What is precisely the reason that a helium balloon ascends?

A simple question with no clear answer for me: Helium is lighter than air and lighter air rises. That's it!?

• I) A helium atom is approx. 4 times as light as an an air molecule. With 4 times less mass helium should be less attracted by gravity of the Earth. But its inertia is equally to its gravitational pull. Do masses in vacuum not have the same attraction and speed? Can it be said that for air molecules the atmosphere is a vacuum? So that all together helium should have the same attraction towards Earth as air molecules?

• II) Because helium atoms are much lighter, perhaps they could have a higher speed than for example $O_2$ or $N_2$? Ok, but those helium atoms are in a balloon so they push at all sides of the balloon equally so the balloon shouldn't move at all?

• III) When a balloon starts ascending from the ground there is more air (pressure) above it than beneath. So the air pressure above it should push the balloon to the ground?

Perhaps there are more influences, but considering the three effects mentioned, helium balloons shouldn't ascend. But they do! So what is wrong or forgotten?

• In your three points, you are confusing the buoyancy force with the gravitational force, the balloon's pressure, and the drag, respectively. You actually haven't mentioned anything to do with buoyancy anywhere. – knzhou Oct 9 '16 at 20:27
• See this question for an explanation of how buoyancy works. – knzhou Oct 9 '16 at 20:30
• I know Archimes'law, and comparing it with a ball of air pushed at the bottom of a bath of water it will also rise above. – Marijn Oct 9 '16 at 20:44

I) But haven't masses in vacuum not the same attraction and speed.

No. Their weights are different, so they are not "attracted" / pulled in by gravity equally.

Think of this: If you find 100 heavy perfectly round stones, and you put 5 plastic balls full of air with exactly the same size in the basket with them, what will then happen when you shake them a bit? Will the lighter plastic balls fall to the bottom or "float" to the top?

They will float to the top.

The point simply is that it is easier for helium atoms to move up than for air molecules. If you shake the basket violently, the stones might jump a bit while the plastic balls can jump much higher. So on average, the helium atoms will move much higher upwards, and as soon as they do that, some oxygen molecules will take their previous location. Now they have a new location higher up, and the same happens.

Overall this causes the effect of buoyancy, sometimes called updrift, which is the force that this lighter material is pushed up with. And this upwards force is exactly the same as the force, with which the heavier materials pulls downwards - in other words, the lighter material is pushed up with the weight of the displaced heavier material, which now pushes to come back in place.

This was Archimedes' discovery.

Now to your other sub-questions:

Can be said that for airmolecules the atmosphere is a vacuum?

Well, no, a vacuum is a vacuum. If there are molecules present, it isn't vacuum, and the atmosphere isn't a vacuum.

So all together helium should have the same attraction to earth as the other airmolecules?

No, their "attraction" to Earth are different, because that "attraction" must be weight. And the helium atoms weight is lower.

II) Because helium atoms are much lighter, perhaps they could have a higher speed than fe O2 or N2?

Mass (or weight) doesn't influence possible speed. It only influences how hard it is to make them reach the speed.

Ok, but those helium atoms are in a balloon so they pushes at all sides of the balloon equal so the balloon shouldn't move at all?

If only the balloon with helium was present, and no gravity or outside atmosphere, then you are completely correct. The inside pressure cannot make the balloon move. But with gravity present, the whole thing is pulled downwards, and with the atmosphere present, there is a buoyancy force upwards as discussed above. Which-ever of these forces is greater, makes the balloon move.

III) When a balloon starts ascending from the ground there is more air (pressure) above him than beneath. So the airpressure above him should push the balloon to the ground?

Incorrect. You actually said it yourself just before: Inside the balloon, the pressure equalizes throughout so the push at any point on the balloon is the same. Same goes for this air column: All the air in the column above presses down, but the tiny bit of air below pushes up with the same force to balance out the pressure.

• But isn't a feather and a hamer falling with the same speed on the moon? So it isn't the weigth/mass that causes the speed/attraction because gravity equals to inertia. Only the friction with the air and/or the upward force of the atmosphere is causing the hamer to fall faster. Although there was on the moon a hamer and a feather for the hamer and feather they were in a vacuum. And therefore if you drop one helium atom and one oxygen atom on earth the would fall with the same speed. But why shoudn't they fall with equal speed when there are many of them, that's my point? – Marijn Oct 10 '16 at 9:29
• @Marijn Their accelerations are equal, not their speeds necessarily. Only if you drop them at the same time will the speeds at all later moments be equal. You are correct about this happening in vacuum, and as explained in the answer the difference on Earth is simply that there are other forces than gravity. Because the helium atom must push away air molecules in order to fall freely, it does not fall with the same acceleration as in vacuum. In fact the air molecules also try to push away the atoms under them, and because they are heavier, they succeed! And so helium is pushed up. – Steeven Oct 10 '16 at 17:24

Your question is why the helium balloon ascends. So you have to explain why there is a net force on the ballon driving it upwards called buoyancy. You can explain this in different ways but the simplest is probably considering the different density of air and of helium which is, of course proportional to the molecular masses because, as is well-known, the same volume of (ideal) gas at the same temperature and pressure contains the same number of molecules. The only other thing you have to know is that the hydrostatic pressure difference 𝛥P (valid approximately also for gases) in a constant gravitational field for a height difference h is approximately given by 𝛥P=𝜌·g·h, where 𝜌 is the gas density, g is the gravitational acceleration. The buoyancy can now be explained by the difference in vertical force on the lower half of the balloon from outside air pressure and the inside helium pressure. If you consider a vertical column of height h of small horizontal area 𝛥A cut out of the balloon, the helium pressure difference inside the ballon will be 𝛥P_hel=𝜌_hel·g·h and the air pressure difference outside will be 𝛥P_air=𝜌_air·g·h so there will be a net upward force on this column 𝛥F=(𝛥P_air-𝛥P_hel)·𝛥A=g·(𝜌_air-𝜌_hel)·h·𝛥A. Summing over all vertical columns of the ballon for small 𝛥A gives you the total upward force (buoyancy) on the balloon F=g·(𝜌_air-𝜌_hel)·V, where V is the volume of the balloon. This is called Archimedes law.

(I) The gravitational pull is less on the He atoms (lower molecular mass) than on the air molecules. Therefore the hydrostatic pressure difference is less than that of air giving the upward net buoyancy force.

(II) The He atoms with their lower mass move with a mean speed that is higher than the air molecules. For the same column height, however, due to the smaller gravitational pull the pressure difference is smaller for He than for air. Microscopically the hydrostatic pressure difference leads to a somewhat higher density of gas molecules at the lower area of the columns which explains the higher pressure there in spite of the constant temperature and mean energies of the molecules.

(III) When the ballon starts ascending and also afterwards there is always a lower static air pressure above than below the balloon.

• So when I could make a long vertical cilinder and at the bottom of it a heliumballoon, the cilinder is open at the top but the balloon fit just so well that there can't be any air going underneath the balloon from above, the balloon wouldn't go upwards, because pressure is beneath the balloon at a certain point lower than above the balloon although the balloon is lighter than the air above him? – Marijn Oct 10 '16 at 11:04
• If I understand you correctly, you want to fit your balloon into a cylinder of equal diameter so that no air can pass between the cylinder wall and the ballon and the cylinder part under the ballon has no connection to the atmosphere. Then the ballon would not move upward because this would reduce the air pressure of the remaining air space below the balloon pulling the balloon back. – freecharly Oct 10 '16 at 13:00

You noticed that helium atoms move faster than air molecules (helium atoms are actually 7-8 times lighter than air molecules), so each one encounters the walls more often than air molecules would. However, each helium packs less momentum than air molecules at the same temperature, and combining these facts gives us the ideal gas law, which says that you get pressure balance when the number density of helium atoms is the same as the number density of air molecules, even though the helium atoms are less massive. So if the number density is the same, the mass is 7-8 times less in the same volume, so the force of gravity on a given volume of helium is 7-8 times less than on the same volume of air. Notice how that produces buoyancy, via Archimedes' principle as mentioned.

protected by Qmechanic♦Oct 9 '16 at 22:37

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