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Freezing Speed of Hot Versus Cold Water
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Nominal Animal:
The Mpemba effect is real.  See e.g. Takada, Hayakawa, Santos, "Mpemba effect in inertial suspensions", Phys. Rev. E 103, 032901, 2021-03-08.  The only disagreement is whether it applies to water or not.  Given sufficiently rapid cooling in the experimental setup I described in my previous post in this thread, it can be shown to exist in water.  Anyone claiming otherwise is not sufficiently aware of the peer-reviewed articles on the subject within the last decade or so.  Many papers exist that claim otherwise, but suffer from incorrect assumptions or insufficient cooling rate, and extend the logical result (that the effect does not occur in these conditions) illogically into "the effect does not exist".

At the core of the real Mpemba effect is that heat capacity is not constant in non-equilibrium states.

It is well known that for solids, heat capacity is dependent on the lattice structure.  Essentially, latent heat - energy stored in the material without affecting the temperature of the material –, is associated with the phase change: the change in structure.  Water ice itself has at least nineteen different phases.  Note that while many can only be produced in specific (high) pressures, some of them can remain stable well outside their formation range.  Given temperature and pressure, there is often more than one stable phase.  Indeed, at the triple point, the solid, liquid, and gaseous phases are all in dynamic equilibrium.

For liquid water, the situation is more complicated, because any molecular structures involved are temporary and unstable (with the most stable ones, like water methane clathrates, involving other molecules), and the really interesting physics involves the properties of individual water molecules; the hydrogen-oxygen bonds (and to a lesser extent, the hydrogen-hydrogen bonds) in non-equilibrium states, when cooled or heated rapidly.

To simplify what happens in the real Mpemba effect, is that the liquid at hand is far from an equilibrium state, and because of recently been at much higher temperature, can lose heat energy much faster than the same liquid at the same temperature in an equilibrium state would.  Simply put, the recently-hot liquid has smaller heat capacity.  (The reality is more interesting, especially when the sample starts getting nearer to an equilibrium state of the heat bath, as localized heating can often be detected due to the latent heat.  But close enough for an intuitive understanding, the interesting parts and the actual mechanism, are more like technical details.)

If we had some kind of device or meter that could measure the net energy flow between the heat bath (freezer) and the (originally liquid) sample, we'd find that at the same temperature, the energy flow from the recently-hot sample to the heat bath is higher than for the sample that was not originally that hot.

In other words, there is nothing really odd here, just a variation in the heat capacity, depending on whether the water sample was really hot (boiling) or not.  Nothing anomalous in the everyday life sense, just an interesting physical phenomena.

I am actually a materials physicist (or close enough; I never submitted my thesis on ferrochrome structure providing the corrosion resistance effects), specialized in the numerical simulation aspects.  The Mpemba effect is interesting, because it was only in the last decade or so that we could numerically simulate the effect; and do so with multiple different classical chemical force-field potential models.  (Because of the large number of electrons involved [two per molecule, with hundreds of molecules minimum needed due to periodic boundary conditions inherent in ab initio simulations], and the difficulties in modeling hot water in ab initio simulations, the entire phenomenon hasn't been simulated ab initio (using e.g. VASP, Dalton, Siesta, or similar) thus far, only at specific temperatures showing the differences in the molecular structure of each water molecule, supporting the observations in simulations using classical force-field models.)
CatalinaWOW:
Nominal I have to disagree with just one thing in your response.  The idea that a liquid can have different states with different properties that are stable enough to have macro effects is weird, wonderful and yes, odd.  I guess your extensive experience modelling this makes this strange phenomena seem commonplace to you.

I put this in the same category as super-cooling, which though common enough under certain conditions is certainly generally uncommon and odd.  My son and I were greatly fascinated on a recent vacation when the freezer at the hotel would routinely super cool water bottles.  They could be removed from the freezer and were completely liquid, but a simple rap on a countertop would cause them to freeze solid in a few seconds.  Watching the freeze front chase through the liquid while the bottle was certainly gaining thermal energy from our relatively warm hands was one of the high points of the vacation.  But as relatively repeatable as this was in that set of circumstances, it is the only time in seven decades that I have actually observed the phenomenon.  And even there it only happened in perhaps a dozen bottles out of a couple dozen that were frozen.
Nominal Animal:

--- Quote from: CatalinaWOW on February 21, 2022, 12:26:51 am ---Nominal I have to disagree with just one thing in your response.  The idea that a liquid can have different states with different properties that are stable enough to have macro effects is weird, wonderful and yes, odd.  I guess your extensive experience modelling this makes this strange phenomena seem commonplace to you.
--- End quote ---
Not commonplace.  And I would be very surprised if it did happen in equilibrium conditions, without significant energy flow in/out.

I meant more in the sense of anomalies or strange phenomena as used in e.g. History channel TV shows.


--- Quote from: CatalinaWOW on February 21, 2022, 12:26:51 am ---I put this in the same category as super-cooling, which though common enough under certain conditions is certainly generally uncommon and odd.  My son and I were greatly fascinated on a recent vacation when the freezer at the hotel would routinely super cool water bottles.  They could be removed from the freezer and were completely liquid, but a simple rap on a countertop would cause them to freeze solid in a few seconds.  Watching the freeze front chase through the liquid while the bottle was certainly gaining thermal energy from our relatively warm hands was one of the high points of the vacation.  But as relatively repeatable as this was in that set of circumstances, it is the only time in seven decades that I have actually observed the phenomenon.  And even there it only happened in perhaps a dozen bottles out of a couple dozen that were frozen.
--- End quote ---
Funnily enough, the only requirement for that to happen is that the water does not contain seed kernels, either surface defects in the container, or "impurities" in the water that the freezing process can start from.  Boiling the water, then bottling it while relatively hot, is often enough to remove the seed kernels.

The same can also occur when boiling water, especially when boiling water in a glass or glazed ceramic cup or mug in a microwave oven.
When you take the water out from the oven, it is steaming hot, but does not boil.  Drop a spoon in it, and it basically explodes, boiling all at once.

You are absolutely right in that this does belong to the same category, though.  In these cases, the water is not really in an equilibrium condition; it is in a meta-stable state, where a tiny little nudge in the parameter space is needed for the entire system to roll down into a more stable and closer to equilibrium state.  In the case of superheated or supercooled water, something needs to start the phase change reaction; after which the entire sample will change states almost at once, in a continuous wavefront, like Dominoes falling.

In liquid water, in the Mpemba effect, it is the energy flow (heat flowing out of the sample) that maintains the non-equilibrium properties of the water molecules.  In the simulations, it can be seen how the energy is lost in molecular interactions ("collisions") isn't equally distributed in the degrees of freedom; that it takes considerable time (considering typical time steps are in the femtosecond range, 10-15 seconds per time step) for each water molecule to "relax" to something close to an internal equilibrium state after each collision.  Both when the molecule loses or gains energy from the collision, too.  In this non-relaxed state, the chemical properties of the molecule, including heat capacity, differs from that when it is in relaxed state.

Put another way, if you somehow isolated one water molecule in the middle of the Mpemba effect, even without any energy flow in/out, the temperature and heat capacity of that molecule would still change, until it reached the relaxed state (in equilibrium with its surroundings).  (I have no idea how long that would take.  There are different simulations for different time scales, and I am not aware of any work trying to find out how fast that internal relaxation takes.  I know of a few methods how one could start to find out –– from the average collision interval between water molecules at standard pressure at different liquid temperatures –– but no idea if anyone has done the work needed.)

Water methane clathrates are similar, in that e.g. an earthquake (at the continental shelf at arctic or antarctic latitudes) is enough to make the clathrates release the methane into the water and from there to the atmosphere.  They, too, tend to be supercooled, in the sense that they stay liquid although their temperature is less than the freezing point of water.  (In tropical latitudes, methane tends to be generated in the seabottom mud due to biological reactions, with the organic mud forming a more or less methane-impermeable layer.  When the methane pocket pressure becomes high enough, it bursts through the mud.  No clathrates are involved there.  These methane pockets/bubbles, by the way, are suspected to be the reason for a few sunken ships in the Sargasso Sea near Bermuda, by the way; if the water is deep enough for the methane to mix into the water, it reduces the water density, and therefore the buoyancy.  The Sargasso weed itself, decaying at the seabottom, being the source for the methane.)
T3sl4co1l:
Holy shit, you mean "structured water" actually exists?! -- Just, not in anything like the fantastical claims usually ascribed to that term, just in the more mundane matter of heat capacity -- in other words, that there's, apparently, degrees of freedom which don't equilibriate quickly with the bulk.  And it's not like, nuclear spins, obviously, which wouldn't have nearly enough heat capacity to be sensible (even in a strong magnetic field(?)), and yet, with an equilibrium time constant on that order?

Mind blown.

Tim
CatalinaWOW:
The boiling out of a microwave phenomenon is widely reported, but uncommon enough that no one I have spoken to has personally encountered it.  These things show how inadequate terms like easy, common, rare and the like are to make useful decisions about risk and necessary precautions.  I have no idea how likely these events actually are.
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