain your answer.

Explanation / Answer

a) density of air at 20 deg C = 1.2754 kg / m^3

mass of 1 mol air = 28.6 g = 0.0286 kg

density = mass / volume

1.2754 = 0.0286 / Volume

Volume = 0.0224 m^3

b) volume of ballon = 4 pi R^3 / 3 = 4 pi (10^3) / 3 = 4188.79 m^3

buoyant force , Fb = density of air x volume of ballon x g

= 1.2754 x 4188.79 x 9.8 = 52355.35 N

c) Weight is only 90% of buoyant force.

so Net force on ballon is upward. hence it will have downward acceleration.

and it will rise .

it willl rise only upto when density of air becomes less than 90% of given value.

after that acceleration will be downwards and it will start decelerating then it will stop and
come downward.

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