Sublimation of Ice at Atmospheric Pressure

[rude man]

Homework Statement

How can ice sublimate at atmospheric pressure? Looking at the p-T diagram for water, the sublimation curve does not extend above a tiny fraction of atmospheric (triple point of water, p = 4.58mm Hg). Yet my ice box tells a different story.

Homework Equations

p-T diagram for water, available at your local friendly hydrology book store (?).

The Attempt at a Solution

I have no clue.

 

[dynamicsolo]

At any temperature above 0 K, there will always be a tiny (much tinier, the colder it get) fraction of water molecules at the surface of the ice which can obtain a kinetic energy sufficient to overcome the weak intermolecular bonds with their neighbors and escape the surface. In that sense, the process isn't much different from the evaporation of liquid water at temperatures well below the boiling point (for instance, water at 300 K does have a vapor pressure). The sublimation is really slow, but it is there.

This process is exploited in "frost-free" refrigerators. The escaped molecules from the ice form a (rather thin) vapor, which fans in the refrigerator chamber perioidically vent out of the fridge, thereby removing the frost...

 

[rude man]

dynamicsolo - thanks for your post. But to me, water evaporation below the boiling point is different. There, H2O changes from a liquid to a vapor. In sublimation, the change is directly from solid to vapor. Why doesn't the ice change to water first, as the p_T diagram would indicate? What happened to the heat of fusion?

 

[Fewmet]

Why doesn't the ice change to water first, as the p_T diagram would indicate?

I've always assumed there is melting of traces of ice, followed by its evaporation. Do you evidence that it is instead sublimation?

I suspect some of the melting is from regelation.

 

[dynamicsolo]

dynamicsolo - thanks for your post. But to me, water evaporation below the boiling point is different. There, H2O changes from a liquid to a vapor. In sublimation, the change is directly from solid to vapor. Why doesn't the ice change to water first, as the p_T diagram would indicate? What happened to the heat of fusion?

Why would the water molecules at the surface "know" what the phase of the "bulk object" is? The departure from the surface is a local phenomenon, so it seems escape only depends on the energy available to individual molecules and the strength of the intermolecular bonds in their vicinity. Molecules at the surface don't require the entire block of ice to change phase in order to separate off.

Quantities such as "heat of fusion" are "bulk" measures, based on an average temperature for the object in question. At the microscopic level, though, every single constituent molecule does not have this same average temperature: there is always a distribution of individual energies, with some few molecules close to the amount needed to leave the surface, fewer just at that energy, and still fewer beyond that level. "Leakage" from bulk systems is always taking place; it just becomes exponentially more common as the mean temperature of the system rises.

 

[rude man]

<< When in doubt, draw a picture. >>

Like the p-T diagram? Heh heh.

I remain dubious, although there has to be SOME explanation, and yours is as good as any, if not better.

 

[dynamicsolo]

<< When in doubt, draw a picture. >>

Like the p-T diagram? Heh heh.

I remain dubious, although there has to be SOME explanation, and yours is as good as any, if not better.

Remember that a phase diagram is a characterization of the overall "macroscopic" system, something we observe at "laboratory-scale". The phenomenon you are asking about concerns physical behavior at the "microscopic" (in this case, molecular) scale. Large-scale averages can only give limited insight into what happens locally at small scales (much as, for instance, "classical" (1920s-1960s) cosmology tells us little about the formation of galaxies, much less of stellar systems).

 

[rude man]

Sublimation in my ice-box IS on a laboratory scale. It's a bloody nuisance, in fact. I have to replace the ice frequently!

If what you say is right then tell me where the cutoff point is: at what rate of sublimation is the p-T diagram correct, and when is it not?


EVERYTHING is at 'microscopic' scale since everything comprises molecules, not so?

Fewmet, i did not mean to ignore you. But no, in sublimation there is no going thru the liquid phase. There can't be, since sublimation occurs well below the freezing point.

 

[Fewmet]

Fewmet, i did not mean to ignore you. But no, in sublimation there is no going thru the liquid phase. There can't be, since sublimation occurs well below the freezing point.

I understand that sublimation means the transition from solid to gas without passing through the liquid phase. I was suggesting melting and evaporation in small amounts rather than sublimation.

Let me restate what dynamicsolo expressed: not every water molecule in the ice crystal has an identical vibrational energy. Temperature is based on the average energy. A small number of water molecules in the crystal are moving fast enough to break free of the ice crystals. (On reflection, it seems more likely that this would generate gas than liquid, so it is sublimation rather than the melting and subsequent evaporation I previously suggested.)

The question for me is whether the fraction of molecules able to sublimate is plausibly great enough to generate the level of frost buildup that is seen. I've had a frist fee model for so long I no longer have an intuition for this.

There is also, of course, frost forming from moisture in the air that gets into the freezer whenever you open it. I do recall the build-up of ice being greater in humid weather.

 

[rude man]

Thanks guys for your willingness to help.

I'm peretty sure ice buildup in a freezer is mostly if not wholly due to condensed humidity. Would ice sublimate & then return to ice? I mean, can't it make up its mind what it wants to do? :-)

 

[dynamicsolo]

Sublimation in my ice-box IS on a laboratory scale.

Yes, of course. I am saying that an understanding of the process must include investigation of what is happening on the molecular scale. All sorts of "large-scale" phenomena have properties determined by "microscopic" physics.

If what you say is right then tell me where the cutoff point is: at what rate of sublimation is the p-T diagram correct, and when is it not?

The phase diagram is a product of "classical" thermodynamics; it is the result of investigating the behavior of a "large" (typically milligrams and bigger) system. It is the wrong "tool" for understanding a process like sublimation. The boundary lines between phases are only the result of observations of behavior for a large system. At molecular scales, those lines would "blur out" considerably, because there is a distribution of energies for the molecules, so they are not all behaving in the same way. What looks like a single chip of ice to a human eye is a system consisting mostly of bound water molecules on an irregular surface, surrounded by a vapor layer of molecules, some breaking loose from that surface, some bonding up again, and some few escaping entirely.

The broad answer to your question is that there is no cutoff. Sublimation is always taking place; it is just an extremely slow process at low temperatures and becomes more significant as the ice approaches the phase boundary with vapor.

Another thing to consider is that a line is a phase diagram really tells us nothing more than that the bulk system is in transition. It is "all" (but not quite) one phase on one side of the line and "all" (but not quite) the other phase on the other side. The question of what is happening in the bulk system becomes more difficult to answer when it is very close to that line.
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[dynamicsolo]

The question for me is whether the fraction of molecules able to sublimate is plausibly great enough to generate the level of frost buildup that is seen. I've had a frist fee model for so long I no longer have an intuition for this.

The phenomenon of sublimation is applicable when the system is closed. The fact that you get frost build-up in a refrigerator is because you keep opening the door and letting more water vapor in. You get a process called "diffusion-limited aggregation" where the water molecules accrete onto bits of solid water already formed (or sometimes start new ones), which leads to the delicate "fractal-like" collections of frost.

 

[rude man]

<< Another thing to consider is that a line is a phase diagram really tells us nothing more than that the bulk system is in transition. It is "all" (but not quite) one phase on one side of the line and "all" (but not quite) the other phase on the other side. The question of what is happening in the bulk system becomes more difficult to answer when it is very close to that line. >>


Huh? A phase diagram represents an equilibrium condition of state, not a transition picture. Maybe we're not talking about the same diagram. Mine graphs p on the ordinate and V on the abscissa, and shows the isothermals (flat between all-liquid and all-vapor states of course, etc.).

And the bit about being "very close to that line" ? Sublimation is supposed to stop at < 5 mm Hg whereas my refrigerator is around 760 mm Hg. Pretty big slopover, wouldn't you say?

 

[dynamicsolo]

<< Another thing to consider is that a line is a phase diagram really tells us nothing more than that the bulk system is in transition. It is "all" (but not quite) one phase on one side of the line and "all" (but not quite) the other phase on the other side. The question of what is happening in the bulk system becomes more difficult to answer when it is very close to that line. >>Huh? A phase diagram represents an equilibrium condition of state, not a transition picture. Maybe we're not talking about the same diagram. Mine graphs p on the ordinate and V on the abscissa, and shows the isothermals (flat between all-liquid and all-vapor states of course, etc.).

I am aware of what diagram you are speaking of. According to the phase diagram for water, it should be a "liquid" at one atmosphere and room temperature. Yet, I can leave towels out to dry and the film of water at the bottom of a glass is gone in a matter of hours. I have been saying that a phase diagram tells you little about what is happening at the surface of a substance; it only tells you what the great majority of the substance is like. Away from a phase boundary, little of the material is in other than the phase indicated; very close to a boundary, the material takes on characteristics of both phases. (At the triple point of water, it cannot be said to be solid, liquid, or vapor.)

And the bit about being "very close to that line" ? Sublimation is supposed to stop at < 5 mm Hg whereas my refrigerator is around 760 mm Hg. Pretty big slopover, wouldn't you say?

I have not had enough thermodynamics, but this is relevant here:

http://www.science.uwaterloo.ca/~cchieh/cact/c123/clausius.html

[The fact that mid-19th Century physicists investigated this indicates that they were also bothered by then about this question of evaporation far from a phase boundary...]

This is what is used to calculate vapor pressure. The sublimation (evaporation) curve doesn't say that it "stops" at 5 mm Hg; the vapor pressure of ice reaches (a bit less than) that value at 0º C. This indicates a rate at which surface molecules are escaping, and is greatest then; at lower temperatures, the vapor pressure is lower, so the rate of sublimation is lower. [Sublimation "stops" only in the sense that the bulk of the ice is now changing phase.]

Humidity in the surrounding air matters because it will affect the net rate of sublimation. The ice has a vapor pressure and has water molecules escaping, but the surrounding air has water molecules that can be captured by the ice. So there is presumably a critical level of humidity at various temperatures at one atmosphere at which "net sublimation" stops. A "frost-free" refrigerator avoids this by drawing water vapor out of the chamber to prevent the partial pressure of water vapor from matching the vapor pressure of the frost.

 

[rude man]

<< According to the phase diagram for water, it should be a "liquid" at one atmosphere and room temperature. Yet, I can leave towels out to dry and the film of water at the bottom of a glass is gone in a matter of hours. >>

There is a perfectly good reason for that, and entirely consistent with the p-V chart: V in this case is huge, like off-the-chart in the +V direction, practically infinite in fact; miles to the right of the vapor saturation curve - so OF COURSE the water evaporates. Note that this is the STEADY-STATE i.e. equilibrium situation. It does take time to reach equilibrium, of course.

I will look at your link, then I think this subject should be considered closed.

 

[Borek]

How can ice sublimate at atmospheric pressure? Looking at the p-T diagram for water, the sublimation curve does not extend above a tiny fraction of atmospheric (triple point of water, p = 4.58mm Hg). Yet my ice box tells a different story.

You are comparing apples and oranges. 5 mm Hg is a partial pressure of water vapor, 760 mm Hg is atmospheric pressure, completely unrelated.

 

[dynamicsolo]

There is a perfectly good reason for that, and entirely consistent with the p-V chart: V in this case is huge, like off-the-chart in the +V direction, practically infinite in fact; miles to the right of the vapor saturation curve - so OF COURSE the water evaporates. Note that this is the STEADY-STATE i.e. equilibrium situation. It does take time to reach equilibrium, of course.

For a solid or liquid, V on the phase diagram does not represent the volume of the enclosure. V represent the volume of the substance in question in all its phases.

I will look at your link,...

That would indeed be most gracious of you.

then I think this subject should be considered closed.

OK with me...

 

[rude man]

This finally makes sense. I should have thought of that a long time ago. Thank you!

 

[rude man]

dynamicsolo, I apologize for my lack of tact in the last post. I just didn't feel I was getting anywhere and got frustrated.