Why Hot Air Rises and Cold Air Sinks: Understanding Air Density

[member 529879]

Why does hot less dense air rise and cold more dense air sink? Also, why is hot air less dense than cold air?

 

[Lok]

Hi, Scheuerf.
Hot air is more energetic, thus the air molecules are faster moving and collide more often than in a cold air situation. So for the same volume and number of molecules, a higher temperature would give a higher pressure (pressure is somewhat number of collisions*impulse/time/surface).
In the case of a given volume with two halves of different temperature yet the same number of molecules, this would result in two regions with two pressures, which would tend to go to a more balanced state. So the hot air has higher pressure, and pushes the cold air into a smaller volume than the starting half. Now you get differing densities as the hot air will occupy a bigger volume and the cold air less. And with differing densities, Archimedes law tells us that the less dense a will float above the denser air as the gravitational potential energy of the denser air is higher, which means hot on top of cold is energetically more favorable than vice-verso.

 

[Chestermiller]

According to the ideal gas law, the density of a gas is given by:
$$ρ=\frac{PM}{RT}$$
where M is the molecular weight, R is the universal gas constant, P is the pressure, and T is the temperature. For constant pressure, the density of the gas decreases with temperature.

Regarding hot air rising and cold are sinking, imagine that there is a parcel of hot air immersed in an ocean of cold air. If the hot air were encased in a balloon, then you would say that the buoyant force exerted by the cold air on the balloon would cause the balloon to rise (because the hot air inside the balloon is less dense). Basically, the same thing would happen even if a balloon were not encasing the hot air.

Chet

 

[member 529879]

But if you had a region of less dense air surrounded by more dense air, why wouldn't the less dense air be filled with air from the more dense area?

 

[Chestermiller]

But if you had a region of less dense air surrounded by more dense air, why wouldn't the less dense air be filled with air from the more dense area?

If the system is not at hydrostatic equilibrium, there are also viscous forces involved, and these need to be taken into account in the momentum balance. With natural convection like this, the pressures are close to being equal, but not quite. The small difference in density results in small differences in vertical pressure gradients between the hot and cold regions, and this gives rise to the buoyant forces. When you get into natural convective heat transfer, all these factors will be taken into account in determining the flow and the heat transfer. For such a detailed analysis, see Bird, Stewart, and Lightfoot, Transport Phenomena.

Chet

 

[rootone]

Attempt at simple answer:
Denser stuff is 'heavier', it gets more pull from gravity.
'Lighter' stuff gets less pull, so it floats 'up' above 'heavier ' stuff.

 

[Lok]

But if you had a region of less dense air surrounded by more dense air, why wouldn't the less dense air be filled with air from the more dense area?

As Chestermiller said ... yet in my wording.
If you have a region of less dense air and one denser, with NO temperature difference, the dense air will flow (a.k.a. "wind") into the less dense region and the two will fall in a pressure balance. There will be some thermal heating from the flow and pressure balancing but let's assume they can be ignored for small density differences.
If the less dense region is hotter than the dense region and the system is in equilibrium, then it will be able to keep it's density until the temperatures mix.
A third situation is a given volume (chamber) of uniform gas in a gravitational potential, which leads to a pressure gradient, which in it's turn leads to a temperature gradient in the vertical direction. To visualise this one, let's just set the gravity so strong that only the most energetic molecules have a chance to reach the top of the chamber. So at any given time the molecules found in the top portion will be more energetic than the ones in the bottom part, and of course their density will be different.