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Mpemba effect

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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 (95 °F) and 5 °C (41 °F) to maximize the effect.[1]

Historical observations

Similar behavior was observed by ancient scientists such as Aristotle,[2] and Early Modern scientists such as Francis Bacon[3] and René Descartes.[4] 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".

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 (95 °F) and the other at 100 °C (212 °F), and put them into a freezer, the one that started at 100 °C (212 °F) freezes first. Why?" only to be ridiculed by his classmates and teacher. After initial consternation, Dr. Osborne experimented on the issue back at his workplace and confirmed Erasto's finding. They published the results together in 1969.[5][6] As of 2002 Erasto Mpemba is retiring from being Principal Game Officer for the African Forestry and Wildlife Commission.[7]

Causes

Osborne observed that the top is warmer than the bottom in a beaker of water being cooled, the difference being sustained by convection. Blocking heat transfer from the top with a film of oil drastically slowed cooling. Also, the effect of dissolved air was accounted for by using boiled water. The beakers were also insulated from the bottom.

At first sight, the behaviour seems contrary to thermodynamics. Many standard physical theory effects contribute to the phenomenon, although no single explanation is conclusive. Several effects may 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? Some experiments have instead measured the time until the water reached 0°C.[8]
  • Evaporation: Reducing the volume to be frozen.[9] Evaporation is endothermic, but this alone probably does not account for the entirety of the effect.[10]
  • Convection: Accelerating heat transfers. Reduction of water density below 4 °C (39 °F) tends to suppress the convection currents that cool the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling. Higher convection in the warmer water may also spread ice crystals around faster.[11]
  • 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 that 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.[12] 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.[13]
  • The effect of heating on dissolved gases; however, this was accounted for in the original article by using boiled water.

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."[10]

This effect is a heat transfer problem,[14][15][16][17] 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.[14][15][17][16]

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." He pointed out that investigations of the phenomenon need to control a large number of initial parameters (including type and initial temperature of the water, dissolved gas and other impurities, and size, shape and material of the container, and temperature of the refrigerator) and need to settle on a particular method of establishing the time of freezing, all of which might affect the presence or absence of the Mpemba effect. The required vast multidimensional array of experiments might explain why the effect is not yet understood.[8]

References

  1. ^ How to Fossilise Your Hamster: And Other Amazing Experiments For The Armchair Scientist, ISBN 1846680441
  2. ^ Aristotle, Meteorology, 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.
  3. ^ Francis Bacon 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"
  4. ^ 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.
  5. ^ Mpemba, Erasto B.; Osborne, Denis G. (1969). "Cool?". Physics Education. 4. Institute of Physics: 172–175. doi:10.1088/0031-9120/4/3/312 begin_of_the_skype_highlighting              0031-9120/4/3/312      end_of_the_skype_highlighting begin_of_the_skype_highlighting              0031-9120/4/3/312      end_of_the_skype_highlighting. {{cite journal}}: Check |doi= value (help); no-break space character in |doi= at position 58 (help)
  6. ^ Mpemba, E B; Osborne, D G (1979). "The Mpemba effect" (PDF). Physics Education. 14. Institute of Physics: 410–412. doi:10.1088/0031-9120/14/7/312.
  7. ^ "Report of the 14th session of the Working Party on the Management of Wildlife and Protected Areas" (PDF).
  8. ^ a b Ball, P. (2006). "Does hot water freeze first?" ([dead link] – Scholar search). Physics World. 19(4): 19–21. {{cite journal}}: External link in |format= (help); Unknown parameter |month= ignored (help)
  9. ^ Kell, G. S. (1969). "The freezing of hot and cold water". Am. J. Phys. 37: 564–565. doi:10.1119/1.1975687.
  10. ^ a b Jeng, Monwhea (2006). "Hot water can freeze faster than cold?!?". American Journal of Physics. 74 (6): 514. doi:10.1119/1.2186331. arXiv:physics/0512262v1. Retrieved 2008-03-18.
  11. ^ CITV Prove It! Series 1 Programme 13
  12. ^ 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. doi:10.1016/j.physa.2007.10.029.
  13. ^ Katz, Jonathan (2006). "When hot water freezes before cold". {{cite web}}: Unknown parameter |month= ignored (help)
  14. ^ a b Knight, Charles A. (1996-05). "The Mpemba effect: the freezing times of hot and cold water". American Journal of Physics. 64 (5): 524. doi:10.1119/1.18275. {{cite journal}}: |access-date= requires |url= (help); Check date values in: |date= (help); Cite has empty unknown parameter: |coauthors= (help)
  15. ^ a b Auerbach, David (1995). "Supercooling and the Mpemba effect: when hot water freezes faster than cold". American Journal of Physics. 63 (10): 882–885. doi:10.1119/1.18059. {{cite journal}}: |access-date= requires |url= (help); Cite has empty unknown parameter: |coauthors= (help)
  16. ^ a b Dorsey, N. Ernest (1948-11). "The Freezing of Supercoold Water". Transactions of the American Philosophical Society. 38 (3): 247–328. doi:10.2307/1005602. {{cite journal}}: |access-date= requires |url= (help); Check date values in: |date= (help); Cite has empty unknown parameter: |coauthors= (help)
  17. ^ a b 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. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)

Bibliography

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