Thursday, May 13, 2010

Mpemba Effect

In 1963, somewhere in Tanzania, a secondary school had just one refrigerator and hundreds of students competed for getting a slot in refrigerator to make an ice-cream. For little Mpemba, ice-cream was a craze but he was often left unsatisfied as the time-slot he used to get in refrigerator wasn’t longer enough for ice-cream to be prepared. He wondered, if he could figure out a way to freeze the water faster. On one fine day, Mpemba experimented with something totally unexpected. He kept the boiled water in the freezer instead of cold water and to his surprise, it got froze within his allotted slot. Next day, he prepared the ice-cream using mixture of milk and warm water. To his surprise, the mixture of milk and warm water froze into ice-cream much faster than mixture of milk and cold water. Now, Mpemba was able to prepare the ice-cream in much lesser duration than his friends. Soon, the news spread around the school. Mpemba asked his physics teacher for scientific explanation for warm water to freeze faster than cold water. The physics teacher had no answer to it.

Mpemba didn’t give up. His curiosity grew with time. During his primary school, he came across something called ‘Newton’s law of cooling’, which clearly stated the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. In simpler words it meant, it takes lesser time to cool a colder body than a hotter body. Soon Mpemba realized, by no means his observations can be correct as per the accepted laws of theoretical physics. However, he was still able to prove it experimentally. Mpemba obsession to understand the real reason behind his observations didn’t go well with the physics teachers at his school. When Mpemba insisted, physics teacher told him ‘All I can say is that is Mpemba’s physics and not the universal physics’. Ever since then, everything Mpemba asked any question or made any mistake, it was criticized as ‘that is Mpemba’s mathematics’ or ‘that is Mpemba’s physics’. But all the criticisms didn’t stop Mpemba from further experimenting.

Six years later in 1969, Dr. Osborne, a physics professor visited Mpemba’s school. At the end of his talk, Mpemba innocently asked the question that has haunted him from last six years. He asked “why water at 100°C freezes faster than water at 35°C? Dr. Osborne couldn’t think of any possible explanation to Mpemba’s question. Sometime later, out of curiosity, Dr. Osborne asked his lab assistant to conduct the experiment which Mpemba suggested. He was astonished seeing the results. The lab assistant reported that, hot water froze first and the same result was obtained even after several attempts. Dr. Osborne was quick to recognize the importance of the discovery but had no idea why it was occurring. He felt, it would be worthwhile to publish the results. In 1969, Dr. Osborne published a paper titled ‘Cool’ in Journal of Physics Education, with due to credit to Mpemba [1].

Physics community saw Mpemba’s effect with the eye of suspicion and mistrust. How can the laws of physics be so wrong? And more notably, if it is true, why did it take so long for this phenomenon to be discovered? It was soon identified that Mpemba’s effect was known from the times of Aristotle but has been ignored. In 350 BC, Aristotle wrote

“…If water has been previously heated, this contributes to the rapidity with which it freezes: for it cools more quickly. (Thus so many people when they want to cool water quickly first stand it in the sun: and the inhabitants of Pontus when they encamp on the ice to fish. . . pour hot water on their rods because it freezes quicker, using the ice like solder to fix their rods.) And water that condenses in the air in warm districts and seasons gets hot quickly”

In 13th Century, Roger Bacon, an English philosopher and advocate of scientific methods wrote in his book ‘Opus Majus’ that

“…Moreover, it is generally believed that hot water freezes more quickly than cold water in vessels, and the argument in support of this is advanced that contrary is excited by contrary, just like enemies meeting each other. But it is certain that cold water freezes more quickly for anyone who makes the experiment. People attribute this to Aristotle in the second book of Meteorologics; but he certainly does not make this statement, but he does make one like it, by which they have been deceived, namely, that if cold water and hot water are poured on a cold place, as upon ice, the hot water freezes more quickly, and this is true. But if hot water and cold are placed in two vessels, the cold will freeze more quickly. Therefore all things must be verified by experience”

In 1637 AD, Descartes, a renowned mathematician, published in his work ‘Les Meteores’, quotes about faster freezing of hot water compared to cold water as

“…We can see this by experiment, if we fill a beaker or some other such container having a long, straight neck—with hot water, and expose it to freezing cold air; for the water level will go down visibly, little by little, until the water reaches a certain level of coldness, after which it will gradually swell and rise, until it is completely frozen. Thus the same cold which will have condensed or shrunk it in the beginning will rarefy it afterwards. And we can also see by experiment that water which has been kept hot for a long time freezes faster than any other sort, because those of its parts which can least cease to bend evaporate while it is being heated”

After the publication by Descartes, Fermat (another renowned mathematician) questioned Descartes whether he actually did the experiment or was he simply stating the rumor. For which, Descartes replied

“…I appreciate once again what you have written me that my reputation is at stake in my response to Mr. Fermat, in which I assure you that there is not one single word that I would like to have changed. . .I dare to assure you that there is nothing incorrect, because I did these experiments myself, and particularly the one which you commented on of the hot water that freezes more quickly than cold; where I said not hot and cold, but that water that one has held for a long time over the fire freezes more quickly than the other; because in order to correctly do this experiment, one must first have boiled the water, then let it cool off, until it has the same degree of coolness as that in a fountain, and having tested it with a thermometer, then draw water from that fountain, and put the two waters in the same quantity in same vases. But there are few people who are capable of correctly doing these experiments, and often, in doing them poorly, one finds the complete opposite of what one should find”

But for all these quotes from legendary figures, the question still remains, how did Mpemba’s effect remained as a mystery all these years? Why didn’t physics tried to understand the actual cause of Mpemba’s effect? According to certain researchers, theory of heat transfer is so well established that scientists are skeptical about the claims and refuse to even carry out advance experiments to understand Mpemba’s effect. Being a passionate physicist, I feel it is a disservice to physics, if researchers don’t carry out experiments just because something contradicts the existing theories.


Nonetheless, in recent times, there has been renewed enthusiasm in unravelling the exact cause of Mpemba’s effect. According to several papers published in this regard, Mpemba’s could be due to impact of evaporation, dissolved gasses, convection, surroundings and super-cooling on water. However, no author was able to confirm the exact reason. Recently, Brownridge published his experimental results on Mpemba’s effect [2]. The above graph, taken from Brownridge paper shows, it took 120 minutes for water at 76°C to freeze compared to 195 minutes for water at 4°C under experimental conditions. However, Brownridge argues that, changing the experimental conditions slightly can produce opposite results. On 6th May 2010, Vladan Pankovic and Darko V. Kapor have suggested a modification of Newton’s Law of cooling to explain Mpemba’s effect [3].

As a student of science, it surprises me that, such a trivial effect has no exact explanation in theoretical physics. Mpemba effect continues to reminds us that, there is long way to go in theoretical physics. I am also deeply inspired by Mpemba, for his curiosity and persistent effort in understanding this phenomenon. He also reminded us that, instead of blindly following the textbooks and teachers, we need to question because… answers can be found only when we question.

References & Suggested Reading

[1] Mpemba, Osborne, "Cool", Physics Education vol. 4, 172-175 (1969).

[2] James D. Brownridge, “A search for the Mpemba effect: When hot water freezes faster then cold water”, arXiv:1003.3185v1 [physics.pop-ph].

[3] Vladan Pankovic, Darko V. Kapor, “A Modification of the Newton's Cooling Law and Mpemba Effect”, arXiv:1005.1013v1 [physics.gen-ph]

[4] Monwhea Jeng, “Hot water can freeze faster than cold?!?”, Am. J. Phys. 74, 514 (2006).

[5] J. I. Katz, “When hot water freezes before cold”, arXiv:physics/0604224v1 [physics.chem-ph]

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