Study may explain counterintuitive effect of why hotter systems can cool more quickly

October 23, 2017 by Lisa Zyga, Phys.org feature
Credit: CC0 Public Domain

Ever since the days of Aristotle, people have made the counterintuitive observation that hot water sometimes freezes faster than cold water. In modern times, the observation has been named the Mpemba effect after Erasto Mpemba, an elementary school student living in what is now Tanzania in the early '60s. When making ice cream, Mpemba observed that using warmer milk causes the ice cream to freeze faster than when using colder milk.

In the last few decades, the Mpemba effect has been studied and observed in several physical systems besides water, including carbon nanotube resonators and ice-like water cages called clathrate hydrates. Despite these findings, the causes of the effect are not well-understood. Proposed explanations include the presence of impurities, hydrogen bonding, and supercooling. Even the mere existence of the Mpemba effect remains controversial, as one recent study found insufficient evidence to replicate a meaningful effect.

Now, their interest rekindled by a recent paper proposing a generic mechanism for similar effects, scientists Antonio Lasanta and coauthors from universities in Spain have returned to the question in a new study published in Physical Review Letters. In their work, the researchers theoretically demonstrate and investigate the Mpemba effect in granular fluids, such as those made of sand or other small particles.

Using simulations of granular systems and a simple kinetic theory approach, the researchers were able to determine that the initial conditions in which the system is prepared play a critical role in determining whether or not the system exhibits the Mpemba effect. Their analysis also enabled them to identify the initial conditions required in order for a granular system to exhibit the Mpemba effect.

"Our work shows that the existence of the Mpemba effect is very sensitive to the initial preparation of the fluid or, in other words, to its previous history," coauthor Andrés Santos at the University of Extremadura in Badajoz, Spain, told Phys.org. "In our opinion, this may explain the elusiveness and controversy of the Mpemba effect in water, as a consequence of the lack of control on the detailed initial preparation of the sample."

As the researchers showed, if a system is not prepared under certain initial conditions, then the colder system cools down more quickly than the warmer one, as expected, and there is no Mpemba effect.

"We theoretically showed, at least in the case of a gas, that a system's temperature evolution and thus its and/or heating rate do not depend on initial temperature alone, but also on the previous history of the system that control the initial value of the additional variables," Santos said. "Therefore, it is perfectly possible that an initially heated system cools down quicker than a colder one with a different history."

As the researchers explained further, the simplicity of the Mpemba effect in granular fluids compared to water and other systems enabled them to reach this conclusion.

"Our results show that the Mpemba effect is a generic non-equilibrium phenomenon that appears if the evolution of temperature depends on other physical quantities that characterize the initial state of the system," Santos said. "In practice, such an initial state can be experimentally achieved if the system is taken by some physical procedure very far away from equilibrium (for instance, by a sudden heating impulse prior to cooling down). Our theoretical and computational work shows that the Mpemba effect is particularly simple in a granular gas, since, in practice, there is one single extra parameter controlling the Mpemba effect. This parameter is the kurtosis, which measures the deviation of the velocity distribution function from a Gaussian distribution."

With this new understanding, the researchers could estimate a range of initial temperatures for which the effect emerges and determine how different the initial values of this parameter must be in order for the Mpemba effect to appear.

The results also support predictions of the existence of an inverse Mpemba effect: when heated, a colder sample may reach a hot target temperature sooner than a warmer sample. The researchers plan to investigate this area and others in the future.

"On the theoretical side, we plan to carry out a similar study in the case of a molecular solute (where collisions are fully elastic) suspended in a solvent that produces a nonlinear drag force on the solute particles," Santos said. "Going back to granular fluids, we also want to analyze the impact of particle roughness and spin on the Mpemba effect. In the latter system, the simplest model would couple the temperature evolution to that of the parameter measuring the non-equipartition of energy between the translational and rotational degrees of freedom.

"On the experimental side, we think that reproducing in a laboratory the Mpemba effect in a granular gas would be a breakthrough. We are currently working on the design of an ad hoc experiment."

Explore further: Mpemba effect: Why hot water can freeze faster than cold

More information: Antonio Lasanta et al. "When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids." Physical Review Letters. DOI: 10.1103/PhysRevLett.119.148001. Also at arXiv:1611.04948 [cond-mat.soft]

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18 comments

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MR166
5 / 5 (1) Oct 23, 2017
Heating water does drive the gas out. Perhaps water without gas freezes at a higher temperature. It would be interesting to take two samples one without dissolved gas and one with the normal amount of gas and see which freezes sooner with both samples starting from say 10 degrees above freezing.
Steelwolf
2.3 / 5 (4) Oct 23, 2017
I would suspect that the thermal energy is freer to leave the hot sample since the space between atoms/molecules is greater and would allow the infrared to leave the mass less impeded by readsorbtion and emmitance times so that yes, the hot mass can cool down quicker at times.

Likewise, with an ice you have the material in a very compact structure such that when heated it actually transmits that heat faster due to the atoms/molecules being that much closer together.

As a welder I ran into both instances in the process of my work.
LED Guy
5 / 5 (1) Oct 23, 2017
So according to the article if you start with hotter water in a non-equilibrium state, it might cool faster. Other than superheated (above boiling point) or subcooled (below freezing point), its not clear to me how you achieve non-equilibrium water.

Adjusting the kurtosis (skew) of the velocity distribution of atoms or molecules in a bulk sample I suspect will remain a theoretical situation (the study didn't contribute much if anything).
baudrunner
4.2 / 5 (5) Oct 23, 2017
Likewise, with an ice you have the material in a very compact structure such that when heated it actually transmits that heat faster due to the atoms/molecules being that much closer together.
But they are not closer together. Water has its greatest density at 4°, and water expands on freezing. That's why ice floats.
Whydening Gyre
3 / 5 (2) Oct 23, 2017
...
Likewise, with an ice you have the material in a very compact structure such that when heated it actually transmits that heat faster due to the atoms/molecules being that much closer together.

Yeah, but...
Why does it (water ice, at least) XPAND when frozen...?
Oops.. I see baud beat me to that one....
r2vettes
1 / 5 (1) Oct 23, 2017

pretty basic thermo and fluid dynamics
f_darwin
2.3 / 5 (3) Oct 23, 2017
it is due to atomic structure of matter. To explain it would not make any sense with current model of matter which is incorrect. When correct structure understood, the reason become crystal clear. MG1
RobertKarlStonjek
3.7 / 5 (3) Oct 23, 2017
I would have thought that freezing requires some disturbance of the fluid. Cooling a liquid down slowly enough can result in a supercooled liquid.

In other words, the catalyst for freezing is the presence of some percentage of more energetic molecules and their presence is far more likely if the liquid is warm to start off with.

Note that the warmer liquid becomes cooler (passes through the cooler liquid's temperature) in the process of cooling, the only difference between the two at the cooler temperature is that there is going to be a higher percentage of molecules still at the higher temperature in the previously warmer liquid. If so, the rapid introduction of heat at one point in a supercooled liquid would freeze it...
mrlewish
3.7 / 5 (3) Oct 23, 2017
I call hogwash. There can't be any "Mpemba effect" either there are measuring errors, or analytical errors, there would even be unmeasured energies in the substances their are measuring that don't show as temp at first. No other words I don't believe a word of this.
Eikka
3 / 5 (2) Oct 24, 2017
The problem of the Mpeba effect was solved seven years ago:

When you stick a glass of hot water in the freezer, it causes warm convection airflows to travel inside the icebox and triggers the thermostat, which turns the compressor on. When you stick a cool glass of water in the box, it takes longer for the thermostat to trigger and the cooling cycle to begin, if it turns on at all.
Seeker2
not rated yet Oct 24, 2017
It was high school physics class. I put a container of cold tap water and a container of warm water out onto the window ledge and shut the window. It was a cold winter day. Really cold. The warm water froze before the cold water. Nobody believed me. I did get a passing grade though. I think it was a C+.
barakn
1 / 5 (1) Oct 24, 2017
The problem of the Mpeba effect was solved seven years ago:

When you stick a glass of hot water in the freezer, it causes warm convection airflows to travel inside the icebox and triggers the thermostat, which turns the compressor on. When you stick a cool glass of water in the box, it takes longer for the thermostat to trigger and the cooling cycle to begin, if it turns on at all.
I don't buy it. Any researcher worth their salt would control for the freezer variable by putting both the warm and cold containers in the freezer at the same time. Doesn't remove all the variables, but reduces them.
MR166
5 / 5 (1) Oct 24, 2017
Well first of all one has to separate absolute temperature change from ice formation. As was mentioned before water can be cooled below 0c and not freeze. Is the question about freezing or about the ability lose calories in a given amount of time? The best test would not involve freezing at all but would be a test of how long each solution takes to get to 1c from different starting temperatures. Measuring the temperatures of one hot and one cool glass of water in the same freezer over time would easily answer some of the questions involved.
MR166
not rated yet Oct 24, 2017
Obviously the hotter water would have a higher delta T/Time due to the higher temperature differential but it should never catch up to the temperature of the cooler water.
MR166
not rated yet Oct 24, 2017
If you ever heated a cup of water in a microwave oven you know that it can go way higher than 100c. Some times when one puts a tea bag into a cup of MW heated water it violently boils over.
barakn
1 / 5 (1) Oct 24, 2017
The hotter water will evaporate more water, leading to a smaller mass of water with a larger surface to volume ratio. So to eliminate yet one more variable, one must cover and tightly seal the containers, which will then inevitably lead to differences in pressure (and vapor pressure) in any gas phase in the container. So all air space must be eliminated. A naive mistake would be to use equal volumes of water (different density, different mass), but using the same mass will lead to different volumes. To achieve the same volume and mass, one must inject the warmer water under high pressure into its container. Ah, but then one has performed work on the warm water... Evidently there is no way to equalize more than two of volume, mass, and pressure if the temperature is different. Is it any wonder that containers of different temperature AND different mass, volume, or pressure water freeze in unexpected ways?
434a
4 / 5 (1) Oct 26, 2017
Unless you isolate the two samples some energy is going to pass from the warmer sample to the colder one, that would slow down the colder one's cooling rate.
barakn
1 / 5 (1) Oct 26, 2017
True, but your freezer should have a fan in it anyways to reduce different levels of convection from the two containers, and a radiation barrier could be placed between them, making the heat from the two containers more likely to encounter the cooling system of the freezer than each other. Your inter-container heat transfer effect would be minimal even before these corrective measures.

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