Can Hot Water Freeze Faster than Cold Water?

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Erasto Mpemba: Investigating the 'Mpemba Effect': Can Hot Water Freeze Faster than Cold Water?

Objective

The goal of this project is to investigate the question, "Can hot water freeze faster than cold water?" Thorough background research, a precise formulation of the hypothesis, and careful experimental design are especially important for the success of this experiment.

Introduction

It may seem counterintuitive, but folk wisdom and a body of published evidence agree that, under some conditions, warmer water can freeze faster than colder water (for an excellent review on the subject, see Jeng, 2005).

This phenomenon has been known for a long time, but was rediscovered by a Tanzanian high school student, Erasto Mpemba, in the 1960s. He and his classmates were making ice cream, using a recipe that included boiled milk. The students were supposed to wait for the mixture to cool before putting it in the freezer. The remaining space in the freezer was running out, and Mpemba noticed one of his classmates put his mixture in without boiling the milk. To save time and make sure that he got a spot in the freezer, Mpemba put his mixture in while it was still hot. He was surprised to find later that his ice cream froze first (Meng, 2005).

When Mpemba later asked his teacher for an explanation of how his hotter ice cream mixture could freeze before a cooler one, the teacher teased him, "Well all I can say is that is Mpemba physics and not the universal physics" (quote in Jeng, 2005). Mpemba followed his curiosity and did more experiments with both water and milk, which confirmed his initial findings. He sought out an explanation for his findings from a visiting university professor, Dr. Osborne. Work in Dr. Osborne's lab confirmed the results, and Mpemba and Osborne described their experiments in a published paper (Mpemba and Osborne, 1969).

How can it be that hot water freezes faster than colder water? Somehow, the hot water must be able to lose its heat faster than the cold water. In order to understand how this could happen, you will need to do some background research on heat and heat transfer. Here is a quick summary, so that you can be familiar with the terms you will encounter. Heat is a measure of the average molecular motion of matter. Heat can be transferred from one piece of matter to another by four different methods:

conduction,
convection,
evaporation, and
radiation.

Conduction is heat transfer by direct molecular interactions, without mass movement of matter. For example, when you pour hot water into a cup, the cup soon feels warm. The water molecules colliding with the inside surface of the cup transfer energy to the cup, warming it up.

Convection is heat transfer by mass movement. You've probably heard the saying that "hot air rises." This happens because it is less dense than colder air. As the hot air rises, it creates currents of air flow. These circulating currents serve to transfer heat, and are an example of convection.

Evaporation is another method of heat transfer. When molecules of a liquid vaporize, they escape from the liquid into the atmosphere. This transition requires energy, since a molecule in the vapor phase has more energy than a molecule in the liquid phase. Thus, as molecules evaporate from a liquid, they take away energy from the liquid, cooling it.

Radiation is the final way to transfer heat. For most objects you encounter every day, this would be infrared radiation: light beyond the visible spectrum. Incandescent objects--like light bulb filaments, molten metal or the sun-- radiate at visible wavelengths as well.

In addition to researching heat and heat transfer, you should also study previous experiments on this phenomenon. The review article by Monwhea Jeng (Jeng, 2005) is a great place to start. The Jeng article has an excellent discussion on formulating a testable hypothesis for this experiment.

Another excellent article, if you can find it at your local library, is by Jearl Walker, in the September, 1997 issue of Scientific American (Walker, 1977). Walker measured the time taken for various water samples to cool down to the freezing point (0°C), not the time for them to actually freeze. He measured the temperature of the water using a thermocouple, which could be placed at various depths in the beaker. Whether you use a thermocouple or a thermometer, it is important that the sensing portion of the device (thermocouple itself, or the bulb of the thermometer) be immersed in the water in order to get accurate readings. Walker used identical Pyrex beakers for his water samples, since they could go from the stove to the freezer without breaking. He used a metal plate over the stove burner to distribute the heat evenly to the beakers as they were heating. He heated the beakers slowly, and he also kept the beakers covered while heating, so that water that evaporated during heating would be returned to the beaker. Walker notes that "You cannot obtain accurate readings by first heating some water in a teakettle, pouring the water into a beaker already in the freezer and then taking a temperature reading. The water has cooled too much by then" (Walker, 1997, 246). Walker also reported that the air temperature in his freezer was between -8 and -15°C. He advises, "To maintain a consistent air temperature be sure to keep the freezer door shut as much as possible" (Walker, 1977, 246). For further details on his experimental procedure and findings, see the original Scientific American article.

The graph in Figure 1 shows some of Walker's data. The x-axis shows the time it took for the sample to reach 0°C (in minutes). The y-axis shows the initial temperature of the sample (in °C). The graph shows data from six separate experiments (a-f), each with a different symbol:

50 ml water in small beaker, non-frost-free refrigerator (black squares),
50 ml water in large beaker, non-frost-free refrigerator (red circles),
50 ml water in large beaker, frost-free refrigerator (green triangles),
100 ml water in large beaker, thermocouple near bottom (blue triangles),
100 ml water in large beaker, covered with plastic wrap, thermocouple near bottom (light blue diamonds),
100 ml in large beaker, thermocouple near top (magenta triangles).
Under some conditions (b, d, f), he found that samples that were initially hotter reached 0°C faster than samples that were initially cooler, confirming Mpemba's results. Under other conditions (a, e), hotter samples took as long or longer than cooler samples to reach 0°C. The results for experiment c are equivocal-it's difficult to say whether the time differences are significant or not.


Figure 1. Some of Walker's results (Walker, 1977). For details, see text.


This project is an excellent illustration that thorough background research, a clear formulation of your hypothesis, and careful experimental design are crucial to the success of an experiment.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

Mpemba effect,
heat and heat transfer,
conduction,
convection,
evaporation,
radiation;
phase change.

More advanced students may also want to study:

supercooling,
nucleation sites for initialization of crystal formation.

Questions


How does your freezer work to make things colder?
What are some of the mechanisms that have been proposed to explain the Mpemba effect?
How would you design an experiment to test one of the proposed explanations?

Bibliography


For a news-type article on the subject, see:
Ball, P., "Does Hot Water Freeze First?" Physics World April, 2006 [accessed March 19, 2007] http://physicsweb.org/articles/world/19/4/4 .
This review by Monwhea Jeng should be considered essential reading for this project:
Jeng, M., 2005. "Hot Water Can Freeze Faster Than Cold?!?" PhysicsarXiv:physics/0512262, v1 (29 Dec 2005) [accessed March 20, 2007] http://arxiv.org/PS_cache/physics/pdf/0512/0512262v1.pdf.
This Scientific American article has data from actual experiments and includes details of the experimental methods used. It is highly recommended :
Walker, J. 1977. "The Amateur Scientist: Hot Water Freezes Faster Than Cold Water. Why Does It Do So?" Scientific American 237 (3): 246-257.
CEC, 2006. "How Does a Refrigerator Work?" California Energy Commission [accessed March 19, 2007] http://www.energyquest.ca.gov/how_it_works/refrigerator.html .
This is the article that renewed interest in the phenomenon, and gave it the name "the Mpemba effect:"
Mpemba, E.B. and D.G. Osborne, 1969. "Cool?" Physics Education 4:172-175.
For contrary views, see this article and the references in it:
Nave, C.R., 2006. "Hot Water Freezing," HyperPhysics, Department of Physics and Astronomy, Georgia State University [accessed March 19, 2007] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/freezhot.html#c1.
It's always a good idea to understand your experimental apparatus. If you use a freezer for your experiment, you should know how it works:
HowStuffWorks, Inc., 2007. "How Does a Frost-Free Refrigerator Work?" HowStuffWorks.com [accessed March 19, 2007]

http://home.howstuffworks.com/question144.htm.

 

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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!

1. 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.
2. 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.
3. 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.
4. 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.
5. 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: http://www.oufusion.org.uk/newswinter05/fusionnewswinter05.htm

 

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"Siasa si hasa, bali visa na mikasa"