# Mpemba effect

The Mpemba effect is the observation that, in certain specific circumstances, warmer water freezes faster than colder water. New Scientist recommends starting the experiment with containers at 35°C and 5°C to maximise the effect.[1]

## Origin

The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in 1963 in Form 3 of Magamba Secondary School, Tanzania when freezing hot ice cream mix in cookery classes and noticing that they froze before cold mixes. After passing his O-level examinations, he became a student at Mkwawa Secondary (formerly High) School, Iringa, Tanzania. The headmaster invited Dr. Denis G. Osborne from the University College in Dar Es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question "If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a refrigerator, the one that started at 100°C freezes first. Why?" only to be ridiculed by his classmates. After initial consternation, Dr. Osborne confirmed Erasto's finding and they published the results together in 1969.[2][3] Erasto Mpemba currently works for the African Forestry and Wildlife Commission.[4]

## Causes

At first sight, the behaviour seems contrary to thermodynamics. However, the Mpemba effect can be explained with standard physical theory. Many effects can contribute to the observation, depending on the experimental set-up:

• Definition of frozen: Is it the physical definition of the point at which water forms a visible surface layer of ice, or the point at which the entire volume of water becomes a solid block of ice?
• Evaporation: Reducing the volume to be frozen.[5] Evaporation is endothermic.
• Convection: Accelerating heat transfers. Reduction of water density below 4°C tends to suppress the convection currents cooling the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling.
• Frost: Has insulating effects. The lower temperature water will tend to freeze from the top, reducing further heat loss by radiation and air convection, while the warmer water will tend to freeze from the bottom and sides because of water convection. This is disputed as there are experiments which account for this factor.
• Supercooling: It is hypothesized that cold water, when placed in a freezing environment, supercools more than hot water in the same environment, thus solidifying slower than hot water.[6] However, supercooling tends to be less significant where there are particles that act as nuclei for ice crystals, thus precipitating rapid freezing.
• Solutes: The effects of calcium, magnesium carbonate among others.[7]
• The effect of heating on dissolved gases.

### Scalar functionality

According to an article by Monwhea Jeng: "Analysis of the situation is now quite complex, since we are no longer considering a single parameter, but a scalar function, and computational fluid dynamics (CFD) is notoriously difficult."[8]

This effect is a heat transfer problem,[9][10][11][12] and therefore well suited to be studied from a transport phenomena viewpoint, based on continuum mechanics. When heat transfer is analyzed in terms of partial differential equations, whose solutions depend on a number of conditions, it becomes clear that measuring only a few lumped parameters, such as the water average temperature is generally insufficient to define the system behaviour, since conditions such as geometry, fluid properties and temperature and flow fields play an important role. The counterintuitiveness of the effect, if analyzed only in terms of simplified thermodynamics illustrates the need to include all the relevant variables and use the best available theoretical tools when approaching a physical problem.[9][10][12][11]

## Recent view of the Mpemba effect

A reviewer for Physics World writes, "Even if the Mpemba effect is real - if hot water can sometimes freeze more quickly than cold - it is not clear whether the explanation would be trivial or illuminating."[13]

## Historical observations

Similar behavior may have been observed by ancient scientists such as Aristotle[14], and Early Modern scientists such as Francis Bacon[15] and René Descartes[16]. Aristotle's explanation involved an erroneous property he called antiperistasis, defined as "the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality".

## References

1. How to Fossilise Your Hamster: And Other Amazing Experiments For The Armchair Scientist, ISBN 1846680441
2. Mpemba, Erasto B.; Osborne, Denis G. (1969), "Cool?", Physics Education, Institute of Physics, 4: 172–175, doi:10.1088/0031-9120/4/3/312
3. "The Mpemba effect" (PDF), Physics Education, Institute of Physics, 14: 410–412, 1979, doi:10.1088/0031-9120/14/7/312
4. Kell, G. S. (1969), "The freezing of hot and cold water", Am. J. Phys., 37: 564–565
5. S. Esposito, R. De Risi and L. Somma (2008), "Mpemba effect and phase transitions in the adiabatic cooling of water before freezing", Physica A, 387: 757–763
6. Katz, Jonathan (April 2006). "When hot water freezes before cold".
7. Jeng, Monwhea (2006). "Hot water can freeze faster than cold?!?". American Journal of Physics. 74 (6): 514. arXiv:physics/0512262v1. Retrieved 2008-03-18.
8. Knight, Charles A. (1996-05). "The Mpemba effect: the freezing times of hot and cold water". American Journal of Physics. 64 (5): 524. Check date values in: `|date=` (help); `|access-date=` requires `|url=` (help)
9. Auerbach, David (1995). "Supercooling and the Mpemba effect: when hot water freezes faster than cold". American Journal of Physics. 63 (10): 882–885. `|access-date=` requires `|url=` (help)
10. Dorsey, N. Ernest (1948-11). "The Freezing of Supercoold Water". Transactions of the American Philosophical Society. 38 (3): 247–328. doi:10.2307/1005602. Check date values in: `|date=` (help); `|access-date=` requires `|url=` (help)
11. Dorsey, N. Ernest (1940). Properties of ordinary water-substance in all its phases: water vapor, water, and all the ices. New York: Reinhold Publishing Corporation.
12. Ball, P. (April 2006). "Does hot water freeze first?". Physics World. 19(4): 19–21.
13. Aristotle, Metereology, Book 1 "The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun. So the inhabitants of Pontus when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their reeds that it may freeze the quicker, for they use the ice like lead to fix the reeds". Trans. by E. W. Webster.
14. Novum Organum, Lib. II, L, "slightly tepid water freezes more easily than that which is utterly cold". In the original Latin "aqua parum tepida facilius conglacietur quam omnino frigida"
15. Descartes, Les Meteores, Discours Premier "One can see by experience that water that has been kept on a fire for a long time freezes faster than other, the reason being that those of its particles that are least able to stop bending evaporate while the water is being heated". In the original French "Et on peut voir aussy par experience que l'eau qu'on a tenue longuement sur le feu se gele plutot que d'autre, dont la raison est que celles de ses parties, qui peuvent le moins cesser de se plier, s'evaporent pendant qu'on la chauffe." Descartes' explanation here relates to his theory of vortices.