Weight of helium in a balloon?

Question

I need a little guidance for a problem in my class.

Archimedes's principle states that the lifting force (buoyancy) of a balloon is equal to the weight of the air displaced by the balloon. What is the buoyancy force generated by a 30x10^6 ft^3 helium-filled, high-altitude balloon, assuming the air density at 120,000 feet is 1.27x10^-5 slug/ft^3 ?

The weight is around 12,200 pounds.

Now:

What is the weight of the helium from the problem above if the specific gas constant for helium is R = 12,425 (ft lb)(slug degrees Rankine)?

the professor said that this problem was a little tricky and that you should write down the equation of state for both air and helium and compare the two.

so the equation of state is:
 pressure = (density)(specific gas constant)(temperature)

I can find the temperature at 120,000 ft with a simple Google search and I know the density of air, as it is given above.

I'm just unsure of how to get helium's weight...

and I know weight = (mass)(gravity)

I'm just a little stuck.

Can one of you show me the way?

Gary H · Accepted Answer

This may be a trick question.   As you say, weight is not the same as mass.

If the balloon is not rising or sinking, then the buoyancy force exactly equals the gravitational force.

This would be different for a cork floating in water because the cork that is above the waterline is not displacing any water.   You would need to know exactly how much of the cork is displacing water.

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Weight of helium in a balloon?

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