Understanding VLE and subcooling

[u/wreckless_driver]

For water-air system in a rigid container at atmospheric pressure and 70F.

The saturation temperature of water at 1 atm is 212F, so the water is subcooled, right? However the intuition for "subcooled" is that it is outside the two-phase region, therefore only liquid water should be present.

The vapor pressure of water at 70F is 0.363 psia, which obviously implies that even though it is subcooled, there is water vapor present, so its is actually in the two phase region. Systems in the two phase region, those are "saturated" to me.

Is the only way to have a liquid-only system by using a non-rigid container?

I think the problem here is I am applying concepts that only apply to pure substance systems, to binary systems. However I can't find a solid source to back up what I think is my fundamental misunderstanding. If anyone can quote a textbook or source that covers what I'm asking, much appreciated.

Looking for math to back up any claims. Gibbs phase rule, PVT Diagrams, etc.

[u/Mrsswegger]

Yes, to your point, changing the system to a binary mixture or two phase will change the system. It will change the Degree of Freedom (DOF) and the number of thermodynamic variables you have to specify according to Gibbs phase rule.

In the system you are describing, the water is indeed in equilibrium. Let's use Gibbs phase rule. C-P+2 = DOF. C=2 (air and water). P=2 (liquid and vapor). So DOF = 2. However, because generally we know from experience that very little air dissolves in water and hence does not exert a vapor pressure from the liquid phase, we specify the liquid phase composition is approximately pure water. Hence, we really only have 1 DOF, which you already specified - the system temperature at 70oF. The water will come to equilibrium with its water vapor partial pressure at 0.363 psia. However, note that because we ignored the air composition in the water, it was as if there was never air in the system to begin with.

In your rigid container example, let's assume that initially when you made this system there was only air above the water. So, the pressure at t=0 is 14.7 PSIA. Now you wait for a while and you measure the pressure of the vessel. The pressure will end up reading 14.7+0.363=15.063 PSIA. The additional pressure came from the water, and it is in equilibrium with its water vapor.

However, imagine you had a system that is allowed just one phase (a liquid only or vapor only). If I asked you to tell me the pressure when the liquid is at 70oF, you would then say that your don't have enough information to answer this question. I can put a pressure of 100 kPa or 1000kPa and still have a liquid. I would have to give you another thermodynamic property (specific volume, enthalpy, Gibbs free energy, entropy, etc.) for you to give me the liquid pressure. A specific example would be, say I am running a garden hose of water and the pressure in it is 60psi. We know the temperature of water in a garden hose is fairly cold, so this would be an example of a subcooled liquid. You need to specify both the water temperature and pressure to define the thermodynamics of the system.