“My name is Erasto B Mpemba, and I am going to tell you about my discovery, which was due to misusing a refrigerator.”

With those words, Tanzanian student Erasto Mpemba entered scientific history, and also sparked a scientific mystery and controversy that remains ongoing today, some 40 years later!

The phenomenon Mpemba found is now known as the Mpemba effect, and is the very counterintuitive idea that, under certain circumstances, a quantity of very hot/boiling liquid can freeze faster than an equal quantity of cold liquid!

How is this possible? The remarkable thing is that nobody really knows, even though the first observations were reported to the scientific community in 1969. The story of the discovery, and the consequent mystery, is worth a bit of exploration — and the Mpemba effect carries numerous important lessons about the nature and method of scientific discovery.

Mpemba made his accidental discovery in Tanzania in 1963, when he was only 13 years old and in secondary school. In spite of widespread disdain from his classmates, he surreptitiously continued experiments on the phenomenon until he had the good fortune in high school to interact with Professor Denis Osborne of the University College Dar es Salaam. Osborne was intrigued, carried out his own experiments, and in 1969 the two published a paper in the journal Physics Education.

This article is, in my opinion, one of the most remarkable in all of the history of physics. Aside from its title, “Cool?”, it is also unusual in being presented in two parts: Mpemba gives a first person account in his own words of his discovery in the first half, and Osborne picks up the story and describes the follow-up experiments in the second half. Mpemba’s own account is so charming and fascinating that it is worth quoting from liberally:

My name is Erasto B Mpemba, and I am going to tell you about my discovery, which was due to misusing a refrigerator. All of you know that it is advisable not to put hot things in a refrigerator, for you somehow shock it; and it will not last long. In 1963, when I was in form 3 in Magamba Secondary School, Tanzania, I used to make ice-cream. The boys at the school do this by boiling milk, mixing it with sugar and putting it into the freezing chamber in the refrigerator, after it has first cooled nearly to room temperature. A lot of boys make it and there is a rush to get space in the refrigerator. One day after buying milk from the local women, I started boiling it. Another boy, who had bought some milk for making ice-cream, ran to the refrigerator when he saw me boiling up milk and quickly mixed his milk with sugar and poured it into the icetray without boiling it; so that he may not miss his chance. Knowing that if I waited for the boiled milk to cool before placing it in the refrigerator I would lose the last available ice-tray, I decided to risk ruin to the refrigerator on that day by putting hot milk into it. The other boy and I went back an hour and a half later and found that my tray of milk had frozen into ice-cream while his was still only a thick liquid, not yet frozen. I asked my physics teacher why it happened like that, with the milk that was hot freezing first, and the answer he gave me was that “You were confused, that cannot happen”. Then I believed his answer.

Here we have the beginnings of a classic story of science — an accidental discovery, scoffed at by the “establishment scientists”.

Mpemba might have given up at that point, but he encountered a friend who sold ice cream for a living, and that friend happened to mention that many vendors would use boiling water to make their ice cream! It was already common knowledge amongst them, apparently, that a boiling mixture could freeze quicker.

After passing my O level examination, I was chosen to go to Mkwawa High School in Iringa. The first topics we dealt with were on heat. One day as our teacher taught us about Newton’s law of cooling, I asked him the question, “Please, sir, why is it that when you put both hot milk and cold milk into a refrigerator at the same time, the hot milk freezes first?” The teacher replied: “I do not think so, Mpemba.” I continued: “It is true, sir, I have done it myself” and he said: “The answer I can give is that you were confused.” I kept on arguing, and the final answer he gave me was that: “Well, all I can say is that that is Mpemba’s physics and not the universal physics.” From then onwards if I failed in a problem by making a mistake in looking up the logarithms this teacher used to say: “That is Mpemba’s mathematics.” And the whole class adopted this, and anytime I did something wrong they used to say to me “That is Mpemba’s…”, whatever the thing was.

Here the high school teacher failed miserably — ridiculing a student is pretty much the worst thing one can do in a science classroom! Fortunately, Mpemba was not deterred:

Then one afternoon found the biology laboratory open, and there was no teacher. I took two 50 cm³ beakers, one I filled with cold water from the tap and the other with hot water from a boiler and quickly put them in the freezing chamber of the laboratory refrigerator. After one hour I came back to look and I found that not all the water had been changed into ice, but that there was more ice in the beaker which had hot water to start with than in the one which had cold water. This was not really conclusive. So, I planned to try it again when I had the chance.

Before he had this chance, however, Professor Osborne came to lecture on physics, giving Mpemba a valuable opportunity:

When Dr Osborne visited our school we were allowed to ask him some questions, mainly in physics. I asked: “If you take two similar containers with equal volumes Of water, one at 35 °C and the other at 100 °C, and put them into a refrigerator, the one that started at 100 °C freezes first. Why?” He first smiled and asked me to repeat the question. After I repeated it he said: “Is it true, have you done it?” I said: “Yes.” Then he said: “I do not know, but I promise to try this experiment when I am back in Dar es Salaam.” Next day my classmates in form six were saying to me that I had shamed them by asking that question and that my aim was to ask a question which Dr Osborne would not be able to answer. Some said to me: “But Mpemba did you understand your chapter on Newton’s law of cooling?” I told them: “Theory differs from practical.” Some said : “We do not wonder, for that was Mpemba’s physics.”

There are many remarkable points in this short passage. First of all, we see an admirable open-mindedness of Professor Osborne in his dealings with Mpemba, and that open-mindedness would quickly benefit them both. Conversely, we see a dangerous “groupthink” amongst Mpemba’s classmates regarding science, in which they are genuinely offended by Mpemba questioning the status quo. Mpemba shows great wisdom in his answer: “Theory differs from practical”. This is an important point for anyone studying physics: we like to create simplified models to explain nature, but those models often lose real-world aspects in the process of stripping them down.

Mpemba actually continued his experiments in a kitchen refrigerator, with the permission of kitchen staff, and convinced his classmates and the headmaster of his school of the accuracy of his findings.

At Dar es Salaam, Osborne was true to his word and looked into the phenomenon himself. As he notes in the continuation of the paper,

It seemed an unlikely happening, but the student insisted that he was sure of the facts. I confess that I thought he was mistaken but fortunately remembered the need to encourage students to develop questioning and critical attitudes. No question should be ridiculed. In this case there was an added reason for caution, for everyday events are seldom as simple as they seem and it is dangerous to pass a superficial judgment on what can and cannot be. I said that the facts as they were given surprised me because they appeared to contradict the physics I know. But I added that it was possible that the rate of cooling might be affected by some factor I had not considered.

Osborne sets a great example for all physics educators! It can be difficult at times, but “No question should be ridiculed” would be a great part of a “Hippocratic oath” for teachers.

One other anecdote from Osborne’s account is worth quotation:

At the University College in Dar es Salaam I asked a young technician to test the facts. The technician reported that the water that started hot did indeed freeze first and added in a moment of unscientific enthusiasm: “But we’ll keep on repeating the experiment until we get the right result.”

I leave it as an exercise to the reader to explain what is scientifically wrong with the technician’s attitude!

So what did Osborne’s research show? He placed a 100 cm³ beaker filled with 70 cm³ of water on a sheet of insulating foam in a freezer, and timed how long it took for the water to freeze. For temperatures up to 20 °C, the time was roughly proportional to the temperature above freezing, up to a maximum of 100 minutes at 20 °C. For higher temperatures, however, the time dropped dramatically, down to 40 minutes for 80 °C water!

Later experiments on the effect have been far less conclusive than Mpemba and Osborne’s. Some have seen similar results, while others have observed no effect at all! The appearance of the Mpemba effect apparently depends very strongly on the specific experimental circumstances, and is much harder to reproduce than the original paper would imply. A number of physicists seem skeptical that the effect truly exists at all!

With this in mind, however, it is worth noting that Mpemba’s observation was in fact noted earlier by others over the course of the past two thousand years. Around 350 B.C.E., Aristotle, in giving an explanation of hail in his book “Meteorology”¹, noted:

The fact that the water has previously been warmed contributes to its freezing quickly; for so it cools sooner. (Hence many people, when they want to cool water quickly, begin by putting it in the sun. So the inhabitants of Pontus when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their rods that it may freeze the quicker; for they use the ice like lead to fix the rods.) Now it is in hot countries and seasons that the water which forms soon grows warm.

Others who argued for the existence of a Mpemba effect, under some circumstances, include Roger Bacon in the 13th century, and Francis Bacon and René Descartes in the 17th century. It was Mpemba and Osborne, however, who brought it to the attention of modern science.

Before delving into some of the explanations for the effect, it is important to explain why the natural objection to its existence is not necessarily applicable. A natural argument is as follows. “Suppose we have two equal glasses of water, one at 100 °C and one at 30 °C. In order for the water at 100 °C to freeze, it must first cool to 30 °C. The time it takes to freeze is therefore the amount of time it takes to go from 100 to 30 plus the time it takes to go from 30 to zero. It therefore must take longer to freeze than the 30 °C water.”

The flaw in this argument is assuming that a body of water is only characterized by a single parameter: its temperature. In general, there are other characteristics of the water that could be changed due to its heating; for instance, the amount of gas in solution, the presence of other solutes, the presence of convection currents, gradients of the distribution of temperature in the container. Any, all, or none of these may in fact be the culprit, but it is important to realize that a body of water not in thermal equilibrium may have its behavior characterized by a number of different properties.

A number of hypotheses have been proposed as explanations, some based on the factors mentioned:

1. Convective heat transfer. When a liquid is heated, it can form convection currents that rapidly bring the hot liquid to the surface, where the heat is lost by evaporation:

Osborne noted that this convection will keep the top of the liquid hotter than the bottom, even when the temperature matches an initially cold liquid that doesn’t possess this convection cooling. This results in a faster rate of cooling that could, under the right circumstances, result in Mpemba’s observation.

2. Evaporation. A boiling or very hot liquid will lose some of its mass due to evaporation. With a lower mass, it will cool faster, possibly giving a “boost” to the Mpemba effect. Osborne already noted that evaporation alone could not account for all of the rate of cooling of the hot liquid.

3. Degassing. In a series of experiments in 1988, a Polish research group² reproduced the Mpemba effect and noted that the effect depended strongly on the amount of gas dissolved in the water. When the water was purged of air and carbon dioxide, the time to freeze became proportional to the starting temperature. The researchers suggested that the presence of gas was substantially slowing the rate of cooling, and that the heated water was purged of it.

4. Supercooling. In 1995, German scientist David Auerbach proposed³ that the Mpemba effect could be explained by supercooling, and performed experiments to back up the assertion.

Liquids begin to crystallize into a solid at the freezing point with the help of impurities around which the crystals can nucleate. In the absence of such impurities, the liquid can be cooled below its normal freezing point while remaining a liquid — it is “supercooled”. Auerbach suggests that the cold water will supercool to a lower temperature than the hot water, thus giving the hot water an “edge”. However, the reason that hot water has a higher supercooling temperature is unclear, and possibly related to the earlier noted effects.

5. Distribution of solutes. In 2009, an interesting explanation was proposed4 by J.I. Katz, who suggested that solutes present in the cold water slow the freezing process, as suggested earlier, but also that those solutes get driven from the freezing water into the as-yet unfrozen water, slowing the process further.

Other suggestions have been made, and other experiments have been done5, though no consensus seems to have been reached regarding the origins and generality of the effect. The confusion about the Mpemba effect is curiously reminiscent of the controversy around the “Archimedes death ray” controversy we have discussed earlier — the answer depends on the question being asked. Does hot water always freeze faster than cold? Almost certainly not! Are there some circumstances under which hot water freezes faster than cold? It seems likely, though nobody is sure exactly what those circumstances are. Does a negative result disprove the Mpemba effect, or was the experiment just done under the wrong circumstances? Nobody knows for certain.

The controversy no longer is of concern to Erasto Mpemba, however, who did not become a physicist himself but ended up studying at the College of African Wildlife Management. With his education, he eventually became the Principal Game Officer for the Tanzanian Ministry of Natural Resources and Tourism, working on wildlife management and conservation.

Erasto Mpemba, circa 1997 (source).

Regardless of the mystery, Mpemba’s discovery is a wonderful illustration of many important lessons in science: the significance of experiment over theory, the danger of clinging to preconceived notions, the difficulty in evaluating even seemingly simple real-world physics problems, and the importance of perseverance in the face of unreasoning denial. Furthermore, as far as I know the Mpemba effect is one of the only (if not the only) physical phenomena named after an African researcher! It is a wonderful and frustrating hint of how much intellectual potential lies untapped on the continent.

So what do I think of all the controversy? I’m not quite sure what to think! I’d love to test the Mpemba effect myself at home, but our freezer is packed to capacity6! Any enterprising experimenters out there want to give it a try? Describe your results in the comments!

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(Thanks to Blake Stacey for providing one of the references used to write this post!)

¹ Aristotle, “Meteorology”, in The Complete Works of Aristotle (The revised Oxford translation), (J. Barnes, ed., Princeton University Press, 1984).

² Wojciechowski, Owczarek and Bednarz, “Freezing of aqueous solutions containing gases,” Cryst. Res. Technol. 23 (1988), 843-848.

³ D. Auerbach, “Supercooling and the Mpemba effect: When hot water freezes quicker than cold,” Am. J. Phys. 63 (1995), 882-885.

4 J.I. Katz, “When hot water freezes before cold,” Am. J. Phys. 77 (2009), 27-29.

5 Esposito, De Risi and Somma, “Mpemba effect and phase transitions in the adiabatic cooling of water before freezing,” Physica A 387 (2008), 757-763.

6 This is a clear indication of my current marital status. Back in my single days, the only thing you would find in my freezer would have been a pair of frozen pizzas!

E.B. Mpemba, & D.G. Osborne (1969). Cool? Physics Education, 4, 172-175