Closed container cooled down...

[MDJH]

Let's say you had a container from which matter could not enter or leave, but energy could enter or leave easily by conduction. This container is filled with warm, humid (but not saturated) air and then its temperature is lowered to far below the dewpoint without being opened.

 

Would the drop in temperature cause condensation, or would the drop in pressure prevent it? Which factor would outweight the other, if either?

[timo]

I am not sure if air is a great example for a liquid<->gas phase transition so I'll just assume you have water vapor in your container. In that case, you'd expect a phase transition under cooling down.

 

In statistical physics, the background field of thermodynamics, one considers the set of all possible particle configurations (positions) and weights them according to the Boltzmann factor. The lower-energetic liquid-like configurations get a higher weight than the vapor weights but the higher total number of vapor-like configurations can cause the system to still be vaporous. As you decrease the temperature, the relative numbers of configurations stay the same. But the weights are shifted towards the lower-energetic liquid states, eventually causing an overall favor of the system being liquid. Pressure is irrelevant for this calculation. (Of course you might in principle just skip the liquid phase and jump towards the crystal directly).

[cypress]

Let's say you had a container from which matter could not enter or leave, but energy could enter or leave easily by conduction. This container is filled with warm, humid (but not saturated) air and then its temperature is lowered to far below the dewpoint without being opened.

 

Would the drop in temperature cause condensation, or would the drop in pressure prevent it? Which factor would outweight the other, if either?

 

The drop would cause condensation. You can confirm this by looking at the partial pressures of the various constituents of humid air. In general,one would have to have very low starting pressures (less than 1*10^-9 atm) in order to prevent condensation until near absolute zero.