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Erasto Mpemba

Erasto Mpemba

The Mpemba Effect

"The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner"

Aristotle (350 BC)    

 

"If two systems are cooled, the water that starts hotter may freeze first”.

Mpemba & Osborne (1969)  [1388]  

 

V Hot water may freeze faster than cold water

V Grossly misleading paper

Hot water may freeze faster than cold water

The ability of hot water to freeze faster than cold seems counter-intuitive as it would seem that hot water must first become cold water and therefore the time required for this will always delay its freezing relative to cold water. However experiments show that unstirred hot water (for example, 90 °C) does often (but by no means always) appear to freeze faster than the same amount of unstirred cold water (for example, 18 °C) under otherwise identical conditions [158] (see also graph below left [2810] ). This has been recognized even as far back as Aristotle in the 4th century BC [2043] but was brought to the attention of the scientific community by the perseverance of Erasto Mpemba [1388] a Tanzanian schoolboy, a who refused to reject his own evidence, or bow to disbelieving mockery, that he could freeze ice cream faster if he warmed it first.

 

Unfortunately, the Mpemba effect (Hot water may freeze faster than cold water) is not well formulated for precise testing as the temperatures are not stated nor is the amount of freezing. It was never meant to be precisely determinable, as are other anomalies such as the temperature of maximum density, but more as an interesting natural phenomenon that has been noticed since the beginning of recorded history and contains an interesting and edifying story for students. No standard experimental setup is described with various cooling regimes being used causing differences in observations and explanations depending on, for example, the base cooling temperature. Generally, it is accepted that typical difference in start temperatures may be about 40°C and the extent of freezing is that it should be visibly extensive but not complete. In the definition, the word 'may' is fairly interpreted as 'more often than not', and certainly not as 'always'.

 

Proof of the Mpemba effect, from [2810]

 

Proof of the Mpemba effect, redrawn from [2810], the red line is a guide for the eye

A number of explanations have been put forward [959, 1921]. b One that has gained some support is that there is sufficient evaporation from the hot water that this causes faster cooling plus a reduction in mass, so faster cooling (even to the extent of the existence of a cross-over temperature between, initially hot and initially colder, cooling curves [1716]) and freezing [1390]. There does not seem to be sufficient mass lost in experiments to support such an explanation to be the sole cause, however, and the Mpemba effect is apparent even when the vessel has a lid. Related to this explanation, part of the cause may be due to the variously sized and persistent convective currents created when hot water cools in different experimental set-ups. The importance of gas content has been shown to be involved with high statistical certainty [2810]. Another scenario concerns the O:H–O hydrogen bond possessing memory, whose thermal relaxation defines intrinsically the rate of energy emission [2227]. This hypothesis, although innovative, needs further substantiation as individual bonds between neighboring oxygen atoms (of H2O molecules) have only fleeting lifetimes, d this explanation describes an effect, which is apparently insensitive to many factors known to have effects such as gas content, convection and evaporation, and the described cooling curves have recently been challenged [2809].

Hot water freezing before cold

 

Graph showing hot water freezing before cold

 

The initial amount of ice produced

on nucleation is about 1.3% for

every degree of supercooling.

 

 

The most likely scenario (described in [158], disputed [1415], but later supported [2047]) is that the degree of supercooling is greater, under some circumstances, in initially-cold water than initially-hot water. The initially-hot water appears to freeze at a higher temperature (less supercooling) but less of the apparently frozen ice is solid and a considerable amount is trapped liquid water. Initially-cold water freezes at a lower temperature to a more completely solid ice with less included liquid water; the lower temperature causing intensive nucleation and a faster crystal growth rate. If the freezing temperature is kept about -6 °C then the initially-hot water is most likely to (apparently) freeze first. If freezing is continued, initially-cold water always completely freezes before initially-hot water. After coming to this conclusion, it was found that this explanation for the Mpemba effect was first experimentally determined in 1775 [1861]. Many factors, including the temperature of the cooling bath, the material in the cooling bath and the physical dimensions and characteristics of the vessels all affect both the rate of cooling and whether, or not, supercooling occurs [2281] such that these factors must be clearly stated and controlled. Such factors must be taken into account when comparing different experimental procedures.

 

Why initially-cold water supercools more is explained in terms of the gas concentration and the clustering of water (an effect on entropy [2961]). Certainly, water behaves differently, and possesses a different structuring, at the same temperature depending upon whether it is being heated or cooled [1697]. Icosahedral clusters do not readily allow the necessary arrangement of water molecules to enable hexagonal ice crystal initiation; such clustering is the cause of the facile supercooling of water. Water that is initially-cold will have the maximum (equilibrium) concentration of such icosahedral clustering. Initially-hot water has lost much of its ordered clustering (higher entropy [2961]) and, if the cooling time is sufficiently short, this will not be fully re-attained before freezing. Experiments on the low-density water around macromolecules have shown that such clustering processes may take some time [4]. Also of relevance here is that the formation of clathrate ices, which have structures closely related to the icosahedral clusters, behaves in an opposite manner. Thus, their supercooling (before clathrate ice formation) from hot water is far greater than that from cold water [1391]. c The basis of this explanation has also been given, more recently, based on differences in hydrogen bonding within clusters [2999].

 

Recently, it has been discovered that the charge on the liquid interface affects the freezing point of supercooled water [1737]. As the surfaces of nanobubbles are thought to be negative, such nanobubbles, with their extensive surface area are expected to increase supercooling. Heating water containing nanobubbles is expected to destroy nanobubbles as they grow in size, due to the lower gas solubility at higher temperatures, and dissipate. The Mpemba effect is then simply explained by the loss of nanobubbles in the hot water which are kinetically too slow to reform on cooling.

 

It is also possible that dissolved gases may encourage supercooling ([2810]; mouse over figure above to see the effect of removing the gasses) by (1) increasing the degree of structuring, by hydrophobic hydration, in the previously-cold water relative to the gas-reduced previously-hot water (the critical effect of low concentrations of dissolved gas on water structure is reported in [294]; re-equilibration taking several days) and (2) increasing the pressure as gas comes out of solution when the water starts to crystallize, so lowering the melting point and reducing the tendency to freeze (see the guest book). Also, the presence of tiny gas bubbles (cavities produced on heating), with their more extensive liquid-gas interface, may increase the rate of nucleation, so reducing supercooling [428]. Recently another possibility has been described depending on changes in any dissolved material with temperature (such as the reduction in bicarbonate in heated 'hard' water), but this has not yet been experimentally tested [1014]. The rationale for the Mpemba effect, in this case, concerns differences in the solute concentration at the ice-liquid interface causing a localized lowering of the melting point [1014].

Grossly misleading paper

Rarely do I take the trouble to criticize scientific publications but a paper that recently appeared in Nature, Scientific Reports [2809], together with its BBC radio commentary, are highly misleading and require a response. e The Mpemba effect concerns supercooling and the formation of ice whereas this paper only involves cooling to 0°C or 4°C but (importantly) avoids supercooling and ice formation and so, in spite of its title, is not concerned experimentally with the Mpemba effect but with the simple cooling of liquid water. The paper does show that cold water cools to 0°C faster than hot water and this seems to support the view given above that the Mpemba effect is down to differences in the supercooling of previously hot and cold liquid water. The paper [2809] neither proves nor disproves the Mpemba effect;' Hot water may freeze faster than cold water'. e

 

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Footnotes

a Erasto Mpemba is now enjoying his retirement from being Principal Game Officer in Tanzania. He describes his discovery on YouTube. [Back

 

b The winning entry in the Royal Society of Chemistry competition concerning the Mpemba effect is given here. [Back

 

c The gas-hydrate clathrate ices also show an anomalously low dissociation rate [1539] that fits well with this hypothesis. Later work has shown ambiguous results [2817]. [Back

 

d The O···H-O hydrogen bond has a lifetime of ~ns and the O···H-O covalent bond has a lifetime of ~ms. Assoc Prof Sun Changqing has strongly disagreed with my assessment of this area of science stating (rather obtusely) 'Fleeting times have nothing to do with the relaxation time for the energy "emission-transportation-dissipation" in the "source-path-drain" cycle system at all. ', Please see his papers [2227] for further details of his work. [Back

 

e Burridge and Linden’s paper [2809] misstates what is known as the Mpemba effect [2877]. In their Abstract the authors state that the Mpemba effect is “the assertion that it is quicker to cool water to a given temperature when the initial temperature is higher. However, the early paper by Mpemba and Osborne  [1388] states “If two systems are cooled, the water that starts hotter may freeze first”. Follow up papers (for example [158, 959, 1921, 2810]) always have included the process of freezing within the Mpemba effect. In the Royal Society of Chemistry’s competition inviting discussion of the effect in 2012, the Mpemba effect was defined as  “The Mpemba effect is the phenomenon where hot water freezes quicker than cold water” and the competition received 22,000 entrants. A similar invitation from the Journal 'Temperature' (ISSN: 2332-8940) gave its definition as "warm water freezes more quickly than cold water" [959c]. All previous discussions of the Mpemba effect have involved a visible formation of ice and include the observation that hot water initially freezes faster than cold water, at least some of the time.

 

Burridge and Linden’s paper takes the view that “Broadly speaking, when two samples of water are cooled to the same temperature, in the same manner with the two samples being identical except for their initial temperature, and the initially hotter sample cools in less time, one can consider the Mpemba effect to have been observed” This mis-definition of the Mpemba effect considers cooling to a low temperature to be (mistakenly) the same as cooling to, and including visible ice formation. Their paper goes on to present experimental results, but only for the cooling process to temperatures well above those of freezing water and certainly not including the freezing process which was never observed.

 

Burridge and Linden go on to dismiss all prior studies that included supercooling and freezing with a blanket statement that they are not meaningful. In so doing they dismiss the observations of many scientists including G. S. Kell [1390], without their own experimental evidence and with no support from any prior experiments. Of the Vynnycky and. Kimura study [158], they state “exhibited no evidence of the Mpemba effect but the paper actually states the contrary in its Abstractthe effect of supercooling leads to a spread in the experimental freezing times, giving results that constitute evidence of the occurrence of the Mpemba effect”. Burridge and Linden disregard data in this paper as it “cannot be fairly included in our analysis, since we exclude the freezing process”.

 

It is unsurprising that Burridge and Linden state “We conclude that despite our best efforts, we were not able to make observations of any physical effects which could reasonably be described as the Mpemba effect” as they never performed any experiments nor made any associated observations in any attempt to do so. It is also clear from their paper that Burridge and Linden misunderstand the correct and widely-understood definition of the Mpemba effect

 

There have been many attempts to explain the Mpemba effect but supercooling has often been cited. 30 years ago Wojciechowski et al [2810] concluded that dissolved gasses caused this supercooling anomaly with persuasive statistically-meaningful (P < 0.001) experimental results that Burridge and Linden failed to find.

 

To conclude, Burridge and Linden’s paper neither proves nor disproves the Mpemba effect and has a misleading Title and Abstract.

 

Burridge and Linden's Reply

Burridge has replied to my points and I give his unedited reply below even though I believe it to be mistaken, misleading and highly contentious. It also misstates comments I have made concerning ice formation.

 

'Thank you for sending these papers. I met with Professor Paul Linden, who as my co-author is well aware of all of our communications, and we discussed your opinions and the specific papers which you consider to be evidence.

 

We regard the results of the 2015 paper published by the group at KTH as very strong evidence that our conclusions are entirely valid. These experiments were carried out carefully, were well documented and used current technology to improve precision - they show evidence that the Mpemba effect can be observed but also strong evidence that the Mpemba effect cannot be observed in a repeatable meaningful way paper - this is precisely what we concluded.

 

With regards to the paper from the 1980's, I am disappointed that I had not found this paper prior to publishing our article - I would have liked to include reference to it, and comment upon it. However, Paul and I agree that it would not have changed our conclusions nor the degree of certainty with which they hold true.

 

The data included is interesting. However, like much of the work published on the Mpemba effect, it is fundamentally flawed. The paper does not clearly define nor describe details underpinning the matter of primary concern, i.e.  how the to time for freezing to first occur was robustly determined. There are many issues concerning the formation of ice crystals at the smallest scale which are not discussed, for example, as you pointed out they can often melt back into the liquid state before ultimately freezing again. These, and numerous other experimental issues, result in observations of the time-for-freezing-to-first-occur being notoriously difficult to make in a robust and repeatable manner. Without discussion of all of the experimental difficulties, mitigating procedures, and evidence as to the extent of their precise effects, it is impossible to know if these results are statistically significant or not. As such, we still feel entirely able to stand by the conclusions of our paper.

 

However, if you are able to repeat this data with documented evidence of all mitigating procedures, error bounds and uncertainties then we would be delighted to review this data and once again consider whether our conclusions remain valid.

 

In the absence of this data, I will cease to respond to any communications, since without this data our communications have ceased to be fruitful.'

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This commentary was established in 2006 and put on its own page in 2014 being last updated by Martin Chaplin on 5 November, 2017


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