Why does hot air really go up?

[michelcolman]

I know a hot air balloon goes up because the density of the hot air inside is lower. But what about free air, not trapped in a balloon?

You often see exactly the same explanation, hot air is less dense so it goes up, but this does not make any sense if you consider the fact that air is just a bunch of molecules flying around freely and bouncing into each other a lot, and temperature is a measure of their average momentum. There's no such thing as a "pocket" of hot air that somehow pushes other air away while going up. All you can say is that in a certain area the average speed of the air molecules is higher.

So why would this cause the air to rise, to such an extent that it even draws surface winds that fill the gap? I mean, the effect is real, gliders use it all the time, but what is really going on on a molecular level? The faster molecules should surely be pushing in all directions, not just up? I would expect them to transfer their excess energy to nearby molecules through collisions until an equilibrium is reached, but can't imagine why a whole "pocket" of air would tend to rise and leave a low pressure underneath, even drawing in surrounding air instead of pushing it away.

 

[Borek]

There's no such thing as a "pocket" of hot air that somehow pushes other air away while going up.

Yes there is - air doesn't mix fast enough.

 

[turbo]

Cool air is dense and tends to fall in the presence of warmer air, while warmer air is less dense, and it is displaced upward by the cooler air. None of this happens in isolation, of course, and the dynamics of air movement due to heating and cooling effects make predicting weather tough because modeling it is complex.

A good example of the dynamics is the cooling provided by onshore breezes along the coast. Today, it was over 90 deg F inland in Maine, while it was in the 70s in Rockland, on the coast. The reason? Solar heating over land made the air less dense, and the cooler, denser air from over the Atlantic moved into displace it.

 

[Gear300]

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).

 

[turbo]

Yes there is - air don't mix fast enough.

And it can't equilibriate through conduction.

 

[Feldoh]

See: https://www.physicsforums.com/showthread.php?t=32331

 

[turbo]

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).

You are not wrong. Density of air equates to "weight" of air.

 

[michelcolman]

Yes there is - air don't mix fast enough.

You are considering air to be a continuous fluid, but it's not. It's a bunch of molecules flying around randomly and bouncing into each other. So, once again, there's no such thing as a "pocket" of hot air. There are no two different kinds of air, hot and cold, that would have to mix somehow. The hot molecules don't have any reason to stick together, each of them just flies ahead through free space until it hits some other molecule.

That was the whole point of my question, but you don't seem to have taken the time to really understand what I was asking.

 

[russ_watters]

Yes there is - air don't mix fast enough.

And even if it did, what you would see (if you could see air) would be big bubbles breaking apart into smaller, less well defined bubbles. And they'd still rise.

 

[russ_watters]

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).

Yes, that density thing referred to in the OP is a reflection of buoyancy. The weight (ie, gravitational force) of a volume of warm air is lower than the weight of an equal volume of cold air.

 

[michelcolman]

You are not wrong. Density of air equates to "weight" of air.

Guys, forget about density for a minute. Just think of little billiard balls flying around and bouncing into each other. That's what air really is.

It is NOT a continuous fluid, even though that coincidentally happens to be a pretty good approximation for a lot of problems.

I want to know what really happens if you consider air molecules to be billiard balls.

 

[negitron]

That was the whole point of my question, but you don't seem to have taken the time to really understand what I was asking.

Yes, he did. He understood it perfectly and answered it correctly.

 

[Borek]

That was the whole point of my question, but you don't seem to have taken the time to really understand what I was asking.

Quite the opposite - I have pointed to a mistake in your understanding of the situation. There is no sharp border of the pocket, but the pocket exists. Given enough time, air will mix and the pocket will disappear, but this process is relatively slow. Slow enough that the pocket has time to rise.

 

[russ_watters]

You are considering air to be a continuous fluid, but it's not. It's a bunch of molecules flying around randomly and bouncing into each other.

What happens when a bunch of warm molecules are bouncing around near the ground and a bunch of cooler ones are bouncing around above them? How do they mix evenly? The warmer molecules near the boundary can just about mix on a one-to-one basis, but the path length of the moving molecules is very small - fractions of a milimeter (bolded, because this is the critical flaw in your understanding). So there can't be much rapid mixing beyond a few centimeters. At the same time, the layer of warm air could be 100m high.

So, once again, there's no such thing as a "pocket" of hot air. There are no two different kinds of air, hot and cold, that would have to mix somehow. The hot molecules don't have any reason to stick together, each of them just flies ahead through free space until it hits some other molecule.

That was the whole point of my question, but you don't seem to have taken the time to really understand what I was asking.

I'm sorry, but you're just plain arguing against reality here. You are the one who doesn't understand that your current understanding (and thus the direction of your question) is simply wrong. We know the way we are explaining it is correct because you can actually see this warm air when it condenses into clouds or fly around in it in a sailplane, using it without seeing it. We (the scientific community) know for certain (as certain as scientist can be) that this is a reality.

 

[russ_watters]

Guys, forget about density for a minute. Just think of little billiard balls flying around and bouncing into each other. That's what air really is.

It is NOT a continuous fluid, even though that coincidentally happens to be a pretty good approximation for a lot of problems.

I want to know what really happens if you consider air molecules to be billiard balls.

Air molecules are a lot of billiards balls and if you have an area where they are moving quickly next to an area where they are moving slowly, the quick moving ones will crash into the slow moving ones and over time they will equalize their energy. But, as I started the explanation, there are a lot of billiards balls and the regions of high and low energy billards balls are much larger than the region in which they interface.

 

[turbo]

Guys, forget about density for a minute. Just think of little billiard balls flying around and bouncing into each other. That's what air really is.

It is NOT a continuous fluid, even though that coincidentally happens to be a pretty good approximation for a lot of problems.

I want to know what really happens if you consider air molecules to be billiard balls.

You have been given some pretty concise replies, and even a simple example of the dynamics involved. Gas molecules that form air are not little billiard balls acting in a vacuum. The molecules act collectively, and that collective behavior can be devastating. Ever hear of a hurricane, typhoon, tornado?

 

[russ_watters]

Also, look into the concept of diffusion:

Molecular diffusion, often called simply diffusion, is a net transport of molecules from a region of higher concentration to one of lower concentration by random molecular motion. The result of diffusion is a gradual mixing of material.[emphasis added]

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

The word "gradual" means it takes some time. How much time? Well it turns out that the rate of diffusion depends on the starting conditions, but the size of the masses of air are not part of those conditions. Ie, the boundary will diffuse at a certain rate (in cm per minute or some similar metric) if the two volumes are 1 cubic meter or 1 cubic kilometer.

 

[negitron]

the path length of the moving molecules is very small - fractions of a milimeter

A very, very, very small fraction. The mean free path of an air molecule at STP is less than 70 nm; that's 1/10th the wavelength of a photon at the far red end of the spectrum.

 

[michelcolman]

We know the way we are explaining it is correct because you can actually see this warm air when it condenses into clouds or fly around in it in a sailplane, using it without seeing it.

You can also "see" lenticular clouds over mountain tops while in reality air is moving at high speeds THROUGH those clouds and vapor happens to be condensing and evaporating again at the same location, giving the appearance of a stationary cloud. Appearances can be deceptive.

Another example, wind is not a pocket of air moving in a particular direction, but an average speed component that has been added to the (much higher!) average speed of the molecules, giving the appearance of a single volume of air moving one way. All of the molecules are zigzagging about at very high speeds in all directions and only have a slight extra tendency towards the direction of the wind.

As I stated in my original question, I do know that sailplanes use rising air to stay airborne (I am a pilot myself) but I want an explanation that does NOT use the approximation that air is a continuous fluid that sticks together.

I mean, I am correct in stating that air is a bunch of molecules bouncing around, right? I even learned how to derive the ideal gas law from this model.

If you look at the big picture, a whole lot of molecules with an area of faster molecules in some area, why do they all want to go up?

You are all drawing an imaginary balloon around the area, and then of course that balloon would go up thanks to the laws of boyancy, but there's no balloon!

It's probably not even the same molecules that stay "hot", the momentum is just transferred to others. Like many of you said, there are a LOT of collisions going on. Maybe the molecules at the top tend to be more likely to transfer energy to the colder molecules higher up while receiving the same amount of energy from below, while the bottom molecules are more likely to lose energy? The sailplane wouldn't notice any difference, it would just be receiving the same extra upward momentum as the air molecules in the vicinity.

 

[negitron]

You've been given the answer, over and over again, by people who, unlike you, know what they're talking about. Why do you steadfastly refuse to listen?

 

[michelcolman]

Also, look into the concept of diffusion: http://en.wikipedia.org/wiki/Molecular_diffusion

The word "gradual" means it takes some time. How much time? Well it turns out that the rate of diffusion depends on the starting conditions, but the size of the masses of air are not part of those conditions. Ie, the boundary will diffuse at a certain rate (in cm per minute or some similar metric) if the two volumes are 1 cubic meter or 1 cubic kilometer.

I do understand this bit. You can consider a boundary around the hot area, which only changes very slowly, but I can't see why that would make the whole pocket go up. The laws of boyancy are very logical when you are talking about an object, for example a ping pong ball with a higher pressure underneath and a lower pressure above. But this mass of hot molecules isn't an object, it's just an imaginary boundary drawn around a bunch of molecules that happen to be a bit faster. Even if the pocket has less density, that will be compensated by the higher momentum so it should not be pushed up so easily by cold air. This is not one single object, but a whole collection of independent objects!

 

[negitron]

This is not one single object, but a whole collection of independent objects!

This is only true at extremely small scales; in a single cubic millimeter of air at ambient pressure and average temperature there are ~3 x 10¹⁶ molecules. That's a huge number in a volume that would fit in here: o. It's nonsensical to consider the behavior of macroscopic quantities of gas in terms of individual particles. Air masses of different temperatures, densitites, compositions or what have you behave as pockets or bubbles, and can be modeled as such, and the boundary between them while diffusive acts as a physical barrier or wall between them, and behaves as such.

 

[michelcolman]

You've been given the answer, over and over again, by people who, unlike you, know what they're talking about. Why do you steadfastly refuse to listen?

Look, there are unfortunately quite a lot of subjects where LOTS of experts claim to know the answer, and only a few actually do:

- How an airplane wing works (I got some very good answers on this forum, but about 99% of flight schools (experts, even including one of my professors who also teaches astrophysics) just say the air above the wing speeds up to get to the trailing edge at the same time, and this makes the pressure drop due to Bernoulli, which is completely and utterly wrong (as admitted later by that same professor)).
- Why a shower curtain is pulled inwards (again, lots of "experts" say this is because the water speeds up the air, and Bernoulli's law then says the pressure must go down, which is completely wrong since Bernoulli only works if no energy is added). There too, I got a few excellent responses on this forum.

I've seen many threads on these physics forums where only after many pages people finally came to the conclusion that a subject was more complicated than they first thought (including the author, but very often including the "experts" as well!).

I'm not claiming to be smarter than everyone else, I'm just asking how to explain this phenomenon without approximating the air as a continuous fluid and all I'm getting is explanations approximating the air as a continuous fluid!

 

[turbo]

But this mass of hot molecules isn't an object, it's just an imaginary boundary drawn around a bunch of molecules that happen to be a bit faster. Even if the pocket has less density, that will be compensated by the higher momentum so it should not be pushed up so easily by cold air. This is not one single object, but a whole collection of independent objects!

The boundary between hotter and colder air is NOT imaginary. It is not as tightly constrained as the skin of a balloon, but it is real. A large mass of hot air in the presence of colder air cannot easily equilibriate heat/energy with the surrounding air mass, so the boundary (though invisible and ever-changing) is real.

 

[michelcolman]

This is only true at extremely small scales; in a single cubic millimeter of air at ambient pressure and average temperature there are ~3 x 10¹⁶ molecules. That's a huge number in a volume that would fit in here: o. It's nonsensical to consider the behavior of macroscopic quantities of gas in terms of individual particles. Air masses of different temperatures, densitites, compositions or what have you behave as pockets or bubbles, and can be modeled as such, and the boundary between them while diffusive acts as a physical barrier or wall between them, and behaves as such.

Finally a helpful answer. I'm not quite there yet, but as far as I understood, you are saying that a statistical distribution of speeds will behave like a single object. So even though these molecules have no real reason to stick together (and the individual molecules probably don't), the area containing high speed molecules statistically behaves as if it was a single object.

(most people were just saying that it IS a single object and one even categorically stated that air cannot be compared to billiard balls, which caused the frustration on my part)

It still doesn't make complete sense to me, but at least it gives me something to think about...

 

[michelcolman]

See: https://www.physicsforums.com/showthread.php?t=32331

Unlike this thread, the qoted thread does contain quite a few attempts at explaining the phenomenon on the molecular scale. Some of them seem to be saying that hot molecules can fly up higher in the field of gravity, which is quite certainly an oversimplification as well since they only fly a few nanometers before hitting some other molecule. But at least it's closer to the point of view I was looking for, which is not using macroscopic approximations.

 

[turbo]

Unlike this thread, the qoted thread does contain quite a few attempts at explaining the phenomenon on the molecular scale. Some of them seem to be saying that hot molecules can fly up higher in the field of gravity, which is quite certainly an oversimplification as well since they only fly a few nanometers before hitting some other molecule. But at least it's closer to the point of view I was looking for, which is not using macroscopic approximations.

I hope that some high-school and junior high-school students might benefit from reading this thread, and that is the ONLY reason that I am adding this. NOBODY has made the statement in bold. People have patiently tried to disabuse you of this notion, to no avail. The molecules in masses of air exhibit group behaviors and the air in any location can experience updrafts, downdrafts, laminar flow, etc that result in our weather, based in large part to the density (temperature-related) of the air masses that make up the atmosphere. The notion that any individual molecule that has higher-than average energy has to go UP is a very flawed idea.

 

[michelcolman]

What happens when a bunch of warm molecules are bouncing around near the ground and a bunch of cooler ones are bouncing around above them? How do they mix evenly? The warmer molecules near the boundary can just about mix on a one-to-one basis, but the path length of the moving molecules is very small - fractions of a milimeter (bolded, because this is the critical flaw in your understanding). So there can't be much rapid mixing beyond a few centimeters. At the same time, the layer of warm air could be 100m high.

Why would a molecule in the middle of the pocket go up faster than the boundary can move? After all, any momentum transmitted to that center molecule would ALSO have to travel, colision by collision, trough the pocket, right?

I can't see why all the molecules would all together start moving up more quickly than the boundary can move. How can the information "let's all go up" travel faster than the "I'm slow and my neighbour is fast" boundary?

Once again, I'm not saying it doesn't, I just want to understand WHY the fluid approximation is correct. Just like you can derive the macroscopic ideal gas law from the microscopic movements of molecules, I want to see your macroscopic "pocket" start moving up molecule by molecule.

I know there are lots and lots of molecules doing lots and lots of collisions and for most practical purposes the macroscopic explanation works very well, but just saying "there's too many molecules to count so you just can't look at it that way" is not a very satisfying answer.

 

[michelcolman]

NOBODY has made the statement in bold. People have patiently tried to disabuse you of this notion, to no avail. The molecules in masses of air exhibit group behaviors and the air in any location can experience updrafts, downdrafts, laminar flow, etc that result in our weather. The notion that any individual molecule that has higher-than average energy has to go UP is a very flawed idea.

NOBODY?!
How about JohnDubYa on June 25-04, 05:24 PM?

I was talking about posts in the quoted thread. And I did say that this explanation was probably an oversimplification because the molecule would transfer its energy at the first collision which is already after a few nanometers.

Look, I will explain once again: I KNOW the molecules exhibit group behaviors. I just want to know WHY a bunch of billiard balls acts as if it's a single object. Because it quite obviously isn't a single physical object. I know you can model it that way, but I don't understand (NOT: I don't accept, I think it doesn't, etc...) why the model works. I want to see the little billiard balls acting in unison.

The "pocket" is the statistical volume containing the hot molecules. Am I correct in stating (guessing) that the "pocket" will be containing different molecules once it is higher up, so basically the motion of the pocket is the motion of a statistical distribution of speeds rather than a physical object?

If the answer is yes, I'm sure that will be a surprise to a few of the posters that were telling me off earlier.

 

[mikelepore]

Here's a guess about something happening at the molecular level. Does this make any sense?

Due to the warmer air having expanded, it has some air below it that has a greater number of molecules per unit volume. Therefore, when molecular collisions happens, the molecules of the warm air are more likely to get hit by other molecules that have a bit more more upward component of average velocity, not just hit by molecules with random x,y,z components of velocity. Statistically, the warm air molecules are getting knocked upward a little bit more frequently than they are getting knocked downward.

(Or did I make a circular statement, assuming the very result that I was trying to develop? I'm not sure.)

I expect that the answer has nothing to do with any boundary. I think it must have to do with each warm air molecule getting tapped downward 1000 times while it gets tapped upward 1,001 times, for a net upward effect.

 

[sir_manning]

Think about icecubes in water. An icecube's average molecular speed is lower than the surrounding fluid. A pocket of hot air's average molecular speed is higher than the surrounding fluid. Yet, they both float/rise due to their smaller density.

Furthermore, the boundary of an icecube might not be well-defined either as it melts inside the water - but it can be treated as one object.

 

[michelcolman]

Think about icecubes in water. An icecube's average molecular speed is lower than the surrounding fluid. A pocket of hot air's average molecular speed is higher than the surrounding fluid. Yet, they both float/rise due to their smaller density.

Furthermore, the boundary of an icecube might not be well-defined either as it melts inside the water - but it can be treated as one object.

If you push a molecule of the ice cube on one side, the force is nearly instantaneously transmitted through the whole ice cube. That doesn't happen in a gas, and that's why I don't understand how this whole pocket of molecules can still move together.

 

[negitron]

If you push a molecule of the ice cube on one side, the force is nearly instantaneously transmitted through the whole ice cube. That doesn't happen in a gas...

You sure about that?

 

[Cyrus]

If you push a molecule of the ice cube on one side, the force is nearly instantaneously transmitted through the whole ice cube. That doesn't happen in a gas, and that's why I don't understand how this whole pocket of molecules can still move together.

There is this lovely word called diffusion rate.

 

[michelcolman]

Here's a guess about something happening at the molecular level. Does this make any sense?

Due to the warmer air having expanded, it has some air below it that has a greater number of molecules per unit volume. Therefore, when molecular collisions happens, the molecules of the warm air are more likely to get hit by other molecules that have a bit more more upward component of average velocity, not just hit by molecules with random x,y,z components of velocity. Statistically, the warm air molecules are getting knocked upward a little bit more frequently than they are getting knocked downward.

(Or did I make a circular statement, assuming the very result that I was trying to develop? I'm not sure.)

I expect that the answer has nothing to do with any boundary. I think it must have to do with each warm air molecule getting tapped downward 1000 times while it gets tapped upward 1,001 times, for a net upward effect.

This is the kind of answer I was looking for!

I am not quite sure if it is correct, but I really appreciate the fact that finally somebody understood what my question was.

It is certainly probable that the cold air underneath has something to do with it, since I have been told about the macroscopic behavior of bubbles of hot air sticking to the surface and then suddenly letting go. They probably only let go when cold air manages to get underneath part of the bubble.

However, even though there are more cold molecules per unit volume, they also have less energy. If the density is 1% higher but the average momentum per molecule is 1% lower, the cold air won't really be transferring more energy to the hot air.

Wait a minute... you haven't used gravity yet...

All molecules are getting the same downward momentum change from gravity (assuming identical molecules, which is of course wrong, I know). If temperature is equal, this downward momentum is compensated by pressure from below (ultimately the surface of the earth). Now replace the cold molecules on top by hot ones that are spaced further apart. Without gravity, the total momentum on both sides of the imaginary boundary is still the same. Cold molecules are spaced more densely, but also have less momentum. Only the hot molecules are now getting less total momentum from the Earth's gravity (same momentum per molecule, times less molecules), while the pressure from below is the same. This finally tips the scale so the hot molecules rise, the pressure below decreases, and fresh air from the sides comes in.

I know I'm basically repeating the macroscopic laws here, but it's now making sense on a small scale too! And that was all I was looking for.