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]

Saturday, May 8, 2010

Tera Na Hona…


It is as if an abnormal silence has taken over my life. Yesterday, while walking through the crowded streets of Mumbai, I continued to feel lonely and isolated. There was noise and voices, there were shops and traders all around and yet there was a strange sense of isolation. I stood watching the pigeons at Gateway of India and kept asking myself, where the life leads from here. I wish I was that pigeon, who can fly away anywhere it wants. In front of me stood the iconic Taj Hotel… maybe it was trying to say me, sometimes you lose people but it isn’t end of it. Or maybe, it just stood there, healing its own wounds.

About thirty minutes later, I found myself walking on Mohammed Ali Road… the streets that have been untouched by the modern development. Yes, government has constructed a bridge over Mohammed Ali Road so that visitors can bypass it without noticing it. I found people everywhere, trying hard to learn livelihood, trying hard to live life… I wondered, how I would react, if I was born among them. Twenty minutes later, every shop on the road was closed. DSC08622Before I panic, I heard the sweetest sound on the earth, the call for afternoon prayers. Yes, everyone was heading to Juma Prayers. I realized, no matter what, there is something that connects all these people. I wish, they find a leader among themselves who can show them a direction… I wish they feel a sense of responsibility. Minutes later, I found myself in a beautiful small mosque. It gave me few moments to spiritually connect with God.

To escape the heat of Mumbai, I took shelter at a mall. While on the way, the taxi driver pointed me to a theatre, that’s been showing ‘Dilwale Dulhaniye Lejayenge”, a Hindi movie from last 750 weeks. He said, “that’s where people go to escape the heat of Mumbai”. For some reasonDSC08657 unknown to me, I preferred going to a mall. Maybe, it was due to some special memories associated with malls. I hurdled through each shop within the mall just to push time around. Yes, there were memories and there was silence.

An hour later, I asked the taxi driver to take me some place, which reminded of ‘hope’. Thirty minutes later, he stopped the vehicle near a mansion. He said, ‘that’s the symbol of hope’. I didn’t take me long to figure out what he meant. I was standing near house of Shahrukh Khan, an ordinary man from Delhi who came to Mumbai twenty years back with hope and won love, money and fame. For most people in Mumbai, he is an ideal example of what you can achieve with hope and hard work and for the rest, he is just another rDSC08672eason to believe, outsiders have taken over Mumbai. I stood there watching in the other direction, towards the ocean. I wish I could decode the signals of water waves.

An hour later, I found myself at Mumbai Airport, probably the worst airport I have been to. No wonder, my flight got delayed for four hours due to some runway problem. Now, that gave me four good hours to think. For about an hour, I read different newspapers. Pictures of some lawyer showing victory sign appeared so stupid. It was a moment to remember those hundreds of innocent people who lost their lives. It was also a moment to recollect that, our security agencies failed to stop the terrorist attack. By merely hanging the culprit isn’t a victory. Anyhow, moments later, I got distracted by a beautiful girl who sat right in front of me. Maybe, it was her perfume that grabbed the attention. Before I could speak a word with her (I mean, I had the intension of speaking), she picked her phone and got busy talking with someone. I felt I should give some privacy to the lady, so, I left from there.

I settled at a quiet corner at the airport lounge with million dispersed thoughts. It’s not the question of challenges, it’s not the question of barriers… the questions that wounded me most are… how can a difference in faith take two people apart? Isn’t ‘faith’ supposed to help people in being together? And who creates these differences in faith? It appears as if, faith and religion have become ‘business models’. People tend to make decisions in life as if they are doing some business… I wonder from when love has become a business! Didn’t realize, how three hours passed by. I was left asking, why is being with uncorrupted mind so painful? I wish, my love towards her was explainable. I wish, I wish…

Finally, reached home at about 12:30 AM… totally exhausted from day long soul searching. Sometimes, I wonder, had I thought so much about cosmological sciences, I would have found a far better theory than the existing ones. The biggest regret is that, even after all this thought process, she isn’t there in my life.