I saw something quite fascinating yesterday. I pulled a cooler out of the freezer where it had been for too long (Irene put it in the day before and forgot about it). I vaguely noted that despite its arctic sojourn, it was still liquid. I opened it up and took a swig... and got a mouthful of frozen mush. I look at it in surprise. The top 1/4 or so of the bottle was frozen. I thought that was funny 'cuz it seemed to me that when I pulled it out I had checked and it was all liquid. But, I decided I must have been wrong. Except Bela was watching too, and said something about the bottle being at its critical point. That made me take another look. As we watched, the bottle I held continued to solidify, moving slowly from top to bottom, fast enough to be able to observe the advance. Within the span of a minute it was a solid chunk. Intriguing. I've never seen supercooling in action before. Time for some experiments.
David and Richard Attenborough are brothers.
Just because I'm pedantic: The near-frozen stuff wasn't near its critical point (the temperature and pressure where the liquid-gas phase transition ends). From the description, it sounds like it was at a temperature below its freezing point at one atmosphere, but kept liquid because it was at high pressure. I think this is what everyone was saying anyway; it's just that it's not called the critical point :') . The pressure might have been maintained by carbon dioxide coming out of solution or the small expansion of water near its freezing point. Or something else I'm not thinking of.
Just because I'm pedantic: The near-frozen stuff wasn't near its critical point (the temperature and pressure where the liquid-gas phase transition ends).
I know. Note that I was quoting someone else :)
From the description, it sounds like it was at a temperature below its freezing point at one atmosphere, but kept liquid because it was at high pressure. I think this is what everyone was saying anyway; it's just that it's not called the critical point :') . The pressure might have been maintained by carbon dioxide coming out of solution or the small expansion of water near its freezing point. Or something else I'm not thinking of.
It was supercooled, not a terribly exotic phenomemon, just one I hadn't previously seen in action. Supercooling occurs when a liquid is brought below its freezing point without crystallization occurring. Crystallization doesn't intrinsically occur when a liquid is brought below its freezing point, though in general it's difficult to prevent it because the process is so easily triggered. The one extra requirement of the process we observed (transition of the entire body of the liquid into solid) is that the liquid must be far enough below its freezing point that the heat of crystallization does not bring it above its freezing point (and for most liquids, including water, that heat is fairly large, so the liquid actually has to be well below its freezing point).
I'm surprised that it was possible to supercool it. On top of that it was in the freezer door, which was probably opened or closed a few times. My guess is that when the cap was removed, the CO2 bubbles created by the pressure drop provided a heap o' nucleation sites, and its time as supercooled liquid was up.
I've tried to reproduce it a couple of times, and even got a similar cooler to not-freeze, but then wasn't able to trigger it to freeze. Might need to be colder than I got it.
Water's heat of fusion is 80 kcal/kg. Its heat capacity is ~1 kcal/(kg*K). In order for the (initially liquid) water to absorb the heat of fusion and still remain below freezing (which it must have if the cooler turned into a solid block), it would have had to have had an initial temperature of -80 Celsius (-112 Fahrenheit). The cooler's freezing point was probably lower than 0 Celsius, since it was a sugar/alcohol/etc. solution, and the required initial temperature would have been correspondingly lower.
This is a pretty low temperature for a freezer to produce, but then again, this is the Armory, so maybe they do have a freezer that can solidify carbon dioxide. I would have expected John to get frostbite from grabbing the bottle in that case, however :') .
I am even more convinced now that it was the overpressure from CO2 leaving solution and maybe the expansion of water near freezing that kept the cooler liquid until the cap came off.
I'm wondering where the heat of fusion went in _my_ pet scenario. I still doubt the idea that it was supercooled below its freezing point (whatever that may have been, depending on the solution and the pressure), since I had thought that that required exceptional purity (from nucleation sites), which I wouldn't expect in a wine cooler, and good vibration isolation, which I wouldn't expect in a freezer door. I also don't know how easy it is to supercool something to 80 degrees below its freezing point.
According to the thermometer, the temperature in the freezer is 260K. According to your figures, that's low enough to freeze only 1/6 of the mass. I wish I could check your number for specific heat of water, but alas my Merck's disappeared many years ago (grrrr).
It's possible that not all of the liquid was frozen; there could have been some liquid in there, bound in an ice matrix. But I really, really doubt that any 5/6 of that thing was bound liquid. It appeared *very* solid. So it looks like we *are* talking cold fusion. Well, I'm glad that's settled.
The heat goes into the air, just as it does when snowflakes form.
Unless the air in the Armory's kitchen was colder than freezing, the heat won't do any such thing. Heat flows from warm to cold, never the other way around. Snowflakes can dump heat to the surrounding air because the surrounding air is _cold_. The air in the Armory's kitchen was comparatively warm.
The only places for the heat of fusion to go once the bottle was out of the freezer were the (colder than 0 C) water and the (similarly cold) bottle. I wonder what the heat capacity of glass is...
But pressure not temperature is the key variable.
They are both key variables.
The temperature will only vary by a small percent while the pressure can change several fold.
This is exactly John's argument against my scenario: You need a huge pressure to change the freezing point much. Possibly more pressure than can be explained by CO2 coming out of solution near the freezing point. I think you can get a pretty big pressure from the expansion of water near freezing, but the bubble of gas at the top of the bottle would mute this effect quite a bit.
No kidding :') . We should probably take it to physics node.
Anyway, Hermit, your first paragraph is basically the same as my guess as to what's happening. I stated it in a couple of posts, but apparently wasn't too clear, as since then several people have (independently) posted the same explanation.
The problem with this explanation (and the supercooling one) is that for it to work, the water would have to be much colder than is reasonable so that it could absorb the heat of fusion produced as the ice forms and still be able to freeze all the way through. My slightly-too-simple calculation implied that the water would have to start at -80 C. The cold bottle will help some, but probably not enough, since the freezer was only at -13 C.
I'd like to see some figures for change in melting point of water with pressure. My Lange's handbook doesn't have that info (no surprise). The only common instances of this I've heard of are in the water at the bottom of large glaciers (under huge thicknesses of ice), and under e.g. ice skates, where the mass of a human body is exerted on the ice through a thin blade. In other words, LOTS of pressure, and in both cases you also have friction helping. The release of gas when I opened the bottle was not unusual in any way.
But again, the water not freezing is NOT what is unexplained. Supercooling is not an everyday occurrence but is no great mystery. There's no need to invoke exceptional pressure, etc. What *is* unexplained is where the heat of fusion went. The mechanisms that prevent the water from freezing (supercooling, pressure, whatever) do NOT allow it to simply freeze without dumping its heat of fusion somewhere. The difference between the cooling available in the water and the cooling needed to account for the heat of fusion is large enough (a factor of 6) that simple things like the bottle glass, etc. are unlikely to account for it.
So just what *are* they putting in those coolers these days? :) Did I accidentally pretrigger the subatomic thermoslurper that has been infiltrating our food supply? Or did my cooler accidentally get a gross overdose of it? Where's Mulder when you need him?
"Melting points are only weakly dependent on pressure, and so a melting point curve is an almost vertical line. For almost all substances, the melting point increases with increasing pressure at a rate of 0.01 to 0.03 K/atm. Water is anomalous in that its melting point decreases with increasing pressure. The melting point of ice decreases by 0.01 K per atmosphere of applied pressure. At 2050 atm, ice melts at -22 C. Between 0 C and -22 C, ice can be melted by the application of pressure. At any temperature lower than -22 C, ice cannot be melted by the application of pressure because of the existence of other high-pressure forms of ice."
This explains ice skates... the edge that presses on the ice is very small, so the weight per square inch is very high.
It doesn't sound like the CO2 pressure has that much to do with the supercooling.
From spcecdt Mon Jul 8 10:28:06 1996
Subject: wacky
Subject: Fun with Booze and Science
I saw something quite fascinating yesterday. I pulled a cooler out of the freezer where it had been for too long (Irene put it in the day before and forgot about it). I vaguely noted that despite its arctic sojourn, it was still liquid. I opened it up and took a swig... and got a mouthful of frozen mush. I looked at it in surprise. The top 1/4 or so of the bottle was frozen. I thought that was funny 'cuz it seemed to me that when I pulled it out I had checked and it was all liquid. But, I decided I must have been wrong. Except Bela was watching too, and said something about the bottle being at its critical point.
no. The (usual) critical point is where the distinction between liquid and gas (texts like `vapor') vanishes; high pressure and well above the usual boiling point. The transition here is between liquid and solid, and is of course the freezing point (or `the melting point')---and indeed you are not at the freezing point but...
That made me take another look. As we watched, the bottle I held continued to solidify,
...below freezing, as your observation of an ongoing process shows the system to be out of equilibrium. Indeed, as you already know, this began as a case of supercooling; the temperature being below the freezing point.
moving slowly
The reason why the motion is slow, is that the freezing expels some latent heat per gram, and that heat will tend to delay further freezing.
from top to bottom, fast enough to be able to observe the advance. Within the span of a minute it was a solid chunk.
showing that in spite of all the latent heat released, the climb of temperature was probably yet insufficient to reach the freezing point; at the end, the iced mixture was now a solid in thermodynamic equilibrium, considerably warmer than before the breaking out of the supercooled metastability, but yet (an unknown amount) below freezing (except that that unknown amount might perhaps have been nothing, an unlikely accident). ---But (see `Second thoughts') I change my mind.
Intriguing. I've never seen supercooling in action before. Time for some experiments.
The supercooled metastable state was of course the quiescent fluid prior to its disturbance; its decay away from that was the action that convincingly proved the metastable quality.
--- eli
...Second thoughts. You describe a slurry, I think, rather than a truly liquid-free crystalline affair. So it sounds as if dendritic growth of the solid got ahead of the inhibition of freezing by release of latent heat, allowing the whole volume to be invaded by partial solidification while yet leaving some fraction of the substance liquid. That would make the final state a mixture of solid and liquid in equilibrium, and that would make the final temperature the freezing point, rather than below freezing---which would instead have had no liquid at all, and I don't think if that were the case you would have used the words, ``swig'', ``mush''.
--- eli
[ general ] Message 57724: Wed July 10, 1996 12:20pm
From: Falling to Pieces (laz)
Subject: Stuff
David and Richard Attenborough are brothers. Just because I'm pedantic: The near-frozen stuff wasn't near its critical point (the temperature and pressure where the liquid-gas phase transition ends). From the description, it sounds like it was at a temperature below its freezing point at one atmosphere, but kept liquid because it was at high pressure. I think this is what everyone was saying anyway; it's just that it's not called the critical point :') . The
Indeed, that was only misapplication of a word.
pressure might have been maintained by carbon dioxide coming out of solution or the small expansion of water near its freezing point. Or something else I'm not thinking of.
The effect of pressure is negligible, as some of your comments below note. The high pressures which might count for something are incompatible with the weakness of the containment vessel.
[ general ] Message 57726: Wed July 10, 1996 1:35pm
From: Zaphod (spcecdt)
Subject: Re(57724): Stuff
Just because I'm pedantic: The near-frozen stuff wasn't near its critical point (the temperature and pressure where the liquid-gas phase transition ends).
I know. Note that I was quoting someone else :)
From the description, it sounds like it was at a temperature below its freezing point at one atmosphere, but kept liquid because it was at high pressure. I think this is what everyone was saying anyway; it's just that it's not called the critical point :') . The pressure might have been maintained by carbon dioxide coming out of solution or the small expansion of water near its freezing point. Or something else I'm not thinking of.
I am surprised that `everyone' got caught up with pressure---though some later > comments don't make that mistake.
[ general ] Message 57740: Wed July 10, 1996 5:13pm
From: Falling to Pieces (laz)
Subject: Supercooling
Water's heat of fusion is 80 kcal/kg. Its heat capacity is ~1 kcal/(kg*K). In order for the (initially liquid) water to absorb the heat of fusion and still remain below freezing (which it must have if the cooler turned into a solid block), it would have had to have had an initial temperature of -80 Celsius (-112 Fahrenheit). The cooler's freezing point was probably lower than 0 Celsius, since it was a sugar/alcohol/etc. solution, and the required initial temperature would have been correspondingly lower.
I agree with the gist of the above, but not with the detail; I also like to drop extra `kilo' prefixes; yes, 80cal/gram, and 1 cal/gram*Kelvin, for water---but about .5cal/gram*Kelvin for ice. The 80cal/gram latent heat is at 0degC. Let me follow one gram of water from supercooled temperature T to ice also at T, by first heating it to 0degC = T0, then freezing that at T0, then cooling that ice back down to T. I give the water 1.0(cal/K)(T0-T) to heat it up to T0, it gives up 80cal in freezing at T0, but then I must extract .5(cal/K)(T0-T) to get the ice back down to T0. The net heat given up then in going from 1gram of water at T to ice at T is -1.0(cal/K)(T0-T)+80cal+.5(cal/K)(T0-T) = 80cal-.5(T0-T)/Kelvin. So the latent heat at a lower T is less than 80cal/gm. But it only drops one cal/gram for every two Celsius degrees---starting actually at 79cal/gram. So even if your freezer got it down to -40degC=-40degF, a bit ridiculously low, the latent heat would only have been reduced to about 60cal/gram. Hence, while I do edit the numbers a little, I agree in the main, that it is implausible that a home freezer got things cold enough to allow complete freezing. But just as a piece of wood has lots of air in it yet can be used to build houses, so a dendritic crystalline growth through an incompletely converted liquid mass can be rigid rather than necessarily mushy.
By the way, Fahrenheit's zero is 32 Fahrenheit degrees below the normal freezing point of water, which amounts to a Celsius temperature of -32(5/9)degC = -18degC. This is significant, as Fahrenheit's silly idea was to define his `zero' as the lowest temperature to which he could supercool water. So -40degC is rather far out, not only on the basis of what one expects from a home freezer. ...Of course, the stuff is not water, but a concoction. Maybe said concoction faces a more difficult situation for freezing, and supercools easier than pure water... Still, I don't see numbers coming up with anything other than a falling short of complete freezing.
But while I am being pedantically complete, I should also mention that if the number of different ingredients is n , then the number of thermal parameters is n-1 (there being one dimension of scale that doesn't count, thermal parameters being intensive). For pure water, n is three: one ingredient is Volume , a second is Energy , the third is Water (in grams, or counted out in molecules, or whatever). So that gives one dimension of extension, and leaves two dimensions for the intensives---which checks out with Temperature and Pressure . Suppose I consider the stuff to be a mix of Volume and Energy and Water and Sugar and Alcohol . That counts to five degrees of freedom, hence the dimensionality of intensives is up to four . Though two-dimensional intensive space has different regions of itself separated by curves---and we are interested in the freezing curve which separates solid from liquid---what separates different regions of four-dimensional intensive space from each other is three-dimensional sheets. (Add Carbon Dioxide , and the dimensionality goes up one more; I am guessing that it doesn't count much.) So even if we go back to plain water, we have a freezing curve, rather than a freezing point---but the low sensitivity to Pressure of a few atmospheres is what roughly justifies talking about a freezing point here. But if one wishes to discuss the higher dimensionality, then the most commonly cited extra parameters are called Chemical Potentials . So one would enlarge the list Temperature , Pressure , to include also chemical potentials for the various `ordinary chemical' ingredients ( Temperature being very crudely like a chemical potential for Energy and Pressure a chemical potential for Volume: this statement is intentionally false except for getting the count of how many parameters right! ) So you would list chemical potentials for Water, for Sugar, and for Alcohol ... but you will then have five instead of four parameters; if you go back to pure water, you would have Water's Chemical Potential and would have three instead of two parameters. But it turns out that all these intensive parameters satisfy one relationship---and that is used to reduce the list Temperature , Pressure , Chemical Potential of One Pure Substance down to just Temperature and Pressure . But add in sugar and alcohol, and getting rid of one intensive parameter does NOT any longer allow you to ignore chemical potentials. ...But as your other correspondent(s) note, the bet is that alcohol and (I think) sugar will depress the normal freezing point, and that will make the interval T-T0 smaller. So I don't see anything to interfere with the notion of incomplete freezing---just thought I would acquaint you with some conceptual approximations here.
`Experiments'? If supercooling leads to a slurry, then the final temperature is the normal freezing point (the sharpness of which could be blurred by the chemical-potential parameters!). If it leads to a totally frozen mass, then the final temperature should lie below freezing. A way to test for which, is to ask whether applying heat to partially and obviously melt some but not all of the mass, raises the preparation's temperature. IF THE MULTIPLICITY OF CHEMICALS CAN BE IGNORED, then the temperature will not rise until all is melted.
If the temperature does vary, then we can still have incomplete solidification, but with the sugar and alcohol playing a significant role, though; to look up wisdom on this area, some terms (beyond chemical potential) are Gibbs phase rule , and eutectic (the term used for that balance of ingredients which gets to the lowest freezing point---hence anything sensible about that has to go into how the freezing point in fact varies with the chemical composition) .
[ general ] Message 57751: Thu July 11, 1996 1:35pm
From: Falling to Pieces (laz)
Subject: Second law of thermodynamics
The heat goes into the air, just as it does when snowflakes form.
Unless the air in the Armory's kitchen was colder than freezing, the heat won't do any such thing. Heat flows from warm to cold, never the other way around. Snowflakes can dump heat to the surrounding air because the surrounding air is _cold_. The air in the Armory's kitchen was comparatively warm. The only places for the heat of fusion to go once the bottle was out of the freezer were the (colder than 0 C) water and the (similarly cold) bottle. I wonder what the heat capacity of glass is...
nonsense. The 2nd law: Entropy of an isolated system increases. If the isolated system is system1 and system2 separated by a membrane which will allow ONLY ENERGY to flow, THEN, for entropy to increase, the energy must flow from the system whose entropy is LESS sensitive to energy, into the system whose entropy is MORE sensitive---that way, the increase of entropy of the more sensitive system dominates the decrease in entropy of the less sensitive system, and entropy overall does increase. The sensitivity of entropy to energy, i.e. d(entropy)/d(energy), IS THE BASIC MEASURE OF COLDNESS, and the temperature T is for historic reasons defined as the reciprocal of the coldness.
As soon as other conserved quantities can be exchanged, FORGET the rule that energy flows only from hot to cold, the similar rule that chemical can flow only from high chemical potential to low chemical potential, and that volume can flow only from high pressure to low pressure. Instead, whether a flow can happen spontaneously has to be calculated on the basis of the net change that would result from simultaneous transmission of the several quantities---and if the overall change in entropy of the two systems together is an increase, then the 2nd law allows it---even if the flow of energy alone within this may be from cold to hot.
Note that the above does NOT get directly at the thermodynamics of freezing; it is intended to rather send `heat from hot to cold' folks back to their thermo texts---although ones defeat from modeling freezing as transmission of energy only from system1 to system2 should generate a strong suspicion that one must get beyond that oversimple first lesson.
But pressure not temperature is the key variable.
They are both key variables.
The temperature will only vary by a small percent while the pressure can change several fold.
This is exactly John's argument against my scenario: You need a huge pressure to change the freezing point much. Possibly more pressure than can be explained by CO2 coming out of solution near the freezing point. I think you can get a pretty big pressure from the expansion of water near freezing, but the bubble of gas at the top of the bottle would mute this effect quite a bit.
John has got it right. And if the bubble of gas wouldn't do it, the cracked bottle would. My bet is that Sugar and Alcohol may also not be of gross importance, still, of more importance than Volume .
The ability to supercool---by the way---indicates that the bottler has produced something very clean. Or that the concoction is easier to supercool than pure water. And probably, both. Natural food folks should shun the product---because it is unnatural for stuff to be clean.
[ general ] Message 57762: Thu July 11, 1996 5:03pm
From: Zaphod (spcecdt)
Subject: pressure
I'd like to see some figures for change in melting point of water with pressure. My Lange's handbook doesn't have that info (no surprise). The only common instances of this I've heard of are in the water at the bottom of large glaciers (under huge thicknesses of ice), and under e.g. ice skates, where the mass of a human body is exerted on the ice through a thin blade. In other words, LOTS of pressure, and in both cases you also have friction helping. The release of gas when I opened the bottle was not unusual in any way. But again, the water not freezing is NOT what is unexplained. Supercooling is not an everyday occurrence but is no great mystery. There's no need to invoke exceptional pressure, etc. What *is* unexplained is where the heat of fusion went.
Indeed. So I say it didn't; most of the water didn't freeze, even though the structure appeared rigid. AND ANOTHER TEST than thermal stability occurs to me: If the event can be reproduced, then the apparently solid mass, when put back into the freezer, should in solidifying further, swell in volume and do so even more than in the observed swelling upon decay of supercooling. So, open the bottle, watch it seemingly freeze solid, slice off any tongue that sticks out, recap, and put it back into the freezer. NOW, it should, in truly freezing hard, burst the glass. <---HERE IS YOUR `EXPERIMENT'.
There can no longer be any supercooling inhibition to thorough freezing, because the supercooled metastable state has given way already to a stable state, and one thoroughly nucleated all over, for freezing or thawing.
--- eli
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