Thermodynamics – Why Hot Air Rises and Cold Air Presses Down

gasthermodynamics

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.

Best Answer

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.