Why does helium rise?

[Gray_Ghost]

Chronos,** JWT Kottekoe**:

Do the different chemical structures for each gas molecule make a difference when we look comparing gas temperatures to mean individual particle velocities? Or is that addressed in the different heat capacities for each gas?

For example, Helium’s a monoatomic gas. Any energy it receives from its environment goes towards its kinetic energy. (And rotational energy if individual atoms can be said to rotate—do they?) But Oxygen, say, is a diatomic gas. Energy that the O2 molecule receives can go to kinetic energy, but some also goes into the bond between the two atoms, and some goes into rotational energy of the gas molecule. Does that change the h = kT/mg relationship that JWT mentioned?

It’s been awhile since P. Chem and I truthfully didn’t do all that well when the material was fresh.

[Asympotically_fat]

@KarlGauss

Outstanding! Your answers have really helped me. I am much obliged.

The idea that lighter atoms or molecules must move faster and are, thus, statistically more likely to go farther in any interval in any direction, also explains why even single atoms/molecules of hot air rise (a process that I might have thought, incorrectly, would have depended on ‘cells’ of warn being formed).

Thank you.

As others have pointed out temperature is a bulk property, so there is no such thing as a molecules of hot air surrounded by molecules of cold air as the temperature (of an ideal gas) is not about the velocities of individual atoms, instead it is a measure of the distribution of velocities.

The important thing to realize though is that, whilst the average velocity of particles in the rest frame of an ideal gas is 0 (i.e. is a zero vector), regardless of temperature/mass and so the average displacement of a molecule from it’s original position after a certain amount of time is also 0, the variance of the displacement along any given axis is greater for lighter and hotter gases and so the average distance traveled is greater along any axis.

[OldGuy]

@Exapno_Mapcase

Helium is the lightest molecule, equal to a hydrogen molecule and less than oxygen or nitrogen or carbon dioxide.

A helium molecule actually has about twice the mass of a hydrogen molecule. Most (99.98%) hydrogen nuclei are a single proton. Most (about 99.9999%) helium nuclei are two protons and two neutrons. So helium atoms (and molecules) are about four times as heavy as a hydrogen atom and twice as heavy as a hydrogen molecule. Hydrogen is a much better lift gas than helium, but is usually not used so because it is more dangerous.

[Dr.Strangelove]

@OldGuy

A helium molecule actually has about twice the mass of a hydrogen molecule. Most (99.98%) hydrogen nuclei are a single proton. Most (about 99.9999%) helium nuclei are two protons and two neutrons. So helium atoms (and molecules) are about four times as heavy as a hydrogen atom and twice as heavy as a hydrogen molecule. Hydrogen is a much better lift gas than helium, but is usually not used so because it is more dangerous.

It’s better, but it’s not much better. The densities of the gases under discussion:
He: 0.1786 g/L
H2: 0.08988 g/L
Air: 1.2754 g/L

And the lifting capacities in air (just the differences in the above values):
He: 1.0968 g/L
H2: 1.18552 g/L

So, hydrogen is about 8% better (not twice as good, as one might naively think).

[JWT_Kottekoe]

@Gray_Ghost

Chronos,** JWT Kottekoe**:

Do the different chemical structures for each gas molecule make a difference when we look comparing gas temperatures to mean individual particle velocities? Or is that addressed in the different heat capacities for each gas?

For example, Helium’s a monoatomic gas. Any energy it receives from its environment goes towards its kinetic energy. (And rotational energy if individual atoms can be said to rotate—do they?) But Oxygen, say, is a diatomic gas. Energy that the O2 molecule receives can go to kinetic energy, but some also goes into the bond between the two atoms, and some goes into rotational energy of the gas molecule. Does that change the h = kT/mg relationship that JWT mentioned?

It’s been awhile since P. Chem and I truthfully didn’t do all that well when the material was fresh.

Excellent question. In thermodynamic equilibrium, the average energy of every degree of freedom is kT/2. For a monatomic gas, there are three degrees of freedom, motion in x, y, and z; so helium atoms have a total of 3kT/2. For nitrogen, hydrogen, or oxygen, each of the rotational and vibrational modes also has kT/2, but this doesn’t change the velocity distribution. As you suggested, this affects the heat capacity, but not the particle velocities.

[AaronX]

Gases do not rise or separate in the atmosphere, any more than alcohol and water separate. Your bottle of vodka does not have more alcohol at the top, despite alcohol being lighter. Similarly, we do not see more radon and carbon dioxide on Earth’s surface (besides the excess due to them being produced down here), then oxygen, then nitrogen as you go up. This is a property of solutions - they are not separated by gravity. A “worse” mixture is colloids - do not separate by gravity but can be separated by centrifuges (eg watercolor), then suspensions - separates under the influence of gravity.

[Chronos]

That’s not quite right. They mix fully, but there is still some “separation” from them having different scale heights: Even if radon production were to stop, it would still form a larger proportion of the air at sea level than at altitude, as explained earlier in the thread.

[AaronX]

Ah, you’re right, they fall off at different rates. Thanks.

@JWT_Kottekoe

To the first level of approximation, the distribution of helium is controlled by the ideal gas law. The density is greater at sea level because of the pressure of helium atoms above it. If you write down the equations, you find that the rate of decrease of helium density with altitude is proportional to the helium density at that altitude, thus leading to an exponential decline with altitude. This means that there is a certain “half height” at which the density is half as much as at sea level. At twice that height, the density is one quarter as great, etc.

This is true for any ideal gas. The only difference is that each gas will have a different “half height”. The half height is inversely proportional to the mass of the molecule*. For Nitrogen, the half height is about 5 kilometers. A Helium atom is about seven times lighter than a Nitrogen molecule, so it’s half height should be about 35 km.