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Ok, this looks like a dumb question or even near trolling, but I really don't understand it.

When air is heated over an oven plate, it rises. Obviously, I can check by blowing some smoke in.

The common explanation is that hot air has less density than cold air, and consequently, it rises.

Fair enough, the hot air will end above the cold air, but why is it rising in a column?

With the same argument, I could deduce (and I know that it's wrong) that the cold air above is denser, so it will go down, pressing the hot air away sideways.

What additional fact am I (and the common explanation) missing?

(I'm pretty sure that the tags I found are not optimal.)

Edit: in my mind I envision a picture of (red) hot air molecules separated more than the (blue) cold molecules which slip down between the red ones. I'm aware that this is a very crude model, and moreover ends in a wrong prediction.

Edit (about the duplicate): I'm not sure if the other question is about the way in which the hot air raises. At least, the answers over there do not (or not clearly) address this aspect.

The accepted answer here explains what is going on by stating formulas for pressure above the heat plate as well as next to it.

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Possible duplicate of Does hot air really rise? – honeste_vivere Feb 11 at 12:34
    
@honeste_vivere I don't think so. This question takes as a given that hot air does rise and asks about the pattern in which it moves. – David Z Feb 11 at 13:22
    
@DavidZ - Ah okay... How do I link to that... Oh nice it is already linked. Thanks – honeste_vivere Feb 11 at 13:53
    
@ToddWilcox This would be a variant, I didn't ask about diffusion explicitly (but implicitly with my mind-picture of hot and cold molecules). What I intended to ask was why the convection cell (idea acquired by the answers here) rotates one way and not the other. (Uuups, your comment has gone, will remove this after some time so you have a chance to see it) – Gyro Gearloose Feb 11 at 19:15
    
Cold air does NOT sink. The earth sucks. – Bob Jarvis Feb 11 at 21:27

12 Answers 12

up vote 10 down vote accepted

You ask why a column of hot air (as in a chimney) rises, given that denser cold air is above it, pushing down. It rises, because denser cold air around the BOTTOM of the chimney is under higher pressure than the cold air at the top of the chimney. The extra pressure due to a chimney-height of cold air is pushing it down. The lesser density of hot air means that the chimney-height of hot air causes less pressure than the surrounding cold air.

In formulae, the situation is: outside the chimney,

$$ P_\textrm{(chimney-top)} + \rho_\textrm{(cold-air)}\cdot g \cdot h_\textrm{chimney} = P_\textrm{(cold-chimney-bottom)}$$

for the cold air, and inside the chimney

$$P_\textrm{(chimney-top)} + \rho_\textrm{(hot-air)} \cdot g \cdot h_\textrm{chimney} = P_\textrm{(hot-chimney-bottom)}$$

where '$\rho$' is the density of the air.

$$\rho_\textrm{(cold-air)} \gt \rho_\textrm{(hot-air)}$$

Thus, the cold air at the chimney bottom is higher pressure than the hot, it pushes its way in, and the hot air is displaced (it rises).

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@NauticalMile Why are there no pressure gradients normal to the plate? The column of air adjacent to the plate is lower density. The weight of hot air from above is less (lower density), so the pressure falls as you go towards the floor faster than the cold adjacent air? Or is it just the fact that this answer talks about the cold air above the hot column? That is a direct reference to the OP's question, no? – Yakk Feb 11 at 19:03
    
@Samuel This effect would not occur zero-g or microgravity. – NauticalMile Feb 17 at 1:00

With the same argument, I could deduce (and I know that it's wrong) that the cold air above is denser, so it will go down, pressing the hot air away sideways.

Replace your hot air with a helium balloon. You can see there's no force on the balloon to push it sideways. The buoyancy forces it to accelerate upward (and some cool air around it to accelerate downward). If you don't stop at one, but keep creating balloons (similar to you continuing to heat the air from the pan), then you'll get a trail that forms a column.

The asymmetry in the situation is that you're creating a small amount of heated air in a large amount of cooler air.

If you reversed the situation by placing a block of ice near the ceiling, then you would get a column of cooler air falling through the relatively warmer air.

in my mind I envision a picture of (red) hot air molecules separated more than the (blue) cold molecules which slip down between the red ones.

Molecules in a gas have a distribution of speeds. So the cooler gas has almost as many fast molecules as the warmer one does.

But the problem here is that at such a scale, the size of your heated parcel is huge. A few molecules will do that at the edge (diffusion), but not quickly. The mean free path of an air molecule in your room is less than 100 nanometers, while the size of your heated parcel is probably several centimeters. Most will hit and remain close to their neighbors. It's much faster for the entire parcel to lift, so that process dominates.

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I feel this adds something, but I still can't get it. A balloon has surface tension and will resist deformation or splitting up, thus side-way forces are balanced out. I can't see how this would work on unconnected gas molecules. – Gyro Gearloose Feb 10 at 19:35
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@GyroGearloose: imagine many little balloons then. – whatsisname Feb 10 at 20:53
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If you imagine a surface around your heated parcel, the pressure is the same on both sides except for buoyancy differences. So the only reason for the molecules to infiltrate another parcel is via diffusion. That's a (relatively) slow process, so it can be ignored on short timescales. – BowlOfRed Feb 10 at 21:18
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Check this picture of 1.5 million balloons having been recently released: thevintagenews.com/wp-content/uploads/2015/10/… Notice that they are mostly still in a column becuase wind and other weather effects have not dispersed them. If there's no air current, the hot molecules will just rise straight up together like balloons. Note that this cluster of balloons almost looks like a mushroom cloud, which is formed by a column of rising hot air. – Todd Wilcox Feb 10 at 21:47
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My problem with this answer is that it provides another intuition confirming that the behaviour is true, but didn't give me a obvious sense of why it's true in either case. Not saying it's wrong, just that it's not making anything "click" for me, since my intuition is already that the air will rise in a column. – Paul Feb 11 at 15:07

Welcome to the magic of convection cells =)

The first thing to remember is that you're working with a large number of gas molecules. The effect theoretically occurs no matter how many particles you have, but the effects are much easier to describe using bulk terms that handle many molecules at once, rather than trying to track each molecule. As BowlOfRed mentioned, the free path length in open air is about 100nm, which means almost all effects you see are going to be macroscopic statistical effects, like density and mass transfer.

Consider a volume of hot air above the hot plate. I am going to claim its shape is roughly cylindrical. This is easy to prove early on, when the hot air is all concentrated in a disc shape just above the hot plate. We'll use induction to show that it remains cylindrical as the system evolves.

Now its easy to see that the system is in an energized state. Its ground state would have all of the high energy (low density) particles up high, and all of the low energy (and thus high density) particles down low, because that minimizes the potential energy of the air column. However, we have to figure out how it accomplishes this.

Consider, just for a moment, the radial movement of air. Cold air, trying to work its way down to its lower potentials is willing to displace hot air. Thus the hot air tries to move up, in all directions including outward, and the cold air tries to move down, in all directions including inward. However, we can't have two crossing streams of molecules, because they collide. This collision keeps the inward/outward velocity of most molecules of air very low. But this isn't true everywhere.

Near the bottom, right on the hot plate, there is no hot air clashing with cold air. Once you're down on the surface of the hot plate, there no more hot air trying to go up, but there's still cold air trying to go down. This is where we start to see movement. The cold air sweeps in horizontally, until the pressure equalizes.

Now we can start to see the cycle that forms. Cold air, trying to minimize its potential energy, goes as straight down as gasses ever do, blowing in horizontally along the hot plate. When it does, the slightest of low pressure areas appears above the hot air, as some of the cold air joins this slight breeze around the cylinder.

Remember, the sides of the cylinder don't permit much movement because the radial velocity of the gasses is basically zero. There's only diffusion mixing along that boundary. However, we now have the cold air sneaking in along the hot plate sideways, and the hot air pushing upwards. This is the basis of a convection cell.

To finish the iterative cycle, the hot plate warms some of the cold air that just came in, turning it to hot air. Now we have the same situation we had before, only with two changes:

  • The cylinder is taller now, because the hot air has moved upwards
  • There is now a slight upward current of air in the hot region, and a slight downward current of air in the cold region.

If you repeat the process, the same effect occurs, except now the low pressure area above cylinder is even lower pressure because there's a mass flow of cold air leading away from it.

Eventually material limits do limit the process, but hopefully that explains why the hot air rises straight up. There's a convection cell with a countercurrent of cold air right next to the hot air. Inbetween, the radial velocity is very low, so we see very little mixing. At the bottom, we see cold air moving in sideways, and at the top we see hot air being pulled upwards by lower pressures.

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If you've ever flown a glider, either a radio controlled model glider or a full-size man-carrying glider, then you'd be aware that cold air do in fact fall in a column. Glider pilots call hot air rising "thermals" and cold air falling "sink". Both move in columns, bubbles, sheets etc.

For every "shape" hot air moves in upwards, cold air can also move in the same way downwards. Indeed, as you have noticed, the logic should be applicable to both.

What determines which part of air forms a column is which part is the majority. If a small amount of hot air rises surrounded by cold air then of course that hot air will be a column - simply because of the small amount of air moving up. If the cold air sinks surrounded by hot air then of course that cold air will be a column.

The logic is similar to pouring water. If you pour water out of a bottle into your kitchen sink the water falls in a column. If on the other hand you fill that same bottle submerged in a swimming pool it is air (bubbles) that rise in a column. What determines weather or not water or air becomes a column is which is the majority and which is the minority.

But be aware columns are not the only way hot and cold air can move in.

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The issue with your model is you're only considering the density of the particles rather than their motion. If you heat up a plate, the molecules above it gain thermal energy and begin to move about faster and faster. They bump into each other and the colder particles at the boundary of the column of air above plate.

Since the pressure decreases slightly as you move higher, the path of least resistance for the particles to move is upwards. Through that random motion and the asymmetry in pressure above and below column(below there is a pan, which is a solid and can be modeled by an extremely high pressure gas), they end up forcing their way upwards.

You could also imagine turning a hot plate on its side. At first the molecules would move away from the pan by the same asymmetry and random motion argument. But once they have moved away from the pan a bit, the gas will start to rise.

Summary: Asymmetry in pressure and random motion.

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I'm not sure yet, but your answer looks like it pins down what I was missing: the hot molecules are spaced at greater distance, overcompensate this by moving faster. Still, I would like to see a formula about this. – Gyro Gearloose Feb 10 at 20:24

There are two things at work here - gravity, and gas pressure. In the beginning, due to gravity, denser air is at bottom and lighter air is at the top. You may ask why it is this way to begin with and the answer is in the word "denser". At every level, there is an equilibrium density in the beginning and it is higher at the bottom and lower at the top. When some air near bottom is heated, it does not push up, all it does, is expands in all directions due to its increased temperature (and so increased pressure). Due to expansion, its density goes lower. And due to this lowering of density, the density equilibrium is disturbed. Then gravity brings back the density equilibrium by pulling dense air down more than it pulls the hot air. So hot air only expands, gravity does the rest.

Now you may ask why gravity pulls denser air more than the lighter air. Because denser air has more mass per volume and so more gravitational force per unit of volume. (GMm/(r*r)).

Therefore in actuality, even though it is dense air that is pushing down (due to gravity), the hot, less dense air has no where to go except up, and so it appears it is pushing up but it really does not (or we can say it pushes in all directions, not only up, due to its increased pressure). The cold air moves down only from sides, it can not move down from directly above because of increased pressure of hot air..

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This only explain why hot air rises, not why hot air plunes are thinner than the downward cold air. It can well be reversed if there is cooking at the top. – Vladimir F Feb 11 at 9:23
    
Read " the hot, less dense air has no where to go except up". That "upward only" freedom causes the thinner plunes. I am not sure if the questioner really cares about this though. – kpv Feb 11 at 9:53
    
Actually, you are right, the question is more basic than how I interpretted it at first. – Vladimir F Feb 11 at 9:55
    
Also, "The cold air moves down only from sides" leaving a narrow path for the hot air to rise up. – kpv Feb 11 at 10:01

A more thorough explanation involves the energy of the atoms/molecules in air rather than the density.

What happens is a combination of the two following phenomena:

1) When you heat the air above the plate, the atoms in the air get energised depending on the temperature. This additional energy is manifest as the velocity of the air atoms. In doing so, they tend to move about which creates a depression in the pressure over the plate since all the atoms tend to fly away.

2) This drop in pressure brings in cold air which replaces the hot air over the plate. So you see, this is not about the density fundamentally but rather the energy and the drop in pressure which brings in cold air.

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Honestly, I don't understand. Why would this make the difference between the cold air getting in sideways (as experiment shows) instead of from above? Are there some formulas I can apply? (This would at least split the problem into 1) applying the formulas and 2) explaining/proving the formulas.) – Gyro Gearloose Feb 10 at 19:02
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This is because everything in nature loves to be energetically stable i.e. have zero energy. When the atom of air is energised, its energy jumps by +E. Now, it wants to get rid of this energy as soon as possible and therefore tries to do work against gravity by rising up instead of flowing horizontally. In doing so, its energy reduces until it reaches the mean temperature. Interestingly, this is why in a low-gravity environment, the flame differs to what it is like in a normal gravity scenario like on Earth. ( goo.gl/MPBqut ) – Eh-whaaa Feb 10 at 19:18
    
That's easily answered: in a no or low gravity environment, there's no or less energy difference if the high density air is above or below the low density air. – Gyro Gearloose Feb 10 at 19:23

You say 'why does it rise in a column'. My answer would be - why wouldn't it? (at least initially). There is no sideways force acting. As already stated, over short timescales the drift of the individual molecules (which is much slower than the molecules speeds themselves) can be ignored, and you can treat the gas as small packets. You heat a packet and its pressure increases (molecules have higher speeds). It now tries to expand, as it has more pressure than surrounding gas - it wants to get to a lower density to reach pressure equilibrium with its surroundings. It pushes out in all directions to try, but it is easier to push upwards than downwards so it begins to acquire an upward velocity.

What I think is much more interesting is what happens next...

As the packet rises it will expand. It will either hit an obstruction (e.g. the ceiling) or find a new equilibrium. Eventually of course it will cool (I am still ignoring diffusion here). But what goes up, must come down, so the gas which is rising is matched by an equal mass of falling gas. When you start to think about how exactly you would have flows rising and falling you realise that there is no 'neat' or smooth way to do it. Instead the flows will become chaotic and turbulent; tiny variations in flow across the room will trigger all sorts of exciting instabilities and a constantly changing pattern of convection. This is a hydrodynamics problem which will have no analytic solution, but would probably make cool videos!

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Just my 2 cents: nobody seems to have mentioned Archimedes principle so far.

That is basically what happens here. Hot air expands in a bubble of lesser density, that gets an upward lift equal to the weight of displaced cold air.

Of course the hot air is not contained inside an enclosed volume (like it would in a baloon), but the temperature equalization by mixing of cold and hot air is a comparatively slow process that happens only in a relatively thin boundary layer.

Rising and dilution are competing phenomena, though. Pour some oil from the bottom of a water glass and it will soon float up. Replace oil with alcohol and it will be diluted before having a chance to reach the top.

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In any case you do have warm air going up and cold air going down. It depends on the situation. Imagine a chimney, warm air goes up the chimney, cold air goes down on the outside of the chimney. If the cold air tried to push the warm air down the chimney, this would push less denser air down, which wouldn't work. So it's the horizontal asymmetry which allows warm air to go up one way and cold air to go down another way.

Now, imagine an very large heated plate. In a situation where the air starts out completely still, warm air doesn't go up (as long as the temperature doesn't get too high), It stays because there is no asymmetry. Only when there is a disturbance or too high a temperature difference, will convection start. In which case, once again, warm air goes up in one place and cold air comes down in another place.

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The thing you are missing is gravity.

You are right: Hot air is less dense than cold air. Trying to stick to a visual explaination: Imagine a small volume element (a cube) of the hot air. The gravitational force acting upon it is $F = gm = gV \rho_{\textrm{warm}} < gV \rho_{\textrm{cold}}$, since $\rho_\textrm{warm} < \rho_\textrm{cold}$. The surrounding cold air is pulled downwards stronger than the warm air - so the warm air rises and is replaced by cold air.

Basically, it is buoyancy.

Also, there is no such effect in space. Maybe you have seen a similar effect in some educational movie clips, where oil and water are mixed in space: They also do not separate into two layers as they would on earth.

So, the answer is: You were missing gravity that imposes a preferred direction upon your system under investigation.

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Sorry, your answer explains perfectly that the hot air ends above (in a less gravity area), but does not explain the way it get's there. – Gyro Gearloose Feb 10 at 19:52
    
In my answer, I assumed that the standard acceleration due to gravity $g$ is constant everywhere. Hence, there is no "less gravity area" in my explaination. The example with space was only given as a motivation that when there was no gravity, no separation between the hot and the cold air would occur. – M529 Feb 10 at 19:58
    
Yes, I see, I used the wrong term. Given the gravitational gradient, it is energetically favorable for the hot part of the gas to be away from the gravitational center. Still it won't explain the way it get's there. Ignoring other effects, you could even hypothesize that the molecules stay in place (with rspect to each other) and only the heat energy moves upwards (nonsense, I know)). – Gyro Gearloose Feb 10 at 20:03
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Ah, OK, you are really focussed towards this molecular aspect. Indeed, then my answer is not sufficient. I am curious what people will answer, since kinetic gas theory is not my strength and I assume this question must be answered by a statistical physics approach. – M529 Feb 10 at 20:17

Hot air doesn't rise because it is hot, and cool air doesn't fall because it is cool. Hot air rises because it is pushed upward by cooler air, and that is because the bulk air has a pressure gradient, and that is due to gravity. The air below any object pushes upward more than the air above pushes down. If the object's weight is less than the net upward force then it will rise.

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Hello, and welcome to Stack Exchange. This doesn't really answer the question; perhaps some clarifying statements would help. – Daniel Griscom Feb 10 at 22:42

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