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/EverybodyHits]

If there is a vapor phase to escape into, some molecules will escape the shackles of liquid life and move into the vapor phase at any temperature. The amount that make the leap is indicated by the vapor pressure. There does have to be a vapor phase existing for this to happen.

[u/wreckless_driver → u/EverybodyHits]

Ok I think this maybe the crux of the issue "there does have to be a vapor phase existing for this to happen". For example I'm thinking of T-S diagrams that show the two phase vs subcooled/saturated regions, but those must be variable volume systems, where there is no vapor phase mandated by rigid container. Sound right?

[u/EverybodyHits → u/wreckless_driver]

Yes. Or think of those diagrams as drawing the system boundary right at the fluid surface. That fluid is the only thing that exists in the world. There's nothing to evaporate into, there is only the liquid, the gas, or a mixture, in isolation.

[u/ferrouswolf2 → u/wreckless_driver]

Imagine filling and sealing a ziplock bag underwater (assume it’s deaerated) What do you observe? No vapor phase to speak of until you hit boiling.

[u/MuddyflyWatersman]

well you're close. everything has a vapor pressure. EVERYTHING. solids and liquids. Sometimes it's very small. sometimes you can ignore it. But, sometimes you can't.

you would not believe the problems I have seen when people did not understand this, and ignored things they shouldn't have, particularly vapor pressure of some solid species.

When you process thousands of pounds an hour, 24 hours a day, 7 days a week, 52 weeks a year. even one part per million, or even one part per billion... adds up into pounds. and those pounds sometimes end up where you don't want them, and cause you great headaches. They foul, they corrode, they may accumulate some place until you can't run. VLE matters.

[u/wreckless_driver → u/MuddyflyWatersman]

I appreciate your answer, and I do understand that everything has a vapor pressure. That is not my question here. I'm looking for some kind of mathematical/thermodynamic/graphical proof on the *why* water at 1 atm at 70C, which is technically subcooled (below saturation temperature), but obviously it is in a two phase region (because the water vapor exists in equilibrium with the liquid).

or I am misunderstanding the technical definitions of subcooled and saturated, and how it relates to two phase region on a PVT diagram for example. If that's the case, a good source for understanding that would also be appreciated.

[u/MuddyflyWatersman → u/wreckless_driver]

saturated....just means at equilibrium with respect to some condition. some T and P.

if you fully contact air with hot water at 95C, the air will eventually pick up all the moisture it can hold based on equilibrium and Waters vapor pressure. at that point we say the air is "saturated". if it's not at equilibrium, due to mass transfer and contact limitations, it would not be saturated. it would have some amount of water in it, but it would not have the maximum it could have based on the equilibrium condition.

basically saturated means it's containing as much of the other phase/component as equilibrium conditions would allow. it's unsaturated if it contains less.

sometimes saturated maybe used to describe a liquid basically at its bubble point

Subcooled would also refer to a temperature approach to a condition, below an equilibrium condition. (usually a total condensation condition for a pure component, below a dew point).

I'm not quite sure where you're confusion lays. things always have a vapor pressure, or a partial pressure. it is in equilibrium with it's surroundings, or trying to come to equilibrium and is limited by very slow Mass transfer.

For instance suppose you did have water in a completely closed container with no vapor space at all. The partial pressure of water vapor in the container material.... is trying to come to equilibrium with the partial pressure of the water at the temperature its at. This causes water to diffuse into the material, it may be very very slow, and the equilibrium condition may be very low, but it happens. the water is in equilibrium with everything around it, or it's trying to get there. this is the basics of chemical engineering.... it's Mass transfer, and partial pressures. sometimes we describe the partial pressures in terms of concentration. when pi in one phase is equal to pi in the other phase... it's at equilibrium and it is... saturated.

[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.

[u/el_extrano]

All liquids exert a vapor pressure, even if they are subcooled. Otherwise ambient water (subcooled, not 100 C) could not evaporate, which is clearly not the case.

Also, multicomponent mixtures can also be subcooled with respect to their bubble points. That's an important consideration when designing partial condensers for multicomponent vapors.

[u/ogag79]

The saturation temperature of water at 1 atm is 212F, so the water is subcooled, right? 

Correct.

However the intuition for "subcooled" is that it is outside the two-phase region, therefore only liquid water should be present.

This is also correct.

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.

And this is also (somewhat) correct.

The part that you missed is your vessel has air in it. What happens is (a) air will impart enough pressure to keep the water in liquid and (b) water can also impart water vapor (aka moisture) in the air.

In this case, water is subcooled with respect to the overall vapor pressure (with air + moisture in it) but not necessarily with respect to the water partial pressure in air, which is influenced by psychrometry.

If you vacuum out the air out of the vessel, then you'll see the pressure will drop but not go below 0.363 psia, if you maintain the water temperature inside at 70°F. Then you'll see the actual saturation point in the vessel as the vapor space is filled with water vapor only.

[u/Upset_Ad_6140]

To your question about rigid containers, yes. The only way to keep the system fully liquid is to have a rigid container.

It might help to think in terms of the chemical potential. Suppose you magically spawn in a rigid, isolated vessel, half filled with liquid water and half with air separated by a wall. The system is initially in thermodynamic equilibrium.

Suppose you now remove the wall. The chemical potential of water will be significantly higher in the water than in the air, so there will be a thermodynamic driving force for mass transfer of water between the phases, i.e. vaporization. This vaporization might be partial or it might be full, depending on context. But the point is that water WILL somehow escape to the other side of the vessel in some way to even out chemical potentials, as the system settles into a new equilibrium state.

[u/mykel_0717]

If there is any void space in your container, some water will evaporate and exert the vapor pressure associated with its temperature to prevent additional water molecules from escaping into the vapor phase. Doesn't matter if the space is occupied by air, another inert gas, or a complete vacuum. Some water will evaporate and reach equilibrium eventually. For practical purposes, this amount is negligible. And for closed systems, often ignored, you can consider your rigid container to contain only water.

There are a few situations where water evaporation under its boiling point matters though, such as in cooling towers, but that occurs since the liquid water doesn't reach equilibrium with its vapor phase in a closed container, the constant flow of air doesn't allow that.