Mpemba effect

The Mpemba effect is the observation that, in some specific, fairly common circumstances, hotter water freezes faster than colder water.

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The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in the classroom of Eugene Marschall at Mkwawa Secondary (formerly High) School, Iringa, Tanzania, where Mpemba was a student. Eugene Marschall, a member of the Teachers for East Africa/TEA program, taught chemistry and physics at this school from 1965 to 1967. Mpemba first noticed the effect in 1963 after his account of the freezing of hot ice cream mix in cookery classes, and went on to publish experimental results with Dr. Denis G. Osborne in 1969.

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

• Different definition of freezing (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. 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.
• The insulating effects of frost
• The effect of boiling on dissolved gases
• 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. However, supercooling tends not to be significant where there are particles, which act as nuclei for ice crystals, thus precipitating rapid freezing.
• The effect of solutes such as calcium and magnesium carbonate.

According to an article by Monwhea Jeng, there is no unique explanation yet for why, in some specific circumstances, hotter water freezes faster than colder water. The article makes no attempt to focus on the relevant transport phenomena concepts such as temperature and fluid flow fields. Indeed when temperature fields are introduced, the author states:

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. The greatest difficulties with CFD are with turbulent flow; with laminar (streamline) flow, as we have in this case, there is much better consistency between independent analyses, and a CFD analysis could be expected to be illuminating.

This effect is a heat transfer problem, 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.

Similar behavior may have been observed by ancient scientists such as Aristotle, and Early Modern scientists such as Francis Bacon and René Descartes. Aristotle's explanation involved a physical 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". He used the concept of antiperistasis to provide evidence for his conjecture that human bodies and bodies of water were hotter in the winter than in the summer, a theory that was later disproved by Medieval and Renaissance observations.

External links and references

• Cool? - EB Mpemba, DG Osborne - Physics Education, 1969
• David Auerbach, Supercooling and the Mpemba effect: when hot water freezes quicker than cold, American Journal of Physics, 63(10), 1995. Auerbach attributes the Mpemba effect to differences in the behaviour of supercooled formerly hot water and formerly cold water.
• Can hot water freeze faster than cold water? Nov, 1998 by Monwhea Jeng (Momo), Department of Physics, University of California
• The Straight Dope: Which freezes faster, hot water or cold water? by Cecil Adams, The Straight Dope, Chicago Reader Inc.
• HyperPhysics: The Mpemba Effect
• Charles A. Knight, The MPEMBA effect: The freezing times of hot and cold water, American Journal of Physics -- May 1996 -- Volume 64, Issue 5, p. 524
• The Mpemba Effect: Hot Water Freezes before Cold
• Other citations to the Mpemba Effect.
• Monwhea Jeng, 2006. "The Mpemba effect: When can hot water freeze faster than cold?" American Journal of Physics, volume 74, number 6, page 514. preprint
• Why water freezes faster after heating (New Scientist)

Bibliography

• Ball, P. (2006) "Does hot water freeze first?", Physics World, 19(4), April, 19-21