# Why does hot air really go up?

In a macroscopic context, where you talk about air pressures, densities, volumes convection is pretty easy to understand; air heats up, it expands, is less dense than its surroundings and hence rises.
But the question is how does this work at the molecular level?
Hot molecules weigh the same as cold molecules hence why does a hot molecule rise?

cheers

You will not find an explanation in terms of individual molecules because
there is not one.

rcgldr
Homework Helper
Warm air is not being "pushed up". It rises because masses of warm air are more buoyant because it is less dense.
If "pushed up" means an upwards force, than it's a correct explanation. From wiki:

Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object

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

For the surrounding gas or liquid the pressure at any point (ignoring dynamic pressure effects related to net velocity) is equal to static pressure + density x gravity x height, where gravity is a negative number.

In the case of warm air, the pressure component related to height is less because of the lower density, but the surrounding air will compress the warmer air's static pressure component with height.

The thing to note is that the static pressure component isn't directional, but the gravitaional pressure component is directional, it decreases with height. For the surrrounding air, the downwards force of gravity is equally opposed by the upwards pressure differenital force and that air doesn't move. However in the case of the warmer, lower density air, the downwards force from gravity is exceeded by the upwards pressure differential force, and that volume of air is "pushed upwards" by the imbalance in the forces.

At the molecular level, in the surrounding air, the pressure decreases with height, but the movement of the molecules remains random so there is no net movement. In the volume of lower density hotter air, the movment of the molecules is less random there is a net upwards component of velocity. The cold air directly under a thermal bubble is moving upwards along with the bubble, and cold air surrounding the bubble is moving downwards to fill in what would otherwise be void created by the upwards movement of the lower density bubble.

There's some initial state where a thermal is released and accelerates, but quickly reaches some relatively low vertical velocity. I don't know what causes thermal inversions or how thermal layers get trapped near the ground and get released as bubbles.

The erratic movement of each molecule due to the fluids inner energy is not a matter here. THe point is that as a consequence of this movement a "hotter molecule" takes up more space than a cooler.

That said, speaking in terms of "billiard balls", where each ball represents one molecule, the hotter molecules are balls of the same mass, yet a larger diameter than the cooler ones.

Why would the bigger balls be pushed upwards? Good question, given that every molecule is exerted the same graviational force on, and honestly I can't explain with my limited knowledge of inter-molecular correlation. It has something to do with pressure (force/area) at last - that's all that I can certainly state. I could only try to give a vivid illustration, but I think, judging from your OP it will 1.) not really satisfy you 2.) be something you can probably think of yourself.

You will not find an explanation in terms of individual molecules because there is not one.
I gave one earlier in this thread.

I really don't see your problem. Molecules do behave, to a great degree of accuracy, like perfectly elastic billiard balls. You can derive the ideal gas law from the average velocities and masses of the individual molecules in exactly this way. There is absolutely no reason whatsoever why it would be impossible to describe the rise of hot air in the same way too.

Macroscopic explantations (buoyancy, etc...) are very useful and simple, but they will always remain an approximation. They work because statistical distributions of molecules do, for most intents and purposes, behave like continuous fluids (even though no such thing actually exists in reality). It is obviously much easier to just pretend air is a continuous medium rather than consider quadrillions of tiny molecules bouncing around at well over the speed of sound.

But that does NOT mean it is impossible to do. It is not as easy as it first looks, and you will need to use some statistical averaging, but is is possible! It has to be, after all, air IS a bunch of molecules and NOT a continuous medium.

There's some initial state where a thermal is released and accelerates, but quickly reaches some relatively low vertical velocity. I don't know what causes thermal inversions or how thermal layers get trapped near the ground and get released as bubbles.
In order for hot air to rise, it has to be surrounded (horizontally) by cold air. The cold air forms a pressure gradient, which is horizontally transmitted to the hot air so it takes the same gradient. For cold air, this pressure gradient is exactly what's required to keep the cold air in place (otherwise it would rise or descend, changing the pressure gradient). For the hot air, which is less dense, the pressure gradient exceeds the weight of the hot air, so it is pushed up by the differential pressure.

Thermal layers and inversions can remain trapped for a long time if they are not horizontally connected to surrounding cold air. For example, a large area of land that is heated simultaneously, an area surrounded by higher terrain, etc... In this case they simply create their own pressure gradient which is exactly adapted to their weight.

From a molecular point of view:
- pressure is simply the net effect of billions of collisions of molecules.
- a volume of hot air with the same density as cold air will naturally have more pressure since every molecule carries a lot more momentum, and the collisions will be more frequent too.
- hot air expands because fast molecules tend to push the slow ones away. The situation stabilises when the density of the hot air has decreased enough to make the pressure equal (less molecules times more momentum per molecule makes the same pressure). Since any molecule on the boundary now gets the same total amount of push momentum from both sides, it will not tend to go anywhere on average. Individual molecules will still move about randomly, of course, but there will no longer be a general tendency for expansion.
- The vertical pressure gradient means each cold air molecule is getting slightly more collisions (or slightly more energetic ones) from below than from above which, on average, is just enough to support its weight. Obviously individual molecules are still moving in all directions randomly, but there is no general tendency for all the cold air molecules to start moving in any particular direction.
- The hot air molecules, too, are getting slightly more pushes from below than from above. Only, the same amount of total momentum (all the collisions from below vs. above) is distributed over a smaller number of hot molecules due to the lower density. On average, the hot molecules get more than their fair share of momentum from below, more than what would be required to support their weight, so they start moving up. Once again, individual molecules may very well go in opposite directions, you just add a small upward vector to the random vectors of the individual molecules, so that on average they tend to move up.
- The random motions of the molecules are very fast (a bit more than the speed of sound) but they don't go very far between collisions, only a few nanometers at a time before dashing off in another direction again. Therefore, this random brownian motion does not tend to take individual molecules very far. That's why the small upward tendency turns out to be very noticeable and does move pretty much the entire volume of hot air up as if it was one physical object (even though it isn't really). In fact this is precisely why macroscopic approximations work so well.

Obviously, once the upward motion starts, there will be a pressure reduction below the bubble and an increase above, which will stabilise the speed of the bubble.

That said, speaking in terms of "billiard balls", where each ball represents one molecule, the hotter molecules are balls of the same mass, yet a larger diameter than the cooler ones.
That is not correct. This may be a useful way of looking at solids (vibrating molecules approximated by larger balls) but for gasses, all that changes is the velocity of the molecules. They are all the same size. Hot air expands because if you put a volume of hot air next to a volume of cold air at the same density, the hot (fast, energetic) molecules will push the cold ones away until the pressure reaches an equilibrium with the hot air less dense than the cold air (less molecules times more speed makes the same pressure).

This notion is WRONG. Warm air is not being "pushed up". It rises because masses of warm air are more buoyant because it is less dense. Do you have some alternative physics in which an envelope of hydrogen gas is being "pushed up"? Please don't mislead young people who might come here to learn.
And how do you explain buouancy then? O, are you one of those people that thinks objects become lighter because of buoyancy? I'm afraid I'm going to have to disappoint you, the objects keep the same weight, they are pushed up by the differential pressure, a higher pressure below and a lower pressure above.. For example in water, the higher pressure below the object is just enough to support a similar volume of water (otherwise the water itself would not be stable). If the object is lighter than that, the pressure differential will exceed its weight and... guess what... it will be PUSHED UP.

Please don't mislead young people by suggesting buoyancy makes things lighter. They are pushed up by the different pressures above and below.

Of course when we start talking about gasses, at a microscopic level, we are no longer talking about large objects but rather about statistical distributions of speeds over quadrillions of molecules. But it turns out there's still a lot of pushing going on, just a lot of small pushes instead of one big one. The end result is coincidentally very similar.

As I stated in a previous post ,the geometry and structure of the surroundings have a large effect on the net movement of the air.Consider an imaginary, gravitational free environment where there is a source of heat and where the surrounding are so positioned that their effects are negligible.The heat will spread from that source, by the mechanisms outlined above, but the spread will be multidirectional.If the same source is now close to the earths surface the downward spread is restricted by the solid/liquid parts of the earth (and any other obstacles that may be around).The earth will heat up as a result and if some of this heat is transferred back to the atmosphere the net movement will be upwards, any downward flow heating up the deeper layers of the earth.If the same heat source is taken to a higher altitude there will be less restriction on the downward flow.A fuller analysis will bring gravity and other factors into account.

There are some really nice pics of what a candle looks like burning in Zero-G at

A microgravity flame forms a sphere surrounding the wick. Diffusion feeds the flame with oxygen and allows carbon dioxide to move away from the point of combustion, so the rate of burning is slowed. The flame of a candle burned in microgravity is an almost invisible blue color (video cameras on Mir could not detect the blue color). Experiments on Skylab and Mir indicate the temperature of the flame is too low for the yellow color seen on Earth.

Smoke and soot production is different for candles and other forms of fire in space or zero gravity compared to candles on earth. Unless air flow is available, the slower gas exchange from diffusion can produce a soot-free flame. However, when burning stops at the tip of the flame, soot production begins. Soot and smoke production depends on the fuel flow rate.

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Firstly classic thermodynamics, hot air expands which takes up a greater volume. The given mass for that volume is less than the surrounding air hence it rises.

At the molecular level this makes no sense why a hot molecule which weighs the same as a cold molecule should rise.

Anyway my theory is you can't consider it as single molecules because the millions of random collisions the individual hot molecules are coupled with all those molecules around them so rather acting as individuals they are really acting as a macroscopic entity and do have as an entity less mass and hence rises.
(its probably something really subtle like the rings and spaces of saturn, I wonder if you could simulate it, the hot air that is not the rings)

Cleonis
Gold Member
Warm air is not being "pushed up". It rises because masses of warm air are more buoyant because it is less dense. Do you have some alternative physics in which an envelope of hydrogen gas is being "pushed up"?

In earlier replies to you Jeff Reid and michelcolman have pointed out the physics of buoyancy:
- https://www.physicsforums.com/showpost.php?p=2332228&postcount=103
- https://www.physicsforums.com/showpost.php?p=2332327&postcount=108

Obviously I concur with them, and for good measure I give my version here.

For buoyancy effects the atmosphere behaves like a fluid, so I will use the example of buoyancy in the case of a fluid. If you submerge a cube of ice it will move to the surface again, rising up above the surface until the point of neutral buoyancy is reached. Let's say the ice-cube 1 meter on each side; a volume of 1 cubic meter, and that initially it is pushed down to a depth of 2 meters. The top of the cube is supporting a watercolumn of 1 meter high, the waterlevel below the cube is supporting a watercolumn of 2 meters. Hence the force exerted on the bottom of the ice-cube is stronger than the force that is exerted on the top of the ice-cube. the net upwards force that the ice-cube is subject to is the amount of force that is required for neutral buoyancy of a cubic meter of water. The ice-cube is less dense than the surrounding water so it does not have enough weight to keep the water below it from pushing it up.

Cleonis

Let me start with quote devoted to all pseudo-scientists that are unwilling to break out of their textbook scope and who do not understand the initial question:
"A man cannot learn what he thinks he has already learned"

Obviously gravity is the key factor as without gravity air would just equilibrate temperature.
In an environment of some density all molecules will collide after some mean path. As faster molecules spent less time for this path, they aquire less of the gravitational drag downwards while travelling the same path. Therefore they are able to reach higher elevations "before falling back".
Maybe that can explain it.

I hope Michel can update us with his own thoughts.

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.[/Gravity makes any fluid medium have more pressure at the bottom layers. This pressure is greater at the bottom of the balloon than on top as you can easily calculate. If the mass within the bubble is less than the force this pressure difference generates, the balloon rises. It is the same effect which underlies Archemdes principle.]

A.T.