What’s cooler than being cool?

July 7, 2022 8:23 PM

Controversy continues over whether hot water freezes faster than cold water, decades after teenage Erasto Mpemba initiated the first systematic, scientific studies. In the effort to confirm or refute the ‘Mpemba effect’ physicists are developing new theories about how substances relax to equilibrium.
posted by theory (27 comments total)

squirt guns into the swamp cooler in our undies
posted by wmo at 8:40 PM on July 7, 2022

Oh thanks for this!

When this first came up in conversation I absolutely did the science guy "This can't be true" thing. I don't think I was especially rude about it, but I remember saying the temperature of an item is a state function, so hot water needs to shed a certain amount of heat energy to get to freezing temperature, and then freeze. Cold water needs to shed less.

But net energy is not quite the same thing as rate of cooling and I've since read that there have been papers demonstrating that there is a theoretical possibility. This is by far the best layman's explanation I've seen, and am planning to reread it to try and finally get a good enough handle on the argument that I might be able to explain it back.

But they also seem to be suggesting that, empirically, the observable effect on water is at best inconsistent, with most measurements being within the margin of error. So maybe hot water sometimes freezes faster and sometimes doesn't--or maybe it is not actually an observable thing in the first place?

They mention some relatively subtle stuff like measurement locations, I'm assuming that in a home experiment freezer temperature variability has got to be a huge confounding variable too.
posted by mark k at 9:20 PM on July 7, 2022 [3 favorites]

Halfway through the article but I am reminded that everyone nowadays says that global warming thermodynamically causes hotter hots and colder colds. But, why is that true? Is there a theory that explains this? And maybe these things could be related.
posted by polymodus at 10:58 PM on July 7, 2022

But, why is that true? Is there a theory that explains this?

The best metaphor for this phenomenon I've heard is to imagine a stream flowing slowly. There are a few eddies in that flow backwards--also slowly.

Then imagine adding more energy to the stream--that is, make it flow a lot more quickly. Even though the average forward speed is higher, there are still eddies that start flowing backwards faster than before, too (and probably in different places!)

I think this sort of chaotic turbulence is really easy to visualize with fast moving water, but not necessarily with abstract stuff like temperature. Or for that matter in macroscopically "still" water, like that in an ice cube tray
posted by mark k at 11:06 PM on July 7, 2022 [9 favorites]

Halfway through the article but I am reminded that everyone nowadays says that global warming thermodynamically causes hotter hots and colder colds. But, why is that true? Is there a theory that explains this? And maybe these things could be related.

I think right now the predominant evidence is that cold places and cold times of year/day are warming more than warm places; temperature-wise, the world is getting more uniform. There are some possible counterexamples - there are some theories that the polar vortices of years are connected to changes in winds due to melting ice, and until recently there was some counterintuitive growth in Antarctic sea ice (although now that seems to be reversing).

On the other hand, the "dry gets drier, wet gets wetter" paradigm seems to be holding up well.
posted by nightcoast at 12:08 AM on July 8, 2022 [2 favorites]

It is a little bit tangential - but I was contemplating "Just how cold are my ice cubes?" the other day. I found the answer quite interesting - basically one piece of ice need not be at all like another - there may be different crystalline polymorphs as you get colder - and you can cool your ice by adding salt - the question of "How cold would steel ice cubes have to be to be as effective as water ice cubes?" is a notable one too.
posted by rongorongo at 12:39 AM on July 8, 2022

Interestingly too with ice is that the phase change can absorb so much heat that when making a cocktail you can get it down below freezing, If you measure the temp on a martini or manhattan etc, you'll see it down to 27-28 F.
posted by Carillon at 12:52 AM on July 8, 2022 [2 favorites]

the phase change can absorb so much heat that when making a cocktail you can get it down below freezing, If you measure the temp on a martini or manhattan etc, you'll see it down to 27-28 F

Seems likely to me that what's happening there is that your ice blocks will be coming out of the freezer having equlibrated to the freezer's set temperature, which is usually down around -18°C.

The ice will melt at 0°C, and that's the temperature that will be maintained at the melting edge of each piece of ice until all of the liquid part of the cocktail has been pulled down to 0°C, at which point the ice stops melting.

The liquid will then continue to lose heat by conduction into the remaining solid ice, a process that will eventually equilibrate at a temperature somewhere between the 0°C melting temperature and the -18°C that the centre of each ice piece started at. There's scarcely any melting happening while this is going on, so the liquid remains liquid and the ice remains solid. This is made possible by the alcohol that's in the drink, but not inside the ice, lowering the drink's freezing point to somewhere below 0°C.

Meanwhile the whole cocktail has been absorbing heat energy from its surroundings, a process that continues all the way through the above-described internal heat flows. Eventually its temperature will rise to almost exactly 0°C and stay there, stabilized by ice once again responding to incoming heat energy by changing phase rather than increasing its temperature.

Only once all the ice has melted will the temperature of the cocktail start rising above 0°C again.

Roughly similar dynamics can happen if -18°C ice blocks are added to plain water inside a container with really good thermal insulation such as a vacuum flask, except that because there's no alcohol in the water it will start to freeze again as its thermal energy starts being conducted away into the interiors of ice blocks. The refreezing will happen much as it does when any body of water freezes, with newly formed ice crystals floating to the top. In a flask, that will make an ice plug in the neck.

Refreezing means that the water is responding to thermal energy loss not by lowering its temperature below 0°C, just by changing phase back to solid again. Assuming negligible heat gain through the container's insulated walls, and minimal heat gain by conduction through what could easily end up being quite a thick ice plug, the whole thing should equilibrate with both ice and liquid water present inside the container at pretty much exactly 0°C throughout.

That substantial uniformity of temperature also means that there will be almost no convective movement in the liquid, potentially keeping the whole assembly largely stable for quite surprising amounts of time.
posted by flabdablet at 3:21 AM on July 8, 2022 [9 favorites]

As a cocky 17 year old I was absolutely convinced that my naive ideas about freezing points and boiling points were correct. I had it in my mind that if water was below 0°C it was ice, and anywhere from 0°C to 100°C it was liquid, and anywhere above 100°C it was gas. So boiling, for example, was the process of water transitioning from just below 100°C to just above 100°C. Easy, simple, straightforward, right? I was so convinced about this that I argued the point with my physics teacher and just ended up quietly and privately refusing to accept that he was right and I was wrong.

The idea of an assembly of water and ice inside which the temperature of every part, liquid and solid, was at exactly 0°C was something I just could not wrap my head around. All the same, it's how things work. Phase change is a thing that happens instead of temperature change and not as a consequence of temperature change, and an assembly of multiple phases of any given material really can emit or absorb considerable amounts of heat energy without changing its own temperature at all.
posted by flabdablet at 3:38 AM on July 8, 2022 [8 favorites]

What a fascinating article! I wish scientists would do more experiments with ice cream, which is where Mbempa first observed the effect, though I realize that would add the extra complication of the scientists unthinkingly eating the carefully prepared experimental subjects.
posted by Kattullus at 3:42 AM on July 8, 2022

TFA:

Over the decades, scientists have offered a wide variety of theoretical explanations to explain the Mpemba effect. Water is a strange substance, less dense when solid than liquid, and with solid and liquid phases that can coexist at the same temperature.

Assuming that the author intended that reference to solid and liquid phases coexisting at the same temperature to exemplify the strangeness of water, it seems that cocky 17 year old me was not the only person ever to be confused on this point.

Water being less dense when solid than liquid does make it unusual, but the ability of its solid and liquid phases to coexist at the same temperature does not.
posted by flabdablet at 3:50 AM on July 8, 2022

The other thing to keep in mind when thinking about temperature is that temperature is a statistical property, useful only to the extent that the internal motions of whatever you're measuring the temperature of are random. So the smaller the region whose temperature you're measuring, the less precise your result can possibly be.

On the very smallest scales, temperature as an idea disappears altogether and the only observable you have left is the kinetic energy of individual particles. And that is why my cocky-17-year-old arguments about the temperature of an individual water molecule as it makes the jump from liquid surface to free gas ultimately don't make sense.
posted by flabdablet at 4:06 AM on July 8, 2022 [6 favorites]

The discovery of the 'Mpemba effect’ is inspiring, because it shows that a curious young person using household equipment can make a significant discovery.

Another one like that was an elementary school science class that used blue food dye on their tongues to highlight taste buds, and then count how many taste buds there are per square centimeter. The previously-unrecognized results were that the number of taste buds vary by an order of magnitude person to person. This gave rise to the concept of "super tasters"

So kids, stay in school don't do drugs, and make scientific discoveries in mom's kitchen.
posted by StickyCarpet at 6:23 AM on July 8, 2022 [7 favorites]

Part of the problem seems to stem from imagining the temperature of the water as uniform, when in fact it certainly is not when out of equilibrium. With higher temperature differentials within the water, hot water may set up convection cells and lose heat faster by advection, whereas cooler water may be dominated by heat diffusion alone. I'm surprised the article doesn't even mention advection. Another issue may relate to movement of semi-gelid blocks of water as a block, which is a form of correlation that upends all the statistical definitions of temperature, pressure, entropy, and even equilibrium itself.
posted by hypnogogue at 7:07 AM on July 8, 2022 [3 favorites]

I would bet my house that boiling water does not freeze faster than cold water on average.

I have also been wrong about very many things in the past and am not sure I'm right about this. (I have taken several grad stat mech classes. The energy/position diagram looks very unlike a cup of water in the kitchen. It's cool to think about, but that's some serious fine-tuning.)

Fun post. Thanks!
posted by eotvos at 7:52 AM on July 8, 2022 [1 favorite]

I would bet my house that boiling water does not freeze faster than cold water on average.

I'd take that bet, but only after running enough tests to establish the exact experimental conditions I'd need to set up in order to win it. Not at all convinced that no such conditions could possibly exist.
posted by flabdablet at 9:49 AM on July 8, 2022 [1 favorite]

Another issue may relate to movement of semi-gelid blocks of water as a block, which is a form of correlation that upends all the statistical definitions of temperature, pressure, entropy, and even equilibrium itself.

This. I can easily imagine the existence of self-insulating cells with very cold outsides and quite warm interiors which, at some point, suddenly swap their internal temperature gradients for a full phase change. But I also suspect that it would likely be easier to create the conditions for the emergence of such things in overtly non-uniform mixtures like ice cream than in relatively pure water.
posted by flabdablet at 9:56 AM on July 8, 2022

this sort of chaotic turbulence is really easy to visualize with fast moving water, but not necessarily with abstract stuff like temperature

For explaining to beginners, it helps that the temperature anyplace on Earth is strongly affected by the way the fast moving atmospheric streams are meandering or stuck. We can taste whether our winds are northerly or tropical or jammed in place, and get video images of how that relates to the whole planet…

Seconding StickyCarpet's delight at how much there is left to be observed at any scale! Plus delight that if the puzzle also requires Incredibly Fancy Science, now we have that, too.
posted by clew at 10:26 AM on July 8, 2022 [1 favorite]

though I realize that would add the extra complication of the scientists unthinkingly eating the carefully prepared experimental subjects.

I think you’d be surprised how many experiments have to abandoned because of this. The LHC was shut down for eight months once when word got around about how tasty quarks were with a bit of olive oil and salt.
posted by ricochet biscuit at 10:49 AM on July 8, 2022 [2 favorites]

To me, this whole thing is silly, but I want to refute one of the claims in the first paragraph of the article: hot pipes bursting faster than cold pipes when the temperature is below zero.

Of course the hot pipes burst first. Corrosion is directly related to temperature, so if there are two pipes that have basically experienced the same conditions for years, except one of them is hot all of the time and the other is cold all of the time, the corrosion on the hot one is going to be much higher. After years being in this state, when you put a stress on both of them the hot pipes are going to burst first. This is not an argument about the nature of water.
posted by Quonab at 10:49 AM on July 8, 2022 [1 favorite]

> When this first came up in conversation I absolutely did the science guy "This can't be true" thing.

In some histories of this effect, this was the reaction of Mpemba's teacher, who even referred to other misconceptions as "Mpemba physics" during the course. I don't know whether this was the same teacher who helped Mpemba develop a repeatable experiment and publish his paper.
posted by fantabulous timewaster at 11:19 AM on July 8, 2022

The main intuition that initially made me skeptical about it was that at first blush it appears that the hot sample would need to reach the starting temperature of the cool sample on its way down to freezing, by which time the cool sample would obviously have had a head start.

If we were talking about solids then that reasoning would probably be pretty sound, but we're not. We're talking about liquids, and it might well be that there are cooling pathways involving dynamic processes inside the liquid samples that only ever get a chance to get started inside hot ones.

As a very loose analogy for the purpose of reducing the range of possibilities that intuition will immediately rule out as ridiculous, consider the speed at which alcohol will release heat energy while turning into carbon dioxide and water on exposure to air. This reaction runs much faster if enough energy is added initially to some small part of the sample to kickstart the dynamic process we call "fire".

Fire is a non-equilibrium chemical process, but it seems to me that under the right conditions there could well exist roughly analogous purely physical processes inside a cooling liquid sample that require a large initial temperature difference between sample and environment to initiate and self-sustain all the way down to freezing once they have been.

I have done no personal investigations into the Mpemba Effect, but I am in no way willing to bet amounts anywhere near the value of my house against the possibility that it could be a thing.
posted by flabdablet at 11:57 AM on July 8, 2022 [1 favorite]

Another intuition pump worth considering is the way that one can empty a narrow-necked bottle more quickly than can be done by turning it upside down and letting the water just glug out, by giving it a bit of an initial swirl to get a self-sustaining vortex going in the neck that maintains a clear passage up the middle for incoming air.

Self-sustaining processes that maintain vastly more efficient cooling via a self-organizing interplay between temperature gradients, convective liquid motion and phase changes are not a completely mad idea.
posted by flabdablet at 12:06 PM on July 8, 2022 [1 favorite]

Well, having reread the article a couple times it's still the best explanation I've read but it's really frustrating, in that I don't really understand the arguments.

The core detailed bit describes a model system that shows a high-energy "marble" can reach equilibrium faster than a low energy one. Even with (or perhaps because of) my chemistry background can't sort how this would translate to water.

But I guess that's the rub--it seems no one can. One of the physicists (Burridge) states: "I never find a clear physical explanation, and I feel that leaves us with an interesting question as to whether Mpemba-like effects exist in a meaningful way." But being clear about this connection--or lack thereof--still keeps it a cut above most other accounts, which were totally silent on whether the modeled effects are actually relevant.

Here's what I'm getting from the article:

1) There is no clear empirical evidence of the Mpemba effect in water. There have been lots of experiments that don't confirm the original claim.

2) There are empirical (?) tests with non-water samples (like sands and substances that undergo second order phase transitions) where we can measure this.

3) There is advanced work into non-equilibrium systems that can describe systems where hotter samples could freeze faster than colder ones, but none describe conditions that exist for "water in the freezer."

I would add a corollary of (1) that that the folk wisdom / Aristotlean general claim that "hot water freezes faster" is false, or it would have been measured clearly and not be in dispute. Corollar to the other two items though mean you can't dismiss it as impossible on Thermodynamics 101 principles (as I did when I first heard it.)

I'll add that I can kind of picture what's going on in the claim with materials that do second order phase transitions, so that's a help in the abstract. Does nothing at all to help in the case of water.

FWIW I personally think eotvos's house is save.



With higher temperature differentials within the water, hot water may set up convection cells and lose heat faster by advection, whereas cooler water may be dominated by heat diffusion alone. I'm surprised the article doesn't even mention advection

The obvious question here is whether there's any model (or empirical experiment) where this is relevant. I mean, it's a plausible hypothesis, but you'd need the effect to be so strong that when it starts in 99° C water it not only "catches up" to 35° C water and then the (metaphorical or literal) keeps it cooling much faster.

I'm suspecting it's not actually relevant precisely because it is so plausible that it seems people working on this would have starting with macroscopic explanations like that first.
posted by mark k at 12:40 PM on July 8, 2022 [1 favorite]

Water is a difficult one for sure. I'm too young to remember the polywater controversy, where a seemingly anomalous form of water with a higher boiling point (in reality, there were contaminants causing the difference) hung around on the fringes of science for about a decade.

Water at high temperature and pressure does weird things when considered in bulk. But they're weirdly valuable things in thermal power generation, so they're studied and codified in steam tables. It also does weird things at low temperatures, so ice subliming from inside heavy snowbanks triggers avalanches (and less catastrophically, makes your ice cubes disappear in the freezer). The surfaces inside which water is frozen can promote or hinder crystal formation. Similarly, water will stay liquid and apparently stable above boiling point, but will flash to vapour as soon as it's disturbed (I've done this, don't do this).

The level of control required on an experiment to prove or disprove this effect are difficult to attain. Plus, there's ice cream involved. The stakes are just too high.
posted by scruss at 9:56 AM on July 9, 2022 [2 favorites]

Seems likely to me that what's happening there is that your ice blocks will be coming out of the freezer having equlibrated to the freezer's set temperature, which is usually down around -18°C.

Sorry following up here, you'd think that, but Dave Arnold did work in Liquid Intelligence and demonstrates pretty clearly that even if you temper your ice to 0C, you'll still get something even down to -4C. It's due in part to the specific heat of water and alcohol I believe. But The ice is absorbing enough heat from the drink you drop it. He proposes a simple experiment with a martini to confirm it, involving tempering you ice in a water bath then using that ice to stir the martini.
posted by Carillon at 11:08 AM on July 10, 2022

I can help with the question about cocktail cooling.

The reason ice potentially drops the temperature of a cocktail below zero is that water/ethanol is a mixture, so it has a lower freezing (aka melting) point. This is a simple undergrade chem lab observation. That means equilibrium for the system is with the temperature closer to the new freezing point, but some or all of the ice melted. The "heat" it takes to melt the ice comes from the cocktail itself, even when the cocktail is the same temperature as water ice..

If you've ever made ice cream in an old fashioned ice cream maker--a hand cranked one without built in refrigeration--you jacket the mixer with ice, then add salt to the ice to get it below 0° C. It's the same principle, with ethanol serving the purpose of salt.

It may seem weird that a mixture can end up colder than either of the components, but it actually happens quite often. Mixtures have high entropy so two substances will mix even if it's not energetically favorable.
posted by mark k at 11:20 PM on July 10, 2022 [1 favorite]