Saturation Vapor Pressure

I watched a lecture that was explaining Saturation Vapor Pressure of water. I understand that saturation occurs when the amount of water evaporating off the surface of a water source is exactly equal to the amount of water that is condensing out of the air above (one molecule goes from liquid to vapor while another molecule goes from vapor to liquid).

Along with this, the concept of Partial Pressure is also needed in order to understand what’s happening.

Partial Pressure is the portion of the atmospheric pressure that is attributed to a given substance in the air.

Atmospheric pressure is the simple addition of all the Partial Pressures being created by all of the atmosphere’s contents. Therefore, since 78% of the atmosphere is Nitrogen, 78% of atmospheric pressure is due to the pressure being created by Nitrogen. If all the Nitrogen magically disappeared instantly, the atmospheric pressure would drop by 78%.

So far, everything matches my intuition.

But then, the professor said that the Partial Pressure of water alone determines when saturation occurs, and that “it actually doesn’t matter whether there is air above the liquid water or not because Saturation Vapor pressure is a property of the water, not of the air.

“It’s a mistake to to say things like, the air is saturated. That’s not quite right, because it’s the water vapor we’re talking about.

“Now, it’s interesting that that water is mixed into the air, but the air is not really controlling this. This is the property of water alone.

“You’d have the same Partial Pressure of water vapor above a liquid at a certain temperature whether there was air there or not.

“Of course, if there was air there, the total pressure would be higher, but the Partial Pressure of water vapor would be the same value.”

It sounds like to me that the professor is saying that the evaporation of water doesn’t care about all the other things that are exerting pressure on it, that somehow the evaporating water is only being affected by the pressure in the air that’s being created by other water molecules.

What is the physics behind this? I don’t understand that if evaporation is affected by pressure, then why would only certain pressures count rather than all the pressures that are present?
 

Jeff Duda

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Boy...this sounds a bit controversial in the sense that I was never taught that...at least, not to my recollection. Are you sure you're paraphrasing correctly? Precision in wording is pretty important here.

There is likely some underlying true statements in here that are being mixed or confused with others. I am fairly certain that evaporation of liquid water into overlying gas can be controlled by the pressure of the gas. That's what happens in the cores of nuclear reactors...the liquid water reaches temperatures well above the boiling point because the air in the chamber is under much higher pressures than that of the regular atmosphere, which restricts evaporation to some degree.

Take a molecular viewpoint of the situation. Evaporation occurs when a water molecule attains sufficient energy to escape the bonds that it has to other molecules in the liquid state. Without a nucleation point (which I think requires a separate medium for impure water, and maybe for pure water as well), water molecules embedded within a liquid substance will not evaporate and escape the liquid; rather, it's the molecules along the edge of the liquid water that are prone to escape and evaporate. Well, if there is any actual external medium surrounding the liquid (without loss of generality, let's just say we are referring to Earthly atmospheric air), then the kinetic energy of those molecules give them some ability to restrict the motion of the escaping water molecules into the gas. The higher the pressure of that gas, the more KE those air molecules have, and therefore the more prone they are to restrict movement of escaping water molecules.

So your second and third statements:
“Now, it’s interesting that that water is mixed into the air, but the air is not really controlling this. This is the property of water alone.

“You’d have the same Partial Pressure of water vapor above a liquid at a certain temperature whether there was air there or not.
seem to contradict this argument. So either my explanation is wrong or those statements are wrong. Again, I'm not 100% sure of either, but I have my doubts about the quoted statements.

I hope someone else can comment on this.
 
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Jeff Duda

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Okay, so I listened to that segment, and I believe the context is pretty important in settling the issue. The instructor is referring to a closed container, so fixed volume. The real atmosphere does not behave like a closed container (because it has no top).

I can't totally square away every single statement that was made. It is possible there is a gap somewhere in my understanding of the issue. For example, when he talks about saturation vapor pressure being the same at a given temperature whether there is air or not, either one of the two following statements must apply:
1) The x-axis "temperature" must be of the water and not of the overlying air. But that goes against the Clausius-Clapeyron equation unless I'm missing something.
2) "Air or not" either implies i) some other gas aside from the N/O mix typical of Earthly atmospheric air or ii) a vacuum. But temperature becomes undefined in a vacuum (the temperature of a substance is a measure of the average kinetic energy of the molecules that make up that substance; if there are no molecules then there is no temperature), which takes the entire conversation off into Wonderland.

Again, I don't really know how to square this. My understanding has always been that saturation vapor pressure is a function of the temperature of the air into which the water is evaporating. Perhaps I need to check out my Wallace and Hobbs intro book again.

From a standpoint of synoptic scale meteorology, none of this nuance is important to distinguish. You will be successful no matter which method of understanding you use.
 
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Jeff Duda

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Okay. I see why I'm confused now. I looked through the Wallace and Hobbs textbook Atmospheric Science: An Introductory Survey, which is a classic textbook used in introductory meteorology courses. See the attached screenshots for pretty much the exact same statements made in the tutorial video.

I see that the textbook is making an underlying and unvoiced assumption that T represents BOTH the temperature of the water AND the temperature of the air. It is never really explained why this is, unless the assumption is that all states are in equilibrium at all times. But in the real world, air temperature and water temperature are rarely in equilibrium with each other at any given moment. I'm sure there is some degree of conductive heat exchange between the lowest few mm of the atmosphere and the uppermost few mm of the water substance, so that may be the only location at which this statement is actually valid. The rest of moisture flux is then a matter of the ability of air currents to transport the vapor near the water surface to higher levels of the atmosphere. But any true equilibrium between air and liquid water must necessarily be constrained to that very small layer where the two bodies meet. And meteorologists don't really consider this interface when analyzing sensible weather. It's more of a physics/thermodynamics issue than a meteorological issue.

IMO, the macroscopic vantage point I offered before is still valid. When RH = 100%, the vapor pressure is equal to that of the saturation vapor pressure of the air, which is a function of the temperature of the air, not of the water (but again, with this prickly little underlying assumption that the vapor gas has the same temperature as the other constituents of the atmosphere in that location, which makes every bit of sense when you consider it, but you never explicitly consider).
 

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Jeff,

I think I’m understanding your thoughts on this.

It does make sense in your number one above that there may be an assumption that the temperature of the water and the air are the same. But, even with that assumption, I’m not grasping how the pressure of the other molecules in the atmosphere doesn’t have an effect on the evaporation.

Even if we are only considering where the surface of the water comes into direct contact with the air, the problem still seems to be same. There’s still molecules of air present at that scale that it seems we’re being told are irrelevant.

In your number two, I also thought that maybe when the professor said, “air or not”, that he may have been saying that you could replace all the molecules of Oxygen, Nitrogen, etc. with water vapor molecules. But, he seems to clarify that he doesn’t mean that when he says, “Of course, if there was air there, the total pressure would be higher, but the Partial Pressure of the water vapor would be the same value.”
 
The professor in the video replied to an email I sent, and he’s given me permission to post it here:


Your question is whether a background gas such as air alters the saturation water vapor pressure. To a good approximation, the answer is no.

Consider an inverted bucket over a liquid water surface. After some time, the rate of evaporation of water into the bucket will balance the rate of water vapor molecules condensing on the water surface and a state of equilibrium is reached. The pressure of water vapor in the bucket is then the saturation value. For example, if T=0C Psat = 6.1 hPa. If air is added to the inverted bucket, the total pressure will rise of course (gas pressures are additive), but the partial pressure of water vapor will not change. This is because the air molecules, while they frequently collide with the water molecules, do not happen to do so at the same time that water molecules are interacting with each other. It is only water molecules interacting with each other that determines Psat.

Be careful, because the background of air in our atmosphere influences water vapor in other ways such as holding heat, and transporting heat and water. The air temperature will be quickly transmitted to the water molecules and that temperature controls Psat.

A good book on atmospheric thermodynamics or cloud physics could be consulted for more insight. For example: Bohren, C.F. & B. Albrecht (1998). Atmospheric Thermodynamics. Oxford University Press. ISBN 978-0-19-509904-1. Some wiki pages are good too.

I am glad you are enjoying the course.
Prof. Ron Smith



Below are my comments that were not part of the email exchange and haven’t been evaluated by Dr. Smith.
I think I’m understanding better what’s happening. It makes sense that water vapor molecules in the system would sometimes collide with liquid molecules that are on the surface of the liquid “body of water”. Some of those collisions would result in the water vapor molecule giving away some of its energy to the liquid molecule. Thus, that loss of energy could result in that vapor molecule becoming cool enough to condense and become part of the liquid body of water.

At the same time, there would be other places on the surface where a liquid water molecule would be getting enough energy to evaporate and break away from the body of water.

There would be a point where the ratio of evaporating molecules to condensing molecules would be 1:1. At that point, it would look to us on the large scale that nothing much is happening. Any measurement we take of the moisture in the air would show that the value is remaining constant.

I think that it’s making sense that with or without the air present, the same number of water vapor molecules would still need to be hitting the surface of the body of water in order to replace the liquid molecules that are evaporating from somewhere else on the surface.

And, I think this next statement is accurate, but someone please correct me if I’m wrong: my understanding is that the collisions of molecules are random and which molecules gain energy in a collision vs. which molecules lose energy is completely determined by the nature of the collisions (head on, glancing, etc.) and how much energy each molecule had at the time of the collision.

Temperature is the average kinetic energy of all the molecules, but the “temperature” of individual molecules varies widely. Some molecules in the system could have a kinetic energy that would be described as 20 degrees Celsius, some 40 degrees, some 60 degrees. There’s enough moving and bumping going on that the individual molecules are constantly changing their individual kinetic energy.

When one molecule gets lucky enough to put together a run of collisions in which it’s the net winner of the energy, it can achieve 100 degrees Celsius and it escapes as water vapor. If some time later, it randomly collides with the surface, and happens to lose enough energy in that collision, its kinetic energy could be reduced by enough to put its individual temperature below 100 degrees Celsius, and then it would rejoin the other liquid molecules.