Assuming the same pressure in each case, Calculate the mass of hydrogen required to inflate a balloon to a certain volume V at 100 ??° c. If 3.5 g Helium is required to inflate the balloon to half the volume V at25 ° c

RAHUL KUMAR, 11 years ago

Grade:11

1 Answers

Aman Bansal

592 Points

11 years ago

Dear Rahul,

Balloons are buoyant because the air pushes on them. The air doesnt know whats in the balloon, though. It pushes on everything the same, so the buoyant force is the same on all balloons of the same size.

If the "balloon" is just a lump of air with an imaginary boundary, then the lump wont go anywhere because the air isnt moving on average. So the buoyant force must exactly cancel the gravitational force (the weight). Since the buoyant force is the same on everything, the buoyant force on a balloon is equal to the weight of the air it displaces. In symbols this is

F b u o y a n t = ρ g V

where ρ is the density of air, g is gravitational acceleration, and V is the balloons volume.

Hydrogen and helium have less weight than a similar volume of air at the same pressure. That means the buoyant force on them, which is just enough to hold up air, is more than enough to hold up the balloons, and they have to be tethered down.

Assuming they have the same pressure and volume, a hydrogen balloon has less weight than a helium balloon. Things like pressure and volume are roughly decided on a per-molecule basis, at least in gases at low pressure, so at the same pressure and volume hydrogen and helium will have the same number of molecules. Hydrogen is lighter per molecule, so the hydrogen weighs less, and less of the buoyant force is canceled out. That means the net force on a hydrogen balloon is greater. The difference in the net force is small.

Hydrogen is H2, which has atomic mass 2, while air is mostly N2, which has atomic mass 28, so the hydrogen balloon has a net force of about (28-2)/28 = .93 the weight of the air it displaces.

Helium is mostly helium-4, so the net force on a helium balloon is about (28-4)/28 = .86 the weight of the air is displaces.

So net force on the hydrogen balloon is in the neighborhood of 10% more.

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