Why does warm air hold more water vapour than cold air?

[Askance]

My SO asked a science-based question that I couldn’t come up with an answer for, which frankly surprised the hell out of me! Not that I’m any science genius but I consider myself a fairly well-informed layman. Just goes to show you never know as much as you think you do, and that anyone can ask a smart question.

The question is in the title … a bit of Googling shows a bunch of contradictory and fairly silly theories, including that there is more space between the air molecules to fit the water in.

I did find one sensible site that tries to offer an explanation but it seems to lose clarify in trying to be brief. At core it’s saying that the air doesn’t “hold” water vapour at all.

Sure, a cloud may form as the temperature drops, but not because some mystical holding capacity of the air has decreased.

<snip>

The air (mainly nitrogen and oxygen) no more has a holding capacity for water vapor, than, say, water vapor has for nitrogen. The atmosphere is a mixture of gases. While saturation (which involves bonds between different molecules) is a real phenomenon in liquids it does not describe the interaction of atmospheric constituents.

So, what is going on?
Water molecules are constantly coursing back and forth between phases (another word for the three states: vapor, liquid, and solid). If more molecules are leaving a liquid surface than arriving, there is a net evaporation; if more arrive than leave, a net condensation. It is these relative flows of molecules which determine whether a cloud forms or evaporates, not some imaginary holding capacity that nitrogen or oxygen have for water vapor.

<snip>

And therein lies the origin of the myth. The temperature of a cloud droplet or ice crystal will be (nearly) the same as that of the air, so people imagine that somehow the air was to blame. But, if the (other gases of the) air were removed, leaving everything else the same, condensation and evaporation would proceed as before (the air was irrelevant to the behaviour)

I think what it’s trying to say is that it’s not the air or air temperature per se that matter but the temperature of the water itself (whether vapour or not). That is, liquid water which is above freezing point will always evaporate (ie move from the liquid state to the gaseous state) at some rate. This obviously happens faster the closer it gets to 100c, and at some stage this happens faster than the opposite (condensation) occurs. So a volume of air gets warmer for whatever reason and the water in that same volume (whether existing as liquid on the ground or suspended in the air) starts to evaporate into the air at the same time because it too is getting warmer (possibly by radiation, conduction, or convection from that same volume of air, but also possibly from other sources like the ground nearby or sunlight, ie not specifically because the air it’s in or next to is warming).

When the air containing that vapour cools, it’s not that the air itself loses capacity to hold water, it’s that the water vapour which is a component (or perhaps co-habitant) of the air also cools, and thus more water vapour transitions to the liquid state than the other way around.

So clouds are liquid water that has condensed out of the water vapour in the air - not because the N[sub]2[/sub], O[sub]2[/sub] etc can hold less water, but because the water that is co-existing in that air is also cooling, and so is condensing from vapour to liquid state faster than vice versa. When that happens enough the liquid water drops are too heavy to remain suspended and fall as rain.

At core, I think he’s saying that the source of any heat that causes water to evaporate is irrelevant, all that matters are the competing rates of evaporation and condensation, which are driven by the temperature of the water itself, regardless of source.

So: do I have that right?

[Staggerlee]

Sounds fine to me; it’s not the air temperature per se, but the (related) water temperature, with lower temperature/energy giving it a greater tendency to precipitate, rather than hang around.

[Machine_Elf]

You’ve got a pretty good understanding. All of the phenomenon we observe with water vapor in the atmosphere can also be observed in a rigid, sealed container with nothing in it but liquid water and water vapor (no air or other substances).

Substances have a property called vapor pressure. This is the pressure at which the substance can exist as either a vapor or a liquid. That pressure varies with temperature. For water, the vapor pressure at 70F is pretty low, about 0.36 psi. So in a rigid, sealed container with some liquid water and no air, held at 70F, liquid water will evaporate until enough vapor is generated to raise the container’s pressure to 0.36 psi. In 70F atmospheric air that is at 100% relative humidity (on the verge of forming fog/clouds), the partial pressure of the water vapor is 0.36 psi. The mass of water vapor per cubic foot of this air will be the same as it is inside that rigid, sealed container.

Now raise the temperature of that rigid, sealed container. The vapor pressure of water increases with temperature, so the pressure inside the container will increase, and so will the density of the water vapor; you’ll end up with more water vapor per cubic foot. Raise the temperature all the way to 212F, and the vapor pressure of water at this temperature is 14.7 psi. If these numbers sound familiar, they are: 14.7 psi is atmospheric pressure at sea level, and 212F is the temp at which water boils at sea level. Inside that rigid sealed container, the pressure is now 14.7 psi, and you’ve got a good mass of water vapor, quite a bit more than you did at 70F. In open air at sea level, you can’t heat a pot of liquid water past 212 degrees; it’ll just keep making a bigger and bigger cloud of water vapor, holding the temperature of the liquid at 212F. But the sealed container? Go ahead, keep on heating it; you’ll get higher and higher pressures inside that maintain the vapor phase in equilibrium with the liquid phase. That’s pretty much what happens inside a pressure cooker: the higher pressure allows you to achieve higher cooking temperatures without boiling away the liquid water.

So yes, the temperature of the air isn’t exactly the issue, since air isn’t really involved in what’s going on. It’s the temperature of the water that matters, although the water temperature is coupled extremely closely to the air temperature.