How Does Hot Air Rise and Affect Weather Systems?

[Dadface]

Good one. Since the hotter molecules undergo more collisions with the surroundings they lose more heat to the surroundings which intuitively means it expands and cold air comes in.I'm not sure of the mean free path being same everywhere at all instants.Lesser dense air has more free path of its molecules.And remember the hotter air does not remain hot so you cannot say that about the displacement of a single molecule.

Also,don't forget that since the collisions are elastic any kinetic energy lost by one molecule during a collision is gained by the other molecule.

 

[vin300]

Also,don't forget that since the collisions are elastic any kinetic energy lost by one molecule during a collision is gained by the other molecule.

Yes the hotter air transfers energy to the colder and the latter becomes hot, that is what is meant by expansion of hot air and replacement by colder air.

 

[Borek]

That doesn't explain why hot air tends to go up, then.

It does if the heat source is close to the earth.

Trick is, hot air goes up even if it is far from the surface - so you will need different explanation for the same process depending on the distance from the surface.

It is easy to demonstrate,for example,that a flame close to the Earth's surface gives rise to a convection current where there is a bulk upward movement.If the same flame was placed at a higher altitude then the upward movement would be reduced.

Any proof for the latter statement?

 

[Borek]

the point is that the phenomenon is now explained on a molecular level

I admit I have not read through your explanation, but I suspect that if it is correct, it will work also for the baloon with rigid surface. At the scale we are talking about characteristic of the boundary is less important than its existence. That's why these pockets do exist.

 

[Dadface]

Trick is, hot air goes up even if it is far from the surface - so you will need different explanation for the same process depending on the distance from the surface.



Any proof for the latter statement?

Is it agreed that when air is heated the molecules move faster and the air tries to expand?If so do a thought experiment where a heat source is placed in a closed box which is suspended from strings.If a single hole is made in the top of the box the expanding air will move out of that hole.If the hole is at the bottom the air will move out of that hole.The same reasoning applies no matter where the hole is made.It can be concluded that the movement of the hot air is not determined only by gravity and the other factors but is also affected by the structure and geometry of the surroundings.Close to the ground the Earth itself forms a barrier which restricts the downward movement of the hot air but at a higher altitude the downward moving hot air has greater space in which to move.The upward moving air transfers kinetic energy by collision to other atmospheric molecules, as does the downward moving air, but the latter also transfers some energy to the Earth when it arrives there.If the Earth heats up as a result then energy can be transferred back to atmospheric molecules which can only move up or sideways but not down.

 

[jachyra]

If so do a thought experiment where a heat source is placed in a closed box which is suspended from strings.If a single hole is made in the top of the box the expanding air will move out of that hole..If the hole is at the bottom the air will move out of that hole.

If your box has negligible mass, then the entire box would also go up as the air comes out from the bottom hole. Which means your hot air is going up AND down =) I don't know if you can use this thought experiment.

 

[vin300]

Trick is, hot air goes up even if it is far from the surface - so you will need different explanation for the same process depending on the distance from the surface.



Any proof for the latter statement?

The density of air goes on decreasing with altitude, so does the specific heat.You need more heat to raise the temperature of the same volume of air so the temperature difference is less and the convection is less as implied by the formula that follows
The difference of pressure is thus lesser(BtW,g is also a bit lesser)
Air goes up because like static pressure in liquids the difference pressure is due to its depth in the atmosphere
Copied from wiki:
Convection is predicted using the rayleigh number
Ra=ρ0gαΔTL^3/κ μ
Ra=ΔρgL^3/ κ μ
Δρ is the difference in density between the two parcels of material that are mixing
ΔT is the temperature difference across the medium
ρ0 is the average density of the medium
α is the coefficient of volume expansion
κ is the thermal diffusivity
L is the characteristic length-scale of convection
μ is the dynamic viscosity.

The value of L is uncertain

 

[Borek]

The density of air goes on decreasing with altitude, so does the specific heat.You need more heat to raise the temperature of the same volume of air

But we are talking about the difference that have its source in the presence of the near surface, not in the differences that depend on the pressure/density. At least that's where the discussion started and I have not seen anyone stating "we are discussing different case and phenomena now".

 

[michelcolman]

I admit I have not read through your explanation, but I suspect that if it is correct, it will work also for the baloon with rigid surface. At the scale we are talking about characteristic of the boundary is less important than its existence. That's why these pockets do exist.

I am still refining my theory, and now realize that the pocket of hot air is slightly different from a balloon after all (although the behavior looks the same macroscopically).

For the balloon, the momentum is transferred at the surface of the balloon. More pressure (collisions of surrounding air molecules with the tissue of the balloon) below than above, gives boyancy to lift the balloon. Nobody cares what happens inside the balloon (or any other lighter than air object).

In the pocket of hot air, the transfer of momentum is NOT just happening at the boundary! (I only just realized this).

The surrounding area has a pressure gradient that is just enough to keep the cold air stable. A cold air molecule will, on average, receive slightly more collisions from below than from above and this will be just enough to compensate for its weight. That doesn't mean none of them come down: some will still come down, while others will go up, in random brownian motion, but there is no net average tendency. So you won't feel any up- or downdraft.

Inside the pocket of hot air (not just at the top and bottom), the same pressure gradient exists because pressure can even out sideways with the surrounding cold air. So each hot air molecule, too, is receiving slightly more push from below than from above. But this total extra push, summed over all the molecules at a certain altitude, is divided over a smaller number of hot air molecules in the layer above that altitude as compared with the number that would be in a similar slice of cold air. This means the hot ones get more than their fair share of upward gravity-canceling momentum and therefore, on average, all the hot air molecules will tend to go up.

Unlike the rigid balloon, the effect is NOT caused at the boundary but happens everywhere inside the volume of hot air.

Of course you are free to make a statistical consideration about the total momentum being transferred to the volume of hot air from all sides, and come to the correct conclusion that the hot air must be pushed up because otherwise it doesn't add up, but I think my analysis is more detailed.

(At least that's my theory, feel free to correct me if I'm wrong)

 

[Dadface]

If your box has negligible mass, then the entire box would also go up as the air comes out from the bottom hole. Which means your hot air is going up AND down =) I don't know if you can use this thought experiment.

Exactly, the hot air goes up and down,it travels in all directions outwards from the source.The point I am making is that the surroundings have an effect on the net movement of air.

 

[DrGreg]

If so do a thought experiment where a heat source is placed in a closed box which is suspended from strings.If a single hole is made in the top of the box the expanding air will move out of that hole.If the hole is at the bottom the air will move out of that hole.

It is understood that the box itself must be too heavy to rise due to buoyancy. If the hot air is initially under pressure when you drill the hole, air will escape at the top or bottom simply due to the excess pressure.

Consider what happens if you drill two small holes, one at the top and one at the bottom. If there is excess pressure, then at first hot air will escape from both holes due to pressure. But after the pressure has equalised, yes, more hot air will escape from the top, but at the bottom cold air will rush into the box. How does your theory explain that?

 

[michelcolman]

It is easy to demonstrate,for example,that a flame close to the Earth's surface gives rise to a convection current where there is a bulk upward movement.If the same flame was placed at a higher altitude then the upward movement would be reduced.

Then why does my barbecue have an air hole at the bottom? If I open that hole, the coals start burning a lot more intensely and you can actually feel the air current through the hole. So I don't think a flame close to the surface would give more convection, on the contrary. Air below the flame seems to give a significantly faster convection.

For a different example, it is a well-known phenomenon that hot air will tend to build up in a large bubble at the surface and then suddenly let go. This, too, seems to indicate boyancy is lower if the pocket is touching the ground.

(although I can't quite come up with an explanation for that yet)

 

[Dadface]

It is understood that the box itself must be too heavy to rise due to buoyancy. If the hot air is initially under pressure when you drill the hole, air will escape at the top or bottom simply due to the excess pressure.

Consider what happens if you drill two small holes, one at the top and one at the bottom. If there is excess pressure, then at first hot air will escape from both holes due to pressure. But after the pressure has equalised, yes, more hot air will escape from the top, but at the bottom cold air will rush into the box. How does your theory explain that?

Precisely ,hot air rises and cooler air comes into take its place.I am not disputing that but I am stating that the surroundings have an effect on the net movement of hot air which is upwards.The hot air which initially comes out of the lower hole can diffuse sideways beyond the extremities of the base of the box and then this also can rise.Suppose the box was in an atmosphere which for the purposes of this analysis can be considered as being totally remote from the Earth's surface.Can you explain in what direction the net movement will now be?

Then why does my barbecue have an air hole at the bottom? If I open that hole, the coals start burning a lot more intensely and you can actually feel the air current through the hole. So I don't think a flame close to the surface would give more convection, on the contrary. Air below the flame seems to give a significantly faster convection.

For a different example, it is a well-known phenomenon that hot air will tend to build up in a large bubble at the surface and then suddenly let go. This, too, seems to indicate boyancy is lower if the pocket is touching the ground.

(although I can't quite come up with an explanation for that yet)

To answer your question we need to refer to the theory of combustion and perhaps this is irrelevant to the main point being discussed.

 

[Borek]

Unlike the rigid balloon, the effect is NOT caused at the boundary but happens everywhere inside the volume of hot air.

If it happens inside of the volume, there is no need for boundary - nor need for the cold air around...

 

[michelcolman]

If it happens inside of the volume, there is no need for boundary - nor need for the cold air around...

Not so fast. The cold air around creates the pressure gradient. Away from the pocket of hot air, this pressure gradient is exactly sufficient to keep the cold air stable. A hot air pocket, inserted anywhere in this cold air, will necessarily take the same pressure gradient because the pressure can even out horizontally. This pressure gradient, everywhere inside the volume, makes the hot air particles go up like I explained.

 

[michelcolman]

To answer your question we need to refer to the theory of combustion and perhaps this is irrelevant to the main point being discussed.

No need to explain, just clarify that you believe a flame will cause more updraft if it is burning just above the surface of the Earth instead of being higher up with plenty of fresh air underneath? Maybe I misunderstood, but that's what I thought you said. And it seems contrary to my experience, although I could be wrong.

 

[Dadface]

No need to explain, just clarify that you believe a flame will cause more updraft if it is burning just above the surface of the Earth instead of being higher up with plenty of fresh air underneath? Maybe I misunderstood, but that's what I thought you said. And it seems contrary to my experience, although I could be wrong.

For reasons I tried to explain in my earlier posts I think that the higher up the flame the greater the directionality of the hot air i.e less will go up and more travel in other directions.

 

[Lok]

Remove the Earth and leave just the hot and cold air behind - which way is up and which way is down? From this, you could probably say it has something to do with gravity (I might be wrong).

The hotter air would still push the colder air out of it's place because of faster expansion.

 

[rcgldr]

One assumption being made here is that it's the same original heated air molecules that travel upwards. As mentioned heat is trasnferred from the hotter molecules to the colder molcules, increasing the density of the previously hotter molecules, and decreasing the density of the colder molecules.

What is is traveling upwards is a bubble of heat and a somewhat changing set of molecules, not the original set of molecules that initiated a thermal at near ground level. Rather than dissappating in all directions, a heat bubble (thermal) travels upwards and in a circular motion (like a tornado). Cold air tends to flow downwards around the perimeter of the thermal, while hot air rises up internally. At the bottom part of a thermal, the surrounding air is drawn inwards into the thermal, and the thermal expands in diameter with altitude.

http://www.thermikwolke.de/thermals/pdf/page25.pdf

http://www.thermikwolke.de/thermals/pdf/page30.pdf

http://www.rcsoaring.com/docs/thermals_2006.pdf


wiki link:
http://en.wikipedia.org/wiki/Thermal

 

[jachyra]

For reasons I tried to explain in my earlier posts I think that the higher up the flame the greater the directionality of the hot air i.e less will go up and more travel in other directions.

I understand what you are trying to say. Thanks for you earlier post. It helped me look at the phenomenon in a different perspective.

 

[jachyra]

Jeff Reid,

Great links! Really helps to show what Borek and the others have been trying to explain since the beginning.

 

[vin300]

But we are talking about the difference that have its source in the presence of the near surface, not in the differences that depend on the pressure/density. At least that's where the discussion started and I have not seen anyone stating "we are discussing different case and phenomena now".

Good.Now bring to light your theory of convection without pressure difference :zzz:

 

[michelcolman]

One assumption being made here is that it's the same original heated air molecules that travel upwards. As mentioned heat is trasnferred from the hotter molecules to the colder molcules, increasing the density of the previously hotter molecules, and decreasing the density of the colder molecules.

What is is traveling upwards is a bubble of heat and a somewhat changing set of molecules, not the original set of molecules that initiated a thermal at near ground level. Rather than dissappating in all directions, a heat bubble (thermal) travels upwards and in a circular motion (like a tornado). Cold air tends to flow downwards around the perimeter of the thermal, while hot air rises up internally. At the bottom part of a thermal, the surrounding air is drawn inwards into the thermal, and the thermal expands in diameter with altitude.

http://www.thermikwolke.de/thermals/pdf/page25.pdf

http://www.thermikwolke.de/thermals/pdf/page30.pdf

http://www.rcsoaring.com/docs/thermals_2006.pdf


wiki link:
http://en.wikipedia.org/wiki/Thermal

Too bad the links only contain the word "molecule" once (in the rcsoaring one), and even there it's in a different context. So all the links are macroscopic, while the point of the discussion is what happens at a microscopic level.

You did say something interesting in your own text, though. You say that individual molecules are not traveling up, but rather their momentum is transferred up and the bubble ends up containing different molecules?

I can see how this is happening at the boundaries (momentum is always being exchanged there, and molecules move through the boundary in different directions all the time) but for the vast majority of molecules, I thought they should simply move up with the bubble. Am I wrong there? Where did you find this information?

 

[michelcolman]

Jeff Reid,

Great links! Really helps to show what Borek and the others have been trying to explain since the beginning.

The links are interesting, but a bit pointless in this discussion (unless I missed some interesting part of one of them).

Yes, hot air rises, and you can describe the whole thing by looking at densities and pressures, but that's all an approximation, a very useful approximation, but an approximation nonetheless.

I wanted to know what was happening at a microscopic level, with individual molecules being pushed around. Just like I learned how to derive the ideal gas law that way, I now wanted to see convection explained that way too.

Since few people seemed to even understand what the question was, I finally came up with a theory of my own, which nobody has really commented on yet (except by saying "I admit I haven't read it yet")

Too bad, because it's really not far away from the macroscopic view! If the other posters would just take the time to read it, they would find it corresponds pretty much to the macroscopic theories they love so much, only in slightly more detail.

Executive summary of my theory: a pressure gradient has built up in the atmosphere (cold air) which is just right to keep cold air stable in the field of gravity. Each molecule gets slightly more collisions from below which, for a cold molecule, is just enough to support its weight (on average! they are all still moving around randomly, some get more pushes than others, they just don't get a net tendency in any particular direction). Inside the hot bubble, the same pressure gradient exists but the total extra momentum transfers from below are now divided over fewer hot molecules. This means every individual hot molecule (on average) gets slightly more than its fair share of gravity-canceling momentum. The sum of all pushes exceeds its weight, so it goes up. Of course this is only a general tendency, superimposed on their own brownian motion zigzagging faster than the speed of sound, but since it has the same average sign everywhere, it does tend to move the whole bubble up as a whole.

There, was it really that complicated/impossible/"nonsencical"?!

 

[Dark Horse]

Hi,
I had the same thought, 'why does hot air rise', or to put it another way 'why does a more energetic gas molecule rise when it essentially has the same mass as a cold molecule'
This is what I postulated

Air gets less dense as you increase in altitude.
If you heat up a bit of air the average velocity of the individual gas molecules increases, so the pressure of that patch of air increases and in an attempt to equalize with the surrounding air expands. Since the pressure above this parcel of hot air is ever so slightly less than the pressure below this parcel of air there are less molecular collisions from above so the net effect is the pocket of hot air moves upwards; you can feel the draft caused by the mass of air moving.

Watching food dye circulate in a glass of water would sort of confirm that it is the same molecules which are moving rather than just the energy being transferred to another group of adjacent molecules or some form of diffusion is dominant.

It would be an interesting experiment to see how convection currents flow in a centrifuged medium.


cheers
Martin

 

[rcgldr]

Inside the hot bubble, the same pressure gradient exists but the total extra momentum transfers from below are now divided over fewer hot molecules.

Except the hot bubble doesn't rise if the surrounding air is at the same temperature. The hot bubble needs the surrounding air to be cooler (and denser) in order for the hot bubble to rise.

 

[michelcolman]

Except the hot bubble doesn't rise if the surrounding air is at the same temperature. The hot bubble needs the surrounding air to be cooler (and denser) in order for the hot bubble to rise.

The cold air created the pressure gradient. Without the cold air there would be no excessive pressure gradient so the hot air would not rise.

 

[mikelepore]

Here's my hypothesis. You know that toy with the five stainless steel balls in a row that have nearly elastic collisions with each other - I don't know what it's called - Sprott's book 'Physics Demonstrations' just calls it the colliding balls toy ... I think the group of molecules in the hot air do that with each other for a while, exchanging momentum among themselves while they stay segregated in a group to some extent. This allows them as a group to be subjected to the larger pressure below them and the lesser pressure above them.

 

[Dark Horse]

I am going to have to revise my answer to 'I don't know'

Pressure = number of molecular collisions per area * average momentum exchange per collision.

so in a hot body of air each molecule has a statistically higher energy so exerts more force on the surrounding molecules and expands until the number of collisions has decreased to the point where the forces are in equilibrium. Sounds ok so far, agrees with observation that hot gasses expand and cold gasses contract.
Previously I said the hot air rose because there were statistically more collisions from below than from above due to minute changes in are density due to gravity but that is true for cold air as well as hot air and I don't observe cold air rising hence I must revise my answer to 'I don't know'

 

[rcgldr]

I'll take a shot at this. The higher temperature in a thermal decreases it's density compared to the surrounding cooler air. Then it's a buoyancy effect. Ignoring dynamic pressure effects, the total pressure = static pressure + ρ g h, where ρ is density, g is the force of gravity, and h is height. The pressure decreases with altitude, and for any given volume of air, the weight of that volume of air is opposed by an equal and upwards force on that volume of air (otherwise the air would be accelerating upwards or downwards). If that volume of cooler air is replaced by hotter air with lower density, than the upwards force is more than the weight of the volume of the hotter air, and that hotter air is pushed upwards.

http://en.wikipedia.org/wiki/Buoyancy