Mpemba effect

The Mpemba effect is the somewhat surprising phenomenon whereby hot water can, under certain conditions, freeze faster than cold water.

The effect is named for its rediscoverer, the Tanzanian high-school student Erasto B. Mpemba. He first noticed the effect in 1963 after observing the freezing of ice cream in cookery classes, and went on to publish experimental results with Dr. Denis G. Osborne in 1969. At first sight, the effect is contrary to Newton's law of cooling. Despite this, it has been widely reproduced although it is still poorly understood. The effect is not universal under all experimental conditions, so its exact requirements have proved difficult to specify.

It is believed that the effect arises from some interaction between:

• Evaporation reducing the volume to be frozen
• Effect of boiling on dissolved gases and ions (lime scale formation). As more dissolved material is added, the freezing point lowers and more time is required to freeze.
• Convection
• Effects from surroundings such as the insulating effects of frost
• Supercooling, initially hot water may be less likely to supercool than cold water. Therefore ice formation occurs at different final temperatures in hot and cold water.
• Different definitions of the term "freezing". Is it the physical definition of the point at which water reaches 0 C, or the point at which the water forms a visible surface layer of ice, or the point at which the entire volume of water becomes a solid block of ice?
• The material freezing in question. Mpemba's initial observations were with ice cream mixtures, not water. The anecdotal evidence for the Mpemba effect came from a variety of ice cream manufacturers and the food processing industry worldwide, for a variety of water containing foodstuffs.

The effect was known to ancient scientists such as Aristotle, and Early Modern scientists such as Francis Bacon and René Descartes. Aristotle's explanation was that this was due to 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. As the explanations of the freezing effect lacked a testable theory, modern science had reduced the observations to folklore.

Mpemba's story is often given as a cautionary parable to those who reject theories or experiments solely because they seem counterintuitive, or contradict accepted theories, or because their proponent is not an expert. In the six years between Mpemba's discovery and his publication, his ideas were rejected on a number of occasions by his physics teachers and other authorities, and it was only the reproducibility of the effect by himself and others that drove Mpemba to persist against this resistance.

External links and references

• David Auerbach, Supercooling and the Mpemba effect: when hot water freezes quicker than cold, American Journal of Physics, 63(10), 1995. (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000063000010000882000001&idtype=cvips&gifs=yes) 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? (http://math.ucr.edu/home/baez/physics/General/hot_water.html) Nov, 1998 by Monwhea Jeng (Momo), Department of Physics, University of California

"Say that the initially cooler water starts at 30° C and takes 10 minutes to freeze, while the initially warmer water starts out at 70° C. Now the initially warmer water has to spend some time cooling to get to get down to 30° C, and after that, it's going to take 10 more minutes to freeze. So since the initially warmer water has to do everything that the initially cooler water has to do, plus a little more, it will take at least a little longer, right? What can be wrong with this proof? What's wrong with this proof is that it implicitly assumes that the water is characterized solely by a single number -- the average temperature. But if other factors besides the average temperature are important, then when the initially warmer water has cooled to an average temperature of 30° C, it may look very different than the initially cooler water (at a uniform 30° C) did at the start. Why? Because the water may have changed when it cooled down from a uniform 70° C to an average 30° C. It could have less mass, less dissolved gas, or convection currents producing a non-uniform temperature distribution. Or it could have changed the environment around the container in the refrigerator. All four of these changes are conceivably important, and each will be considered separately below. So the impossibility proof given above doesn't work. And in fact the Mpemba effect has been observed in a number of controlled experiments. It is still not known exactly why this happens"de:Mpemba-Effekt