Water Sublimate Rate

Lots here:The sublimation of ice in vacuum - SpringerLink Sublimation points of substances in vacuum [Archive] - The ...

Rate of sublimation of ice at low pressures - SpringerLink

Sublimation rates of ice in a cryo-ultramicrotome.

Thanks Lyn for the links.

It looks like I may be onto something, but sadly the math is above my head.

This is again for one of my High Altitude balloon experiments.

I would assume that Sublimation rates not only are determined by the pressure and temp, and the % of water vapor it is Sublimating into, but I would assume the surface area of the water also? Yes? No?

Normal "Boiling" wouldn't matter, so would this?

OK other numbers I have found is the VOL/VOL of water solid/liquid to gas is 1700 to 1, IE: 1 cuft of water makes 1700 cuft of gas. Also True?

Anyway as before we are trying to extend our balloon flights. And learned that water vapor is actually lighter than "AIR" It actually has the lifting power of 60% that of Helium.

Where we are is too cold for the typical low pressure boiling.

So Lyn, or anyone reading this can anyone please try to get a rough Idea of with the original posting conditions, how many cuft of water vapor would be produced in "X"amount of time?

Anyone Please?

When water turns to steam it expands 1,700 times. I see no reason that this would not also be in the ball park for sublimation. The slight volume change when the water froze probably isn't worth bothering with.

So 1 cu. in. of ice would yield 1,700 cu. in. of water vapor.

If we stay true to form, as a forum, there will be many differing opinions contrary to this and a large circuitous discussion will follow, leaving you, once again, not sure what the real answer is. Goes with the territory.

Care to try to make an estimate of how many cuft is generated at "X" amount of time?

And if it makes any difference while it is at that low pressure, and temp, it is also sublimating into Hydrogen.

Would this be taking place at that factory 10km above sea level, then?

Say 1 Pound of frozen water, or whatever weight unit you wish to use.

Assuming sea level air pressure is, 14.695949 PSI

We lower the temperature of the atmosphere around the ice to -40C

And we lower the pressure to 0.5 psi (roughly 75,000 feet)

The air around the ice is pure dry no water vapor in it at all. It's container, (probably a 2 litre soda bottle) will be vented via a tube to the balloon, that is filled with Hydrogen.

assuming this enviroment, at what rate would the ice Sublime to water vapor?

And how many cuft or cubic meters of water vapor would it produce for "X" amount of time?

Thanks

First, 14.695949 psi is a ridiculous number of significant digits for atmospheric pressure. 14.70 is more precision than ordinary instruments can repeatably measure; a value of 14.696 would require very high precision instruments.

Second, sublimation (as you presumably already know) is the process of converting solid water (ice) into water vapor, without passing through the liquid stage. To convert any solid into a vapor requires the addition of energy (heat), regardless of the pressure. Where does this energy come from? No one can say at what rate the ice will sublimate unless they know from where does the energy of sublimation come, and through which barriers (including the material of the soda bottle) must that energy pass on its way from the source to the destination (the ice). If there is no source of heat, then only enough molecules of ice will evaporate to bring the temperature of the remaining ice down to ambient (-40°C), then it will stop sublimating.

Lyn has already given you the volume answer, but that is assuming there is a source of heat to sublimate the ice.

Sorry,

What you are saying is not what other web sites have been saying.

I know to cause something to vaporize it requires energy.

but then explain why water that is warm enough to remain liquid, when pressure is reduced why does it turn to vapor?

where did it get it's energy gain?

if anything there is a energy loss of the water, the water looses energy.

http://youtu.be/pOYgdQp4euc

From classroom experience I know this answer to be correct. The temp of the ice will continue to drop and the sublimation rate drops with it. Our experiments are done at 50milliTorr in a classroom setting. At your temps and pressure it would take even longer.

When a substance evaporates or sublimates, the fast molecules leave, lowering the temperature of what is left. So how fast this happens depends on how fast heat from the surroundings can seep in to replace the energy of the fast molecules that left. The amount of substance evaporated or sublimated, of course, depends on the heat of evaporation or sublimation. Heat transfer is a function of the temperature differential, surface area, and thermal resistance between the substance and the environment. The temperature differential depends on how well you remove the vapor from the vacinity. The surface area can be increased by aerosolizing the substance.

36K "What"?

Volume increase. My 1,700 figure is at roughly atmospheric pressure.

So it is 35K to 1 VOL/VOL? at 0.5psi?

1 cm3 of ice would produce 35K cm3 of vapor at 0.5 psi?

GA! Good point, although since NSS is talking about the atmosphere. it might be logical to use the ISA of 15°C, or 288K, and -40°C is 233K.

In that case the factor would be ≈ 1700 * (14.7/0.5) * (233/288) = 40.4k.

Yes, NSS, that means one volume of ice will sublimate to roughly 40 thousand volumes of water vapor at 0.5 psi and -40°C.

Me too. GA to the thinker.

All I can say to that is,,,, WOW!

As far as expansion ratios go, the rule is that 1 mole of any substance as a vapour occupies 22.4 litres at NTP (14.7psi, 273K). By my calculation 1 cu in of water will sublime to 1500 cu in at NTP and to 37661 cu in at -40C (233K) and 0.5psi. The sublimation process will take a jolly long time, though, since it is caused by movement of molecules from the surface, and that is not going to happen much at those temperatures.

Note! As we can see from (6) increased moisture content will reduce the density of the moist air - Dry air is more dense than moist air.
From:

water vapor is lighter than dry air.

it has about 60% the lifting capacity of helium.

Recommended: a course in combined heat and mass transfer as part of a degree course in Chemical Engineering.

The 1700 to 1 volume change is a rough rule of thumb at 1 atm absolute pressure and 212 F (100 C) temperature. For the temperature and pressure of the question, the best and quite easy way is to check the Steam Tables, like the classic book of Keenan & Keyes.

The sublimation rate depends on the heat input to the ice and is affected somewhat by its exposed area; the heat being the dominating factor. It takes a lot of heat to convert ice to vapor; the Steam Tables have the enthalpies of both states (solid and vapor) the enthalpy change from one state to the other and the specific volume of water vapor (inverse of its density). Very simple aritmethic is required to solve the problem.

If no heat is added, there is no sublimation.

The problem is well known by airplane manufacturers and pilots; there is a dangerous tendency to form ice on the leading edge of wings and propellers, which may down the plane even at 33000 feet and -60F. The planes have ice elimination systems to avoid this.

From what I have found so far that this is not the case. That there is always sublimation,yes it indeed will vary with temp, but with water, that there always is some. And even at -40C that is heat. It is warmer than -60C or 0K

Snow and ice sublime, although more slowly, below the melting point temperature.^[1] This allows a wet cloth to be hung outdoors in freezing weather and retrieved later in a dry state. In freeze-drying, the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum.

-40C is a temperature that can be observed at high altitude (Himalayas, Denali, Andes)or even closer to sea level in Antarctica. Sublimation will happen (visibly) when the sun is shining, so even when the thermometer shows a low temperature, snow is disappearing when photons hit the surface!

Snow (or ice) will always have a finite partial pressure of water vapor, so if the air around it is "dry" (has zero water vapor pressure), the equations (not shown here) will show a rate of sublimation. If the environment is a closed container, you'll end up with a lump of ice in equilibrium with water vapor at the 100% saturation partial pressure. The key is PARTIAL PRESSURE of water vapor, not the total pressure of the atmosphere! In summary, the variables you need to consider are: partial pressure of water vapor, presence of light shining on the surface and its spectrum, and the velocity of wind in your application/environment.

Hello Mark,

This is the ituation

Assuming sea level air pressure is, 14.695949 PSI

We lower the temperature of the atmosphere around the ice to -40C

And we lower the pressure to 0.5 psi (roughly 75,000 feet)

The air around the ice is pure dry no water vapor in it at all. It's container, (probably a 2 litre soda bottle) will be vented via a tube to the balloon, that is filled with Hydrogen.

assuming this enviroment, at what rate would the ice Sublime to water vapor?

And how many cuft or cubic meters of water vapor would it produce for "X" amount of time?

Thanks

Welcome to CR4!

Of course you are correct on the partial pressure of water vapor...

You have introduced a source of energy (sunlight) to assist sublimation. Another factor that MUST be considered to find the rate of sublimation.

Even without the closed container, energy of some form MUST be added to continue sublimation once the temperature of the remaining ice has dropped to the appropriate level.

Beyond the discussion of entropy and sublimation fundamentals , the vapor capacity of a fixed volume of gas decreases as the temperature decreases and so assuming you have 100% RH at one temperature, you will quickly have vapor cloud (coalesced water droplets) and then ice crystal (snow) formation at lower temperatures in order to remain at 100% RH. Obviously the temperature is dropping at higher altitudes.

Although novel, I would question the ability to create additional buoyancy by adding water vapor to a gas at below freezing temperatures.

You have also not stated if the volume is increasing (what gas pressure is).

NSS specifically stated that the initial RH was zero, and he's only adding one pound of water vapor to an unspecified (presumably large) volume of hydrogen, so I doubt if he will experience any precipitation.

I too assume that he is hoping to create additional buoyancy, and question (without having done any major calculations) the efficacy of the process.

To NSS: Again, I have not done any major calculations, but you must remember that adding, for example, 1.0 m^3 of water vapor at 0.5 psi to 10.0 m^3 of hydrogen at 0.5 psi does NOT produce 11.0 m^3 of mixture at 0.5 psi, but some smaller volume. (any experts - correct me if I'm mistaken). I'm assuming the gas bag is not fully inflated, so the gas pressure inside the bag is virtually the same as the local atmospheric pressure.

Density altitude.

I think this is what your referring to:-

http://en.wikipedia.org/wiki/Partial_pressure

I haven't got time to try to understand it now.

Yep, and ditto!

The goal as stated was to add vapor to gas. Given that has been achieved, reducing the temperature from a given condition results in higher RH until saturation is reached. Beyond that condition, condensation forms and will in fact ultimately turn into rain given enough time. The saturation point reduces by 2x for every 10C drop in temp.

A thunder head is a very good demonstration of this phenomena. Warm moist (less dense) air rises until it is cooled to the point of snow hail and rain.

Considered and ideal gas, 1LB of water is roughly 22L/g*450g/#= a really big volume. Maybe 1# of ice is a little too much?

The assumption here is that whatever vapor is in the gas, it will condense out (in some form) and no longer be effective in achieving the buoyancy goal if the temperature will decrease. Theoretically a very well insulated gas bag might work.

On topic of sublimation, ice has a vapor pressure and will no longer sublime at 100% RH.