back             Detailed explanations          home

If the hot water starts at 99.9° C, and the cold water at 0.01° C, then clearly under those circumstances, the initially cooler water will freeze first. However, under some conditions the initially warmer water will freeze first -- if that happens, you have seen the Mpemba effect. But you will not see the Mpemba effect for just any initial temperatures, container shapes, or cooling conditions.

Evaporation
One explanation of the effect is that as the hot water cools, it loses mass to evaporation. With less mass, the liquid has to lose less heat to cool, and so it cools faster. With this explanation, the hot water freezes first, but only because there's less of it to freeze. Calculations done by Kell in 1969 [11] showed that if the water cooled solely by evaporation, and maintained a uniform temperature, the warmer water would freeze before the cooler water.

This explanation is solid, intuitive, and undoubtedly contributes to the Mpemba effect in most physical situations. However, many people have incorrectly assumed that it is therefore "the" explanation for the Mpemba effect. That is, they assume that the only reason hot water can freeze faster than cold is because of evaporation, and that all experimental results can be explained by the calculations in Kell's article. However, the experiments currently do not bear out this belief. While experiments show evaporation to be important [13], they do not show that it is the only mechanism behind the Mpemba effect. A number of experimenters have argued that evaporation alone is insufficient to explain their results [5,9,12] -- in particular, the original experiment by Mpemba and Osborne measured the mass lost to evaporation, and found it substantially less that the amount predicted by Kell's calculations [5,9]. And most convincingly, an experiment by Wojciechowski observed the Mpemba effect in a closed container, where no mass was lost to evaporation.

Dissolved Gasses
Another explanation argues that the dissolved gas usually present in water is expelled from the initially hot water, and that this changes the properties of the water in some way that explains the effect. It has been argued that the lack of dissolved gas may change the ability of the water to conduct heat, or change the amount of heat needed to freeze a unit mass of water, or change the freezing point of the water by some significant amount. It is certainly true that hot water holds less dissolved gas than cold water, and that boiled water expels most dissolved gas. The question is whether this can significantly affect the properties of water in a way that explains the Mpemba effect. As far as I know, there is no theoretical work supporting this explanation for the Mpemba effect.

Indirect support can be found in two experiments that saw the Mpemba effect in normal water which held dissolved gasses, but failed to see it when using degassed water [10,14]. However, an attempt to measure the dependence of the enthalpy of freezing on the initial temperature and gas content of the water was inconclusive [14].

One problem with this explanation is that many experiments pre-boiled both the initially hot and initially cold water, precisely to eliminate the effect of dissolved gasses, and yet they still saw the effect [5,13]. Two somewhat unsystematic experiments found that varying the gas content of the water made no substantial difference to the Mpemba effect [9,12].

Convection
It has also been proposed that the Mpemba effect can be explained by the fact that the temperature of the water becomes non-uniform. As the water cools, temperature gradients and convection currents will develop. For most temperatures, the density of water decreases as the temperature increases. So over time, as water cools we will develop a "hot top" -- the surface of the water will be warmer than the average temperature of the water, or the water at the bottom of the container. If the water loses heat primarily through the surface, then this means that the water should lose heat faster than one would expect based just on looking at the average temperature of the water. And for a given average temperature, the heat loss should be greater the more inhomogeous the temperature distribution is (that is, the greater the range of the temperatures seen as we go from the top to the bottom).

How does this explain the Mpemba effect? Well, the initially hot water will cool rapidly, and quickly develop convection currents and so the temperature of the water will vary greatly from the top of the water to the bottom. On the other hand, the initially cool water will have a slower rate of cooling, and will thus be slower to develop significant convection currents. Thus, if we compare the initially hot water and initially cold water at the same average temperature, it seems reasonable to believe that the initially hot water will have greater convection currents, and thus have a faster rate of cooling. To consider a concrete example, suppose that the initially hot water starts at 70° C, and the initially cold water starts at 30° C. When the initially cold water is at an average 30° C, it is also a uniform 30° C. However, when the initially hot water reaches an average 30° C, the surface of the water is probably much warmer than 30° C, and it will thus lose heat faster than the initially cold water for the same average temperature. Got that? This explanation is pretty confusing, so you might want to go back and read the last two paragraphs again, paying careful attention to the difference between initial temperature, average temperature, and surface temperature.

At any rate, if the above argument is right, then when we plot the average temperature versus time for both the initially hot and initially cold water, then for some average temperatures the initially hot water will be cooling faster than the initially cold water. So the cooling curve of the initially hot water will not simply reproduce the cooling curve of the initially cold water, but will drop faster when in the same temperature range.

This shows that the initially hot water goes faster, but of course it also has farther to go. So whether it actually finishes first (that is, reaches 0° C first), is not clear from the above discussion. To know which one finishes first would require theoretical modelling of the convection currents (hopefully for a range of container shapes and sizes), which has not been done. So convection alone may be able to explain the Mpemba effect, but whether it actually does is not currently known. Experiments on the Mpemba effect have often reported a "hot top" [5,8,10], as we would expect. Experiments have been done that looked at the convection currents of freezing water [27,28], but their implications for the Mpemba effect are not entirely clear.

It should also be noted that the density of water reaches a maximum at four° C. So below four° C, the density of water actually decreases with decreasing temperature, and we will get a "cold top." This makes the situation even more complicated.

Surroundings
The initially hot water may change the environment around it in some way that makes it cool faster later on. One experiment reported significant changes in the data simply upon changing the size of the freezer that the container sat in [7]. So conceivably it is important not just to know about the water and the container, but about the environment around it.

For example, one explanation for the Mpemba effect is that if the container is resting on a thin layer of frost, than the container holding the cold water will simply sit on the surface of the frost, while the container with the hot water will melt the frost, and then be sitting on the bottom of the freezer. The hot water will then have better thermal contact with the cooling systems. If the melted frost refreezes into an ice bridge between the freezer and the container, the thermal contact may be even better.

Obviously, even if this argument is true, it has fairly limited utility, since most scientific experiments are careful enough not to rest the container on a layer of frost in a freezer, but instead place the container on a thermal insulator, or in a cooling bath. So while this proposed mechanism may or may not have some relevance to some home experiments, it's irrelevant for most published results.

Supercooling
Finally, supercooling may be important to the effect. Supercooling occurs when water freezes not at 0° C, but at some lower temperature. This happens because the statement that "water freezes at 0° C" is a statement about the lowest energy state of the water -- at less than 0° C, the water molecules "want" to be arranged as an ice crystal. This means that they will stop zooming around randomly as a liquid, and instead form a solid ice lattice. However, they don't know how to form themselves as an ice lattice, but need some little irregularity or nucleation site to tell them how to rearrange themselves. Sometimes, when water is cooled below 0° C, the water will not see a nucleation site for some time, and then water will cool below 0° C without freezing. This happens quite often. One experiment found that the initially hot water would supercool only a little (say to about -2° C), while the initially cold water would supercool more (to around -8° C) [12]. If true, this could explain the Mpemba effect because the initially cold water would need to "do more work" -- that is, get colder -- in order to freeze.

However, this also cannot be considered "the" sole explanation of the Mpemba effect. First of all, as far as I know, this result has not been independently confirmed. The experiment described above [12] only had a limited number of trials, so the results found could have been a statistical fluke.

Second, even if the results are true, they do not fully explain the Mpemba effect, but replace one mystery with another. Why should initially hot water supercool more than initially cold water? After all, once the water has cooled to the lower temperature, one would generally expect that the water would not "remember" what temperature it used to be. One explanation is that the initially hot water has less dissolved gas than the initially cold water, and that this affects its supercooling properties (see Dissolved Gasses for more on this). The problem with this explanation is that one would expect that since the hot water has less dissolved gas, and thus less nucleation sites, it would supercool more, not less. Another explanation is that when the initially hot water has cooled down to 0° C (or less), its temperature distribution throughout the container varies more than the initially cold water (see Convection for more on this). Since temperature shear induces freezing [26], the initially hot water supercools less, and thus freezes sooner.

Third, this explanation cannot work in all of the experiments, because many of the experiments chose to look not at the time to form a complete block of ice, but the time for some part of the water to reach 0° C[7,10,13] (or perhaps the time for a thin layer of frost to form on the top [17]). While [12] says that it is only a "true Mpemba effect" if the hot water freezes entirely first, other papers have defined the Mpemba effect differently. Since the precise time of supercooling is inherently unpredictable (see [26], e.g.), many experiments have chosen to measure not the time for the sample to actually become ice, but the time for which the sample's equilibrium ground state is ice -- that is, the time when the top of the sample reached 0° C [7,10,13]. The supercooling argument does not apply to these experiments.

IV References
HISTORICAL
1. Aristotle in E. W. Webster, "Meteorologica I", Oxford U. P., Oxford, 1923, pgs 348b--349a
2. Bacon F 1620 Novum Organum Vol VIII of "The Works of Francis Bacon" 1869 ed. J Spedding, R. L. Ellis and D. D. Heath (New York) pp235, 337, quoted in T. S. Kuhn 1970 "The Structure of Scientific Revolutions" 2nd edn (Chicago: University of Chicago Press), pg 16
3. Descartes R 1637, "Les Meteores" 164 published with "Discours de la Methode" (Leyden: Ian Marie) 1637, quoted in "Oeuvres de Descartes" Vol. VI 1902 ed. Adam and Tannery (Paris: Leopold Cerf) pg 238 (trans. F. C. Frank)
4. Clagett, Marshall, "Giovanni Marliani and Late Medieval Physics", AMS press, Inc., New York, 1967, pgs 72, 79, 94
EXPERIMENTS ON THE MPEMBA EFFECT
5. Mpemba and Osborne, Phys. Educ., "Cool", vol. 4, pgs 172--5 (1969)
6. Ahtee, Phys. Educ., "Investigation into the Freezing of Liquids", vol. 4, pgs 379--80 (1969)
7. I. Firth, Phys. Educ., "Cooler?", vol. 6, pgs 32--41 (1979)
8. E. Deeson, Phys. Educ., "Cooler-lower down", vol. 6, pgs 42--44 (1971)
9. Osborne, "Mind on Ice", Phys. Educ. vol. 14, pgs 414--17 (1979)
10. M. Freeman, "Cooler Still", Phys. Educ. vol. 14, pgs 417--21 (1979)
11. G.S. Kell, "The Freezing of Hot and Cold Water", American Journal of Physics, vol. 37, #5, pgs 564--5, (May 1969)
12. D. Auerbach, "Supercooling and the Mpemba effect: When hot water freezes quicker than cold", American Journal of Physics, vol. 63, #10, pgs 882--5, (Oct 1995)
13. J. Walker, "The Amateur Scientist", Sci. Am., vol. 237, #3, pgs 246--7, (Sept. 1971)
14. B. Wojciechowski, "Freezing of Aqueous Solutions Containing Gases", Cryst. Res. Technol., vol. 23, #7, pgs 843--8 (1988)
GENERAL DISCUSSION ON THE MPEMBA EFFECT
15. New Scientist, vol. 42, #652, 5 June 1969, pg 515
16. New Scientist, 2 Dec 1995, pg 22
17. New Scientist, vol. 42, #654, 19 June 1969, pgs 655--6
18. New Scientist, vol. 43, #657, 10 July 1969, pgs 88--9
19. New Scientist, vol. 43, #658, 17 July 1969, pgs 158--9
20. New Scientist, vol. 43, #658, 25 Sept. 1969, pg 662
21. New Scientist, vol. 44, #672, 23 Oct. 1969, pg 205
22. New Scientist, vol. 45, #684, 15 Jan. 1970, pgs 125--6
23. New Scientist, vol. 45, #686, 29 Jan. 1970, pgs 225--6
24. New Scientist, 2 Dec. 1995, pg 57
25. New Scientist, 16 Mar. 1996, pg 58
RELATED ARTICLES
26. J. Elsker, "The Freezing of Supercooled Water", Journal of Molecular Structure, vol. 250, pgs 245--51 (1991)
27. R.A. Brewster and B. Gebhart, "An experimental study of natural convection effects on downward freezing of pure water", Int. J. Heat Mass Trans. vol. 31, #2, pgs 331--48 (1988)
28. R.S. Tankin and R. Farhadieh, "Effects of Thermal Convection currents on Formation of Ice", Int. J. Heat Mass Trans., vol. 14, pgs 953

Modified for private educational use only. Original Source Copyright
 Written Nov, 1998 by Monwhea Jeng (Momo),
Department of Physics, University of California