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 13^th 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 6^th 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]

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. Before 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 reason 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 reason 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.

Miles away but the pain continues

Yesterday, I witnessed an earthquake in Irvine, California. It took few seconds to realize that ground is shaking and I needed to run outside. Though, there was a moment of fear but I don’t know why, I didn’t care. I was neither terrified nor felt there is an urgent necessity to run. It was like … if this is it…so it is. Probably, I have started not caring about life as much as I used to do earlier. Maybe, it’s due to losing in love and giving up on fate. It’s hard for me to accept his fact. My heart still says, it’s possible and there is a solution ahead.

It’s been over two months since I blogged. To be honest, there was nothing to share. I have just been living life…like a normal person. It isn’t the ‘Abubakr’ who relentlessly tries to produce new ideas anymore. It’s just some common man…living life in shadows of reality and loneliness. Sometimes, I do question myself about what I actually want from life… but after lot of soul searching… I give up. I don’t see an answer… I don’t find something I can relate to. Life appears to be a meaningless passage of time.

I forgot to mention, on 20-21^st of February, I gave an invited talk and co-chaired computer science sessions at ICETE-2010, an international conference held at a local engineering college at Maharashtra. Basically, arranging conferences has become a business model for engineering colleges. Colleges want to arrange conferences because they want to gain publicity and students wants to attend them because they need publications to enter big universities. In between all these, research is abused. At the end I was left asking, where is the actual research? Anyhow, I attended this conference purely because of an invitation from a dear friend. I gave two talks, a technical talk for computer science students on “P v/s NP – Beyond the limits of Computation’ and another talk to general audience on ‘Research- the Search for Knowledge’. In both the talks, my attempt was to induce the passion for research among students. I don’t know how far I succeeded in my attempt but overall feedback seems to be positive. You can download the slides from here.

Standing at the seashore…

I stood there on the sea shore watching the energetic water waves for hours and hours. There was some mysterious force that made me anxious to watch each and every wave. Yes, each wave generated the curiosity as if it’s going to bring something new to the shore. There is something magical about ocean. From times immemorial, human beings have stood on the shored and watched the gigantic oceans with awe.

I walked along the seashore for a while…recollecting some of the painful times of my life. Yes, I am alone and it hurts immensely. But I guess, that’s how life is. Sometimes it becomes important for a person to lose the most precious of belongings to walk on the unseen path. And I was there, walking on the seashore, collecting the seashells and getting fascinated by the beauty of nature. But in the heart, I was hurt and had tears rolling all over my eyes. It’s difficult.

To be honest, I haven’t recovered from the shocks that life has given me. As I write this…my mind is pre-occupied with sadness and helplessness. And whatever that I write is deeply impacted by it. It’s been close to two months since I have spoken a word with her and I know…my dream of being with her is slowly drifting away from me. The vacuum it has created around me is suffocating. It’s like someone has pierced an arrow through the body and slowly pulling it out. It’s like being lost in the waves of ocean. I don’t know whether she thinks about me … but I miss her.

Losing the two precious belongings

 

Another year passed by and life is going on. Every year I make resolutions and promises and in the end, it all ends up at …. awaarapan ….banjaarapan. Yesterday night, I was all alone and awake till six in the morning, thinking about all the up and downs of year that’s about to pass. Professionally, it was an exciting year. I got my first promotion at Microsoft, got an IT Pro Award, visited Australia and Thailand to help Microsoft customers, got to learn various new technologies and more importantly, I lost the tag of ‘rookie’. However, on the personal front, it was a year of lot of surprises and emotions. I realized I am deeply in love with the girl I have been talking for a year. I travelled over thousand miles to meet her and spend two most beautiful days of my life. After meeting her, I realized that she deserves a better guy than me, hence, didn’t get the strength to propose my love towards her. Later she said me that, she waited for me to speak out about it but I didn’t. All was fine till then…and suddenly everything started going worse. So worst that…. we haven’t spoken in last thirty days. During all those thirty days, every conversation that I had, every activity that I did, directly or indirectly was leading towards her. At about six in the morning, tired with all the memories, I went to bed hoping for a changed tomorrow.

Woke up from deep sleep at sound of Azaan… the call for afternoon prayer. What a lovely dream it was… she was in the dream. We both were seated in an auditorium… watching something… maybe it was a science lecture… or maybe a movie. By the way, there was no darkness around…so it wasn’t a movie theatre. Anyhow, it doesn’t matter. I was next to her and that matters to me. After the Salat, I prayed to God about several changes in life and made few wishes. I don’t know what happened by evening, everything appeared so wrong. I had one of my worse nervous breakdowns. My brain went totally heated up and it was going insane. I tried my level best to calm down but it wasn’t controllable. It was as if, I wanted to hit people, bang my head to the walls, break the things around, shout like a wild animal and I can’t describe all the other insane ideas my brain was throwing up. After an hour, I felt, if I stay some more time at my house, I would do something really terrible… I immediately left home…and started walking on the streets. I had no idea where I was going… I was just walking like a mad person. Throughout the distance, there were images flashing all over my eyes. An hour later, I came to my senses. I settled at a nearby hotel, ordered a cup of tea… and tried to calm myself down.

All these years, my life has been just like that mad walk. No idea where I am going…and I am just going without realizing where I will end up. Of course, there were ambitions, hopes and goals… but there wasn’t a clear direction. All throughout my student life, I wanted to be a scientist, a scientist who is purely interested in advancement of human knowledge. I prayed to God for a good job with decent salary so that I can support my research work. And my prayers were fulfilled, I landed up at Microsoft. I should have got back to research but instead I fell in love with a girl. Of course, falling in love with a girl is nothing wrong but the manner in which I went about it was absolutely wrong. She was Shia Muslim and her parents would never agree for Sunni-Shia marriage. I was made to think and it was all me… the stupid mind which always thinks… non-stop. I tried to play the game of chess from both sides. The simplest solution that appeared before me was, if I become a big guy like Isaac Newton or Albert Einstein… obviously, her parents wouldn’t ask whether I am Shia or Sunni… they would be more than happy to give their daughter’s hand. And of course, if I become scientist like that, my parents would be more than happy to accept any girl that I choose. I know, the whole idea sounds crazy to lot of you, it still sounds like a brilliant idea to me. Soon, the sole ambition of life became, ‘do a huge scientific discovery, get fame, convince my/her parents, win her heart and then marry her’.

And after two years of effort, I landed up at a road-side hotel with a heated up brain (actually, sipping the Irani chai at that hotel made me forget for a while that I have just walked five kilometers like a mad dog)… forget about being like Newton or Einstein, all the research papers I wrote were rejected by journals…. and the girl is not even talking with me. How wrong can I go in life! And today, I have lost both the belongings closest to my heart… science and her. I have disrespected science… discoveries don’t happen just like that… and certainly not to the people who want to do it for the sake of something else than scientific knowledge. And love is not won by achieving fame. Both science and love demand sacrifices. I ordered the second cup of tea… the first cup was really tasty.

So, there I was… the guy who lost his love and his passion. My father once told me, ‘you cannot change the mistakes you already committed but you can change the future by not committing them again’. Basically, the question before me was… what am I supposed to do now? For whatever I am, I truly love her and I don’t want to lose her. She might get married to someone else in another six-seven months….and damn… I have not much time left. On the flip side, after she gets married to someone else… I can completely dedicate my life to science. But that won’t be a life… it will be a like a hopeless machine trying to compute a problem. Love and passionate sex is much needed in life. So… that puts me into even difficult situation. Had I used brain for science and heart for love, I would have had both by now. I did the opposite and lost both of them. Damn, I was again thinking about the mistakes which already happened. I need a solution to change the future.

It was about ten in the evening, I received a call from home. Thought of taking an auto back home…can’t walk five kilometers again but then… while walking I would get more time to think. So, decided to reach home by walk. Very bad decision again… there was no energy left for brain to process …it was all consumed by mechanical energy needed for walking.

At about 2 AM, I realized, I don’t have to convince people about my love. If it is meant to be, things will fall in place and it will work out. And if it isn’t meant to be… no matter what I do… it won’t work out. It sounded really cool then. I wrote her an email. But you know, after sending her the email, I re-read it… it all sounded so hypothetical. What a loser I am! Given that I was not able to do anything… I am escaping by using the concept of fate. She will get really confused when she will read it. Damn… I have always been like that. Confusing people…or maybe… after reading all this…you all would think ‘I am confused’. Actually, the truth is somewhere in between. Anyhow, let me focus… I have to come up with a strategy… the strategy to win my love and get my dedication back to science… it’s going to be a long night!