# The Mpemba effect: Can hot water freeze faster than cold water?

Discussion in 'Jukwaa la Elimu (Education Forum)' started by mkama, Nov 6, 2007.

1. m

### mkamaMember

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Nov 6, 2007
Joined: Oct 19, 2007
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Nimeona ni vizuri tujikumbushe kidogo kuhusu Mtanzania huyu dadis aliyefungua fikra za wanataaluma wa sayansi. Ni ndefu lakini nafikiri ni muhimu.

Je watu kama Tanzania tuwaenzije?

========

The Mpemba effect is the observation that, in some specific, fairly common circumstances, hotter water freezes faster than colder water.

The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in the classroom of Eugene Marschall at Mkwawa Secondary (formerly High) School, Iringa, Tanzania, where Mpemba was a student. Eugene Marschall, a member of the Teachers for East Africa/TEA program, taught chemistry and physics at this school from 1965 to 1967. Mpemba first noticed the effect in 1963 after his account of the freezing of hot ice cream mix in cookery classes, and went on to publish experimental results with Dr. Denis G. Osborne in 1969.

At first sight, the behaviour seems contrary to thermodynamics. However, most thermodynamicists believe that each observation of the Mpemba effect can be explained with standard physical theory. Many effects can contribute to the observation, depending on the experimental set-up:

Different definition of freezing (Is it the physical definition of the point at which water forms a visible surface layer of ice, or the point at which the entire volume of water becomes a solid block of ice?)

Evaporation, reducing the volume to be frozen. Evaporation is endothermic.

Convection, accelerating heat transfers. Reduction of water density below 4°C tends to suppress the convection currents cooling the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling.

The insulating effects of frost

The effect of boiling on dissolved gases

Supercooling. It is hypothesized that cold water, when placed in a freezing environment, supercools more than hot water in the same environment, thus solidifying slower than hot water. However, supercooling tends not to be significant where there are particles, which act as nuclei for ice crystals, thus precipitating rapid freezing.

The effect of solutes such as calcium and magnesium carbonate.

According to an article by Monwhea Jeng, there is no unique explanation yet for why, in some specific circumstances, hotter water freezes faster than colder water. The article makes no attempt to focus on the relevant transport phenomena concepts such as temperature and fluid flow fields. Indeed when temperature fields are introduced, the author states:

Analysis of the situation is now quite complex, since we are no longer considering a single parameter, but a scalar function, and computational fluid dynamics (CFD) is notoriously difficult. The greatest difficulties with CFD are with turbulent flow; with laminar (streamline) flow, as we have in this case, there is much better consistency between independent analyses, and a CFD analysis could be expected to be illuminating.

This effect is a heat transfer problem, therefore well suited to be studied from a transport phenomena viewpoint, based on continuum mechanics. When heat transfer is analyzed in terms of partial differential equations, whose solutions depend on a number of conditions, it becomes clear that measuring only a few lumped parameters, such as the water average temperature is generally insufficient to define the system behaviour, since conditions such as geometry, fluid properties and temperature and flow fields play an important role. The counterintuitiveness of the effect, if analyzed only in terms of simplified thermodynamics illustrates the need to include all the relevant variables and use the best available theoretical tools when approaching a physical problem.

Similar behavior may have been observed by ancient scientists such as Aristotle, and Early Modern scientists such as Francis Bacon and René Descartes. Aristotle's explanation involved 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.

2. A

### Asha AbdalaJF-Expert Member

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Dunia nzima inajiuliza Erasto Mpemba yuko wapi? Je, wanasiasa wetu wameshindwa kumuenzi mwanasayansi huyu? Kwanini asijengewe mnara Iringa?

Asha

3. ### SaharavoiceJF-Expert Member

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Nov 25, 2007
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Asha, Labda kwa faida ya wengi ungetoa japo historia fupi ya nini alikifanya huyu mheshimiwa mpaka astahili kuenziwa.

4. ### Nyani NgabuPlatinum Member

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Mpemba effect....sijui significance yake ni nini lakini eti yeye ndio allivumbua

5. M

### MtanzaniaJF-Expert Member

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Nov 25, 2007
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Nilikuwa silijui hili:

The Mpemba effect is the observation that, in some specific, fairly common circumstances, hotter water freezes faster than colder water.

The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in the classroom of Eugene Marschall at Mkwawa Secondary (formerly High) School, Iringa, Tanzania, where Mpemba was a student. Eugene Marschall, a member of the Teachers for East Africa/TEA program, taught chemistry and physics at this school from 1965 to 1967. Mpemba first noticed the effect in 1963 after his account of the freezing of hot ice cream mix in cookery classes, and went on to publish experimental results with Dr. Denis G. Osborne in 1969.

At first sight, the behaviour seems contrary to thermodynamics. However, most thermodynamicists believe that each observation of the Mpemba effect can be explained with standard physical theory. Many effects can contribute to the observation, depending on the experimental set-up:

Different definition of freezing (Is it the physical definition of the point at which water forms a visible surface layer of ice, or the point at which the entire volume of water becomes a solid block of ice?)
Evaporation, reducing the volume to be frozen. Evaporation is endothermic.
Convection, accelerating heat transfers. Reduction of water density below 4°C tends to suppress the convection currents cooling the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling.
The insulating effects of frost
The effect of boiling on dissolved gases
Supercooling. It is hypothesized that cold water, when placed in a freezing environment, supercools more than hot water in the same environment, thus solidifying slower than hot water. However, supercooling tends not to be significant where there are particles, which act as nuclei for ice crystals, thus precipitating rapid freezing.
The effect of solutes such as calcium and magnesium carbonate.
According to an article by Monwhea Jeng, there is no unique explanation yet for why, in some specific circumstances, hotter water freezes faster than colder water. The article makes no attempt to focus on the relevant transport phenomena concepts such as temperature and fluid flow fields. Indeed when temperature fields are introduced, the author states:

Analysis of the situation is now quite complex, since we are no longer considering a single parameter, but a scalar function, and computational fluid dynamics (CFD) is notoriously difficult. The greatest difficulties with CFD are with turbulent flow; with laminar (streamline) flow, as we have in this case, there is much better consistency between independent analyses, and a CFD analysis could be expected to be illuminating.

This effect is a heat transfer problem, therefore well suited to be studied from a transport phenomena viewpoint, based on continuum mechanics. When heat transfer is analyzed in terms of partial differential equations, whose solutions depend on a number of conditions, it becomes clear that measuring only a few lumped parameters, such as the water average temperature is generally insufficient to define the system behaviour, since conditions such as geometry, fluid properties and temperature and flow fields play an important role. The counterintuitiveness of the effect, if analyzed only in terms of simplified thermodynamics illustrates the need to include all the relevant variables and use the best available theoretical tools when approaching a physical problem.

Similar behavior may have been observed by ancient scientists such as Aristotle, and Early Modern scientists such as Francis Bacon and René Descartes. Aristotle's explanation involved 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.

6. K

### KalamuJF-Expert Member

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Nov 25, 2007
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Why? I never heard of him! Where is he now?

We call the phenomenon 'serendipity' or stumbling upon some interesting phenomenon or something without having carried out some painstakingly rigorous and planned and systematic study - where you have to advance hypotheses and prove them by experimental work.

It is more like someone stumbles on a shiny stone kule shinyanga. Kama mtu huyo anao ufahamu wa kutosha wa thamani ya vitu vinavyong'ara namna hiyo atakuwa na hisia ya thamani ya kitu hicho, na anaweza kusema kuwa amegundua kuwa eneo hilo lina vitu vya namna hiyo na kuamua kuwa na hati miliki ya eneo zima bila hata ya kulifanyia utafiti mkubwa.
Kwa upande mwingine, wenye utaalam katika mambo hayo ya geologia, bila hata ya kuokota kwa bahati nzuri jiwe lile linalong'aa, wanaweza kuvutiwa kwanza na hali ya miamba au udongo wa eneo lile na kulifanyia uchunguzi wa kitaalam utakaoweza kuonyesha kuwa eneo hilo linayo vito vya thamani. Hawa wa pili itawabidi waanze na systematic approach.

Hata hivyo, sitopenda kumpunguzia chochote Mpemba katika ugunduzi wake huo wa kujivunia. Alionyesha kuwa anayo 'inquiring mind' na kwa vyovyote alivumbua.

Take the example of

7. ### Mtu wa PwaniJF-Expert Member

#7
Nov 26, 2007
Joined: Dec 26, 2006
Messages: 4,083
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Making Ice Cream and Scientific Thinking
A true story about a thinking student
by Tamás Jávor
What do you think about this question: If you take two containers, fill them with equal volumes of a liquid, one hot and the other cold, and put them into the freezer at the same time, which will freeze first? You might think that the editor confused my manuscript with that of a primary school physics book. We indeed are going to see students and things about children in the article, but I do not suggest that you give a confident answer to the question!

In the 1960s, there was a schoolboy named Erasto B. Mpemba in Tanzania, Africa. At his school the pupils loved to make ice cream. They bought some milk at the market, boiled it, mixed it with sugar, and put it into the refrigerator of the school. There was not much space in it, so the boys always tried to quickly obtain a place for their ice cream.

One day, as Erasto was boiling his milk, he noticed that another boy was putting his milk into the refrigerator without boiling it. He did not want to miss the space and, hurrying, he did not wait until his milk cooled down to room temperature, but put it into the freezer hot (even at the risk of ruining it).

One and a half hours later they went back, and found that his ice cream was ready, while his friend's was not yet completely frozen. Erasto found this unusual and asked his physics teacher at the school why this happened. The teacher answered: "You were confused, that cannot happen." Then he believed this answer, and did not bother to try the experiment again (even when, in his next holiday, he met some ice cream selling friends who told him that they also start freezing the cream while hot, because that way it is ready quicker).

Some years later Erasto Mpemba became a high school student. The first topic they were dealing with in physics was heat. When hearing about Newton's law of cooling, Erasto Mpemba asked the teacher: "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." But the student stated that he had seen it himself. The teacher said: "The answer I can give is that you were confused." And when he insisted on his opinion, the teacher told him: "All I can say is that that is Mpemba's physics and not the universal physics." (And later on, the whole class would criticise all his mistakes saying "That is Mpemba's mathematics" or whatever it was.)

Mpemba did not want to leave this case at that. One day, as he found the biology laboratory of the school open and empty, he quickly went in, filled two beakers with hot and cold tap water and placed them into the freezer. As he returned one hour later, he found that neither of them had frozen yet, but there was more ice in the originally hot water. However, this was not conclusive, so he decided to continue to deal with the topic.

Later, Dr Denis G. Osborne, professor at University College Dar es Salaam (then capital of Tanzania) visited their school. He gave a lecture to the students and after that they were allowed to ask questions. Erasto Mpemba took courage and 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 the refrigerator, the one that started at 100°C freezes first. Why?" The professor did not ridicule the student. He recalls: "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. [...] everyday events are seldom as simple as they seem and it is dangerous to pass a superficial judgment on what can and cannot be." He answered the student: "The facts as they are given surprise me, because they appear to contradict the physics I know. But I will try this experiment when I am back in Dar es Salaam." And he encouraged the questioner to repeat the experiment himself, too.

Mpemba became an anti-hero at his school. His classmates told him that he had shamed them, and that his aim was to ask a question which the professor would not be able to answer, others asked him: "But Mpemba, did you understand your chapter on Newton's law of cooling?"

Newton's law of cooling states that the rate of cooling is proportional to the temperature difference between the object and the cooling environment - under some simplifying assumptions.

But he did continue experimenting at the school. His results were just the same. He showed everyone what happens. When the head teacher of the physics department heard that it worked, he said: "It should not." (But added: "I will try it this afternoon." And found the same results.)

Meanwhile, Dr Osborne, back at his workplace, also let a young technician test the facts. He reported that in the first trial the hot water froze first, and added: "But we will keep on repeating the experiment until we get the right result!" They indeed repeated it. The results are plotted in the figure below where the curve has a maximum at about 30°C.

Results of Dr Osborne's detailed experiments.

Articles were published, experiments were repeated everywhere. The latter is not an easy task, because there are many factors influencing what exactly happens (like the geometry and the material constants of the objects - the freezer, the container and the liquid -, the ratio of the top surface area and the volume of the liquid, etc.) Under some conditions the effect does not even occur: the cooler liquid freezes first.

We shall see some theories which attempted to explain this phenomenon. It is important to know that even today there is no proved or accepted explanation!

Some thought that the hotter glass had melted the frost layer in Mpemba's refrigerators, and this way it got into a much better contact with the freezer (because frost is a bad thermal conductor). In some experiments it might have happened, but eliminating this effect does not stop the phenomenon.
During the cooling evaporation also occurs. Evaporation needs heat and removes mass from the liquid - both let the cooling be faster. Of course in the hotter liquid these effects are stronger. However, from theoretical calculations and experiments eliminating evaporation we know that this explanation is insufficient.
Above 4°C, the density of water increases as temperature decreases. As the top layer (where cooling is the most intensive) has transmitted heat to the environment, it becomes cooler, hence denser. It starts to sink down to the bottom of the beaker, from where warmer water is arriving to the top. These convection currents established by temperature gradient are more intensive in the initially hotter liquid, which makes heat transmission at the top faster. The temperature gradient undoubtedly exists, but these currents have been neither theoretically described nor thoroughly experimentally observed.
Some investigators stated that gases dissolved in the liquid can play a role in causing the effect. Of course there is less dissolved gas in the hot water, and dissolved gases might change the thermodynamic constants of the solvent, but there is no exact theory to explain why and how they do.
Finally, supercooling can give an answer. It was observed that the initially warmer water can be supercooled less. (But there is only a very complicated and not undoubtedly valid explanation why this happens.)
We can say that the faster freezing of the initially hotter water is most probably the result of several effects at the same time.
People also began to look for earlier references in literature. It turned out that this phenomenon could have been a common idea. (Remember the ice cream sellers!) But by official science it was forgotten until 1969. Some historic statements: René Descartes (1637): "Experience shows that water which has been kept for a long time on the fire freezes sooner than other water." Francis Bacon (1620): "Water slightly warm is more easily frozen than quite cold." Giovanni Marliani, medieval physicist dealing with heat: in a debate (c1461) stated that he had taken four ounces of boiling water and the same volume of non-heated water, placed them outside in a cold winter day, and had found that the boiling water froze first. He quotes an even earlier source: Aristotle (c350 BC): "The fact that 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..."

This phenomenon was named the Mpemba effect after this brave student. The story is a parable for everybody forever, not to undervalue the observations of uneducated people, and not to state too quickly that something is impossible. The story warns us that it is worth reflecting on this: Do not we often have serious prejudices in discovering nature? Can we really observe our world clearly and without bias? Like Erasto Mpemba did, and like children do. Can we wonder at the interesting, beautiful things around us? (The younger a child is, the more they do so.) An interesting statement is recorded from Jesus Christ: "Unless you become like little children, you will never enter the kingdom of heaven." It seems so, that important things in life can be correctly, really understood with "a child's mind". Open-hearted and putting aside prejudices. I hope we can all learn to observe the world this way!

Dr Osborne and Mpemba never became famous, their names cannot be found in any biography collection. I would welcome any information about their later destiny.

Tamás Jávor is a student at Budapest University of Technology and Economics in Hungary. This article is based on a lecture given by the author at ICPS 2005, Coimbra, Portugal.

References

E. B. Mpemba, D. G. Osborne, Cool?, Physics Education, May 1969, 4 #3, 172-175.
D. G. Osborne, Mind on ice, Physics Education, Nov 1979, 14 #6, 414-417.
M. Jeng, Can hot water freeze faster than cold water?, math.ucr.edu/home/baez/physics/General/hot_water.html, 1998.
J. Walker, The Amateur Scientist, Scientific American, Sept 1977, 237 #3, 246-257.
R. Descartes, Les Meteores (published with Discours de la Methode), Leyden: Ian Marie, 1637, 164; quoted in Oeuvres de Descartes, Vol. VI, ed. Adam and Tannery, Paris: Leopold Clerf, 1902, 238.
F. Bacon, Novum Organum Vol. VIII of The Works of Francis Bacon, ed. J. Spedding, R. L. Ellis and D. D. Heath, New York, 1869, 235, 337; quoted in T. S. Kuhn, The Structure of Scientific Revolutions, 2nd ed., University of Chicago Press, 1970, 16.
Giovanni Marliani, Disputatio cum Joanne de Arculis, 1461, 71-78, 168; quoted in M. Clagett, Giovanni Marliani and Late Medieval Physics (PhD thesis 1941), AMS Press, Inc., New York, 1967, 72, 79, 94.
Aristotle, Meteorologica I, c350 BC, Oxford Univ. Press, 1923, 348b-349a.
The Bible (New International Version), Matthew ch 18 vs 3.

Making Ice Cream and Scientific Thinking
A true story about a thinking student
by Tamás Jávor
What do you think about this question: If you take two containers, fill them with equal volumes of a liquid, one hot and the other cold, and put them into the freezer at the same time, which will freeze first? You might think that the editor confused my manuscript with that of a primary school physics book. We indeed are going to see students and things about children in the article, but I do not suggest that you give a confident answer to the question!

In the 1960s, there was a schoolboy named Erasto B. Mpemba in Tanzania, Africa. At his school the pupils loved to make ice cream. They bought some milk at the market, boiled it, mixed it with sugar, and put it into the refrigerator of the school. There was not much space in it, so the boys always tried to quickly obtain a place for their ice cream.

One day, as Erasto was boiling his milk, he noticed that another boy was putting his milk into the refrigerator without boiling it. He did not want to miss the space and, hurrying, he did not wait until his milk cooled down to room temperature, but put it into the freezer hot (even at the risk of ruining it).

One and a half hours later they went back, and found that his ice cream was ready, while his friend's was not yet completely frozen. Erasto found this unusual and asked his physics teacher at the school why this happened. The teacher answered: "You were confused, that cannot happen." Then he believed this answer, and did not bother to try the experiment again (even when, in his next holiday, he met some ice cream selling friends who told him that they also start freezing the cream while hot, because that way it is ready quicker).

Some years later Erasto Mpemba became a high school student. The first topic they were dealing with in physics was heat. When hearing about Newton's law of cooling, Erasto Mpemba asked the teacher: "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." But the student stated that he had seen it himself. The teacher said: "The answer I can give is that you were confused." And when he insisted on his opinion, the teacher told him: "All I can say is that that is Mpemba's physics and not the universal physics." (And later on, the whole class would criticise all his mistakes saying "That is Mpemba's mathematics" or whatever it was.)

Mpemba did not want to leave this case at that. One day, as he found the biology laboratory of the school open and empty, he quickly went in, filled two beakers with hot and cold tap water and placed them into the freezer. As he returned one hour later, he found that neither of them had frozen yet, but there was more ice in the originally hot water. However, this was not conclusive, so he decided to continue to deal with the topic.

Later, Dr Denis G. Osborne, professor at University College Dar es Salaam (then capital of Tanzania) visited their school. He gave a lecture to the students and after that they were allowed to ask questions. Erasto Mpemba took courage and 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 the refrigerator, the one that started at 100°C freezes first. Why?" The professor did not ridicule the student. He recalls: "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. [...] everyday events are seldom as simple as they seem and it is dangerous to pass a superficial judgment on what can and cannot be." He answered the student: "The facts as they are given surprise me, because they appear to contradict the physics I know. But I will try this experiment when I am back in Dar es Salaam." And he encouraged the questioner to repeat the experiment himself, too.

Mpemba became an anti-hero at his school. His classmates told him that he had shamed them, and that his aim was to ask a question which the professor would not be able to answer, others asked him: "But Mpemba, did you understand your chapter on Newton's law of cooling?"

Newton's law of cooling states that the rate of cooling is proportional to the temperature difference between the object and the cooling environment - under some simplifying assumptions.

But he did continue experimenting at the school. His results were just the same. He showed everyone what happens. When the head teacher of the physics department heard that it worked, he said: "It should not." (But added: "I will try it this afternoon." And found the same results.)

Meanwhile, Dr Osborne, back at his workplace, also let a young technician test the facts. He reported that in the first trial the hot water froze first, and added: "But we will keep on repeating the experiment until we get the right result!" They indeed repeated it. The results are plotted in the figure below where the curve has a maximum at about 30°C.

Results of Dr Osborne's detailed experiments.

Articles were published, experiments were repeated everywhere. The latter is not an easy task, because there are many factors influencing what exactly happens (like the geometry and the material constants of the objects - the freezer, the container and the liquid -, the ratio of the top surface area and the volume of the liquid, etc.) Under some conditions the effect does not even occur: the cooler liquid freezes first.

We shall see some theories which attempted to explain this phenomenon. It is important to know that even today there is no proved or accepted explanation!

Some thought that the hotter glass had melted the frost layer in Mpemba's refrigerators, and this way it got into a much better contact with the freezer (because frost is a bad thermal conductor). In some experiments it might have happened, but eliminating this effect does not stop the phenomenon.
During the cooling evaporation also occurs. Evaporation needs heat and removes mass from the liquid - both let the cooling be faster. Of course in the hotter liquid these effects are stronger. However, from theoretical calculations and experiments eliminating evaporation we know that this explanation is insufficient.
Above 4°C, the density of water increases as temperature decreases. As the top layer (where cooling is the most intensive) has transmitted heat to the environment, it becomes cooler, hence denser. It starts to sink down to the bottom of the beaker, from where warmer water is arriving to the top. These convection currents established by temperature gradient are more intensive in the initially hotter liquid, which makes heat transmission at the top faster. The temperature gradient undoubtedly exists, but these currents have been neither theoretically described nor thoroughly experimentally observed.
Some investigators stated that gases dissolved in the liquid can play a role in causing the effect. Of course there is less dissolved gas in the hot water, and dissolved gases might change the thermodynamic constants of the solvent, but there is no exact theory to explain why and how they do.
Finally, supercooling can give an answer. It was observed that the initially warmer water can be supercooled less. (But there is only a very complicated and not undoubtedly valid explanation why this happens.)
We can say that the faster freezing of the initially hotter water is most probably the result of several effects at the same time.
People also began to look for earlier references in literature. It turned out that this phenomenon could have been a common idea. (Remember the ice cream sellers!) But by official science it was forgotten until 1969. Some historic statements: René Descartes (1637): "Experience shows that water which has been kept for a long time on the fire freezes sooner than other water." Francis Bacon (1620): "Water slightly warm is more easily frozen than quite cold." Giovanni Marliani, medieval physicist dealing with heat: in a debate (c1461) stated that he had taken four ounces of boiling water and the same volume of non-heated water, placed them outside in a cold winter day, and had found that the boiling water froze first. He quotes an even earlier source: Aristotle (c350 BC): "The fact that 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..."

This phenomenon was named the Mpemba effect after this brave student. The story is a parable for everybody forever, not to undervalue the observations of uneducated people, and not to state too quickly that something is impossible. The story warns us that it is worth reflecting on this: Do not we often have serious prejudices in discovering nature? Can we really observe our world clearly and without bias? Like Erasto Mpemba did, and like children do. Can we wonder at the interesting, beautiful things around us? (The younger a child is, the more they do so.) An interesting statement is recorded from Jesus Christ: "Unless you become like little children, you will never enter the kingdom of heaven." It seems so, that important things in life can be correctly, really understood with "a child's mind". Open-hearted and putting aside prejudices. I hope we can all learn to observe the world this way!

Dr Osborne and Mpemba never became famous, their names cannot be found in any biography collection. I would welcome any information about their later destiny.

Tamás Jávor is a student at Budapest University of Technology and Economics in Hungary. This article is based on a lecture given by the author at ICPS 2005, Coimbra, Portugal.

References

E. B. Mpemba, D. G. Osborne, Cool?, Physics Education, May 1969, 4 #3, 172-175.
D. G. Osborne, Mind on ice, Physics Education, Nov 1979, 14 #6, 414-417.
M. Jeng, Can hot water freeze faster than cold water?, math.ucr.edu/home/baez/physics/General/hot_water.html, 1998.
J. Walker, The Amateur Scientist, Scientific American, Sept 1977, 237 #3, 246-257.
R. Descartes, Les Meteores (published with Discours de la Methode), Leyden: Ian Marie, 1637, 164; quoted in Oeuvres de Descartes, Vol. VI, ed. Adam and Tannery, Paris: Leopold Clerf, 1902, 238.
F. Bacon, Novum Organum Vol. VIII of The Works of Francis Bacon, ed. J. Spedding, R. L. Ellis and D. D. Heath, New York, 1869, 235, 337; quoted in T. S. Kuhn, The Structure of Scientific Revolutions, 2nd ed., University of Chicago Press, 1970, 16.
Giovanni Marliani, Disputatio cum Joanne de Arculis, 1461, 71-78, 168; quoted in M. Clagett, Giovanni Marliani and Late Medieval Physics (PhD thesis 1941), AMS Press, Inc., New York, 1967, 72, 79, 94.
Aristotle, Meteorologica I, c350 BC, Oxford Univ. Press, 1923, 348b-349a.
The Bible (New International Version), Matthew ch 18 vs 3.

Making Ice Cream and Scientific Thinking
A true story about a thinking student
by Tamás Jávor
What do you think about this question: If you take two containers, fill them with equal volumes of a liquid, one hot and the other cold, and put them into the freezer at the same time, which will freeze first? You might think that the editor confused my manuscript with that of a primary school physics book. We indeed are going to see students and things about children in the article, but I do not suggest that you give a confident answer to the question!

In the 1960s, there was a schoolboy named Erasto B. Mpemba in Tanzania, Africa. At his school the pupils loved to make ice cream. They bought some milk at the market, boiled it, mixed it with sugar, and put it into the refrigerator of the school. There was not much space in it, so the boys always tried to quickly obtain a place for their ice cream.

One day, as Erasto was boiling his milk, he noticed that another boy was putting his milk into the refrigerator without boiling it. He did not want to miss the space and, hurrying, he did not wait until his milk cooled down to room temperature, but put it into the freezer hot (even at the risk of ruining it).

One and a half hours later they went back, and found that his ice cream was ready, while his friend's was not yet completely frozen. Erasto found this unusual and asked his physics teacher at the school why this happened. The teacher answered: "You were confused, that cannot happen." Then he believed this answer, and did not bother to try the experiment again (even when, in his next holiday, he met some ice cream selling friends who told him that they also start freezing the cream while hot, because that way it is ready quicker).

Some years later Erasto Mpemba became a high school student. The first topic they were dealing with in physics was heat. When hearing about Newton's law of cooling, Erasto Mpemba asked the teacher: "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." But the student stated that he had seen it himself. The teacher said: "The answer I can give is that you were confused." And when he insisted on his opinion, the teacher told him: "All I can say is that that is Mpemba's physics and not the universal physics." (And later on, the whole class would criticise all his mistakes saying "That is Mpemba's mathematics" or whatever it was.)

Mpemba did not want to leave this case at that. One day, as he found the biology laboratory of the school open and empty, he quickly went in, filled two beakers with hot and cold tap water and placed them into the freezer. As he returned one hour later, he found that neither of them had frozen yet, but there was more ice in the originally hot water. However, this was not conclusive, so he decided to continue to deal with the topic.

Later, Dr Denis G. Osborne, professor at University College Dar es Salaam (then capital of Tanzania) visited their school. He gave a lecture to the students and after that they were allowed to ask questions. Erasto Mpemba took courage and 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 the refrigerator, the one that started at 100°C freezes first. Why?" The professor did not ridicule the student. He recalls: "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. [...] everyday events are seldom as simple as they seem and it is dangerous to pass a superficial judgment on what can and cannot be." He answered the student: "The facts as they are given surprise me, because they appear to contradict the physics I know. But I will try this experiment when I am back in Dar es Salaam." And he encouraged the questioner to repeat the experiment himself, too.

Mpemba became an anti-hero at his school. His classmates told him that he had shamed them, and that his aim was to ask a question which the professor would not be able to answer, others asked him: "But Mpemba, did you understand your chapter on Newton's law of cooling?"

Newton's law of cooling states that the rate of cooling is proportional to the temperature difference between the object and the cooling environment - under some simplifying assumptions.

But he did continue experimenting at the school. His results were just the same. He showed everyone what happens. When the head teacher of the physics department heard that it worked, he said: "It should not." (But added: "I will try it this afternoon." And found the same results.)

Meanwhile, Dr Osborne, back at his workplace, also let a young technician test the facts. He reported that in the first trial the hot water froze first, and added: "But we will keep on repeating the experiment until we get the right result!" They indeed repeated it. The results are plotted in the figure below where the curve has a maximum at about 30°C.

Results of Dr Osborne's detailed experiments.

Articles were published, experiments were repeated everywhere. The latter is not an easy task, because there are many factors influencing what exactly happens (like the geometry and the material constants of the objects - the freezer, the container and the liquid -, the ratio of the top surface area and the volume of the liquid, etc.) Under some conditions the effect does not even occur: the cooler liquid freezes first.

We shall see some theories which attempted to explain this phenomenon. It is important to know that even today there is no proved or accepted explanation!

Some thought that the hotter glass had melted the frost layer in Mpemba's refrigerators, and this way it got into a much better contact with the freezer (because frost is a bad thermal conductor). In some experiments it might have happened, but eliminating this effect does not stop the phenomenon.
During the cooling evaporation also occurs. Evaporation needs heat and removes mass from the liquid - both let the cooling be faster. Of course in the hotter liquid these effects are stronger. However, from theoretical calculations and experiments eliminating evaporation we know that this explanation is insufficient.
Above 4°C, the density of water increases as temperature decreases. As the top layer (where cooling is the most intensive) has transmitted heat to the environment, it becomes cooler, hence denser. It starts to sink down to the bottom of the beaker, from where warmer water is arriving to the top. These convection currents established by temperature gradient are more intensive in the initially hotter liquid, which makes heat transmission at the top faster. The temperature gradient undoubtedly exists, but these currents have been neither theoretically described nor thoroughly experimentally observed.
Some investigators stated that gases dissolved in the liquid can play a role in causing the effect. Of course there is less dissolved gas in the hot water, and dissolved gases might change the thermodynamic constants of the solvent, but there is no exact theory to explain why and how they do.
Finally, supercooling can give an answer. It was observed that the initially warmer water can be supercooled less. (But there is only a very complicated and not undoubtedly valid explanation why this happens.)
We can say that the faster freezing of the initially hotter water is most probably the result of several effects at the same time.
People also began to look for earlier references in literature. It turned out that this phenomenon could have been a common idea. (Remember the ice cream sellers!) But by official science it was forgotten until 1969. Some historic statements: René Descartes (1637): "Experience shows that water which has been kept for a long time on the fire freezes sooner than other water." Francis Bacon (1620): "Water slightly warm is more easily frozen than quite cold." Giovanni Marliani, medieval physicist dealing with heat: in a debate (c1461) stated that he had taken four ounces of boiling water and the same volume of non-heated water, placed them outside in a cold winter day, and had found that the boiling water froze first. He quotes an even earlier source: Aristotle (c350 BC): "The fact that 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..."

This phenomenon was named the Mpemba effect after this brave student. The story is a parable for everybody forever, not to undervalue the observations of uneducated people, and not to state too quickly that something is impossible. The story warns us that it is worth reflecting on this: Do not we often have serious prejudices in discovering nature? Can we really observe our world clearly and without bias? Like Erasto Mpemba did, and like children do. Can we wonder at the interesting, beautiful things around us? (The younger a child is, the more they do so.) An interesting statement is recorded from Jesus Christ: "Unless you become like little children, you will never enter the kingdom of heaven." It seems so, that important things in life can be correctly, really understood with "a child's mind". Open-hearted and putting aside prejudices. I hope we can all learn to observe the world this way!

Dr Osborne and Mpemba never became famous, their names cannot be found in any biography collection. I would welcome any information about their later destiny.

Tamás Jávor is a student at Budapest University of Technology and Economics in Hungary. This article is based on a lecture given by the author at ICPS 2005, Coimbra, Portugal.

References

E. B. Mpemba, D. G. Osborne, Cool?, Physics Education, May 1969, 4 #3, 172-175.
D. G. Osborne, Mind on ice, Physics Education, Nov 1979, 14 #6, 414-417.
M. Jeng, Can hot water freeze faster than cold water?, math.ucr.edu/home/baez/physics/General/hot_water.html, 1998.
J. Walker, The Amateur Scientist, Scientific American, Sept 1977, 237 #3, 246-257.
R. Descartes, Les Meteores (published with Discours de la Methode), Leyden: Ian Marie, 1637, 164; quoted in Oeuvres de Descartes, Vol. VI, ed. Adam and Tannery, Paris: Leopold Clerf, 1902, 238.
F. Bacon, Novum Organum Vol. VIII of The Works of Francis Bacon, ed. J. Spedding, R. L. Ellis and D. D. Heath, New York, 1869, 235, 337; quoted in T. S. Kuhn, The Structure of Scientific Revolutions, 2nd ed., University of Chicago Press, 1970, 16.
Giovanni Marliani, Disputatio cum Joanne de Arculis, 1461, 71-78, 168; quoted in M. Clagett, Giovanni Marliani and Late Medieval Physics (PhD thesis 1941), AMS Press, Inc., New York, 1967, 72, 79, 94.
Aristotle, Meteorologica I, c350 BC, Oxford Univ. Press, 1923, 348b-349a.
The Bible (New International Version), Matthew ch 18 vs 3.

source
Making Ice Cream and Scientific Thinking

8. ### NyambalaJF-Expert Member

#8
Nov 26, 2007
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Well, this is fantastic and offcourse I should admit that I have never heard of the man (Mpemba). I would propose something for us as JF let's research on this in a matter of say a month and come out to let the world know about this wonderful discovery and the man especially.

9. ### NyambalaJF-Expert Member

#9
Nov 26, 2007
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Sorry guys,

Nilikuwa sijui ila inavyoonekana ni sisi watanzania ndio hatumfahamu huyu jamaa. Lakini ni maajabu maana mimi nimesoma pale Mkwawa na hata siku moja sikuwahi sikia jina la huyu jamaa na uvumbuzi wake. Hiyompia inadhihirisha jamii yetu jinsi ilivyo - Mafisadi ni maarufu mno kuliko watu muhimu kama huyu mkuu. Nuff respect!!!!

10. ### MakanyagaJF-Expert Member

#10
Nov 26, 2007
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There is more than just enough evidence here http://www.google.com/search?hl=en&q=Mpemba+effect&btnG=Google+Search
It's very surprising that in my 10 yrs of studying physics, I didn't come across this wonderful Tanzanian Phsycian. But probably "Police wa nyumbani hana MAGAKA=(authoritative, induced threatening power)". Loook here: I once happpened to be in Denmark, and unknowingly, we happened to pass by a cemetery. Just close to the way, I saw a grave and on it there were two names printed, the first one read NIELS BOHR!I screamed, almost to the of my voice. We were accompanied by Professors of environmental science from one of the universities in Copenhagen, who couldn't understand why I was so excited. Their "why" however did not come from the fact that they knew Bohr so much that to them was no longer a surprise, THEY ACTUALLY DIDN'T KNOW ANYTHING ABOUT HIM, NEITHER HAD THEY EVEN HEARD OF HIM IN THEIR LIFE!Surprising eeh! The man who has almost modified the world to where we are now, is not known in his home country! I am not to be surprised about Mpemba's case.

11. ### Bubu MsemaovyoJF-Expert Member

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Kwa kweli ikiwa kipimo cha akili za watu weusi dhidi ya wazungu ni katika vitu hivi, leo mimi nimedhihirisha kwamba hazimo kabisa maana nimeanzna kubisha hata maandishi kwamba si kweli, nikatolea mfano kwamba ni sawa na kulinganisha mbio za kiwete na mtu mzima kwamba atakaye tangulia kumaliza haraka kufika ni kiwete. Baadaye nikaona mada hii si utani ni kweli. Sasa je ni kweli sisi weusi kichwani ni finyu kuliko weupe hilo mimi nakata.

12. K

### KalamuJF-Expert Member

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Mtu wa Pwani:
Tunakushukuru kwa kutuwekea makala hiyo ndefu kuhusu uvumbuzi wa Mpemba.

Makala ni ndefu, na 'technical' sehemu kadhaa, lakini ina mafundisho mengi sana mhimu.

Bado ninauliza Mpemba yupo wapi leo hii?. Huyu atakuwa sio mtu mzee bado. Yupo wapi na anafanya nini?

Na ukizungumzia masomo ya sayansi enzi za miaka hiyo hapa Bongo, Physics au Chemistry hiyo ni ile inayofundishwa College huko majuu!

13. K

### KobaJF-Expert Member

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Nov 26, 2007
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kweli hata mimi sijawahi kumsikia na kibaya zaidi sijawahi kusoma hiyo theory popote pale ingawaje nimesoma physics.

14. m

### mweweSenior Member

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Nov 26, 2007
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Iko haja ya kumtaja kwenye vitabu vya historia, japo kwa kupitia tu.

Mkwawa High SCHOOL sasa hivi ndiyo Mkwawa University College of Education (MUCE). Watafute angalau bweni, maabara au barabara ipewe jina lake. Sivyo hili jina litapotea.

15. ### Mzee MwanakijijiPlatinum Member

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Nov 26, 2007
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Nilipolitaja jina la Mpemba nilikuwa najibu hoja ya kuwa "hakuna watanzania wanaojulikana kwenye mambo ya uvumbuzi wa kisayansi" kuna mtu alisema hivyo. Ukweli ni kuwa bado ni vigumu sana kwa sisi kuwa na mfumo mzuri wa kuwatambua wale walio mahiri kati yetu au waliovumbua vitu katikati yetu. Ni sawa na yule msaidizi mweuzi aliyemsaidia daktari aliyefanya operesheni ya upandikizaji moyo ya kwanza duniani. Hakupata haki yake ya kutambuliwa hadi miaka mingi baadaye.

16. ### Gamba la NyokaJF-Expert Member

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Nov 26, 2007
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Siyo siri ndugu zanguni ,nimefarijika sana na habari hii,kwa sababu muda mrefu nimekuwa nikijiuliza Mwafrika kachangia nini katika maendeleo ya sayansi na tekinolojia(achilia mbali watu wa ma P.h.d na paper zao), kwa kweli kuliuwa hakuna jibu la haraka la mtu gani mweusi hususan kutoka Afrika kafanya uvumbuzi nadharia za kisayansi ambazo zinageuka kuwa fact tena uvumbuzi wenyewe upewe kizio cha jina lake. maana tumezoea kina Achimedes, Newton,Gauss,Faraday, Bohrs,Einstein,na wengine wengi ambao kwa kweli wanatoka nje ya afrika ama kiufupi ni ngozi Nyeupe ,lakini loh habari hii imekuwa ni jibu tosha kwamba nisiangalie mbali bali hapo tu Tanzania kwenyewe kuna kichwa kinaitwa Mpemba Tayari kimeshafanya uvumbuzi. kweli hii inaonyesha na sisi Waafrika Tunaweza, tusiwachape tu watoto wetu kwa Utundu wa udadisi bali tuwasaidie intuition zao ,you never know!,Magenius Tunao!

17. ### PunditJF-Expert Member

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I heard about this experiment but did not know the intricate details and the name Erasto Mpemba. Big up for enlightening us.

18. ### KijakaziJF-Expert Member

#18
Nov 26, 2007
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japo mimi sio mzuri sana wa kiingereza lkni hapo umekosea kidogo kwani mtu anayesoma fizikia kwa lugha ya kiingereza anitwa physicists na sio physician, nafikiri physician ni mganga, na hivyo ni vitu viwili TOFAUTI kabisa.....tumia lugha ya kwetu bro hautachemsha.....

19. ### Gamba la NyokaJF-Expert Member

#19
Nov 26, 2007
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