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 spotin 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 theirexperiments 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 alreadyin 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 separateexperiments (a–f), each with a different symbol:

1. 50 ml water in small beaker, non-frost-free refrigerator (black squares),

2. 50 ml water in large beaker, non-frost-free refrigerator (red circles),

3. 50 ml water in large beaker, frost-free refrigerator (green triangles),

4. 100 ml water in large beaker, thermocouple near bottom (blue triangles),

5. 100 ml water in large beaker, covered with plastic wrap, thermocouple near bottom (light blue diamonds),

6. 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.

This project is an excellent illustration that thorough background research, a clear formulation of your hypothesis, and carefulexperimental 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.

Materials and Equipment

• identical Pyrex beakers for holding water,
• metal plate for stove burner to distribute heat evenly,
• cover for the beaker during heating,
• two thermometers,
• freezer (or other means for cooling water below freezing point),
• stove (or other means of heating the water),
• hot mitt,
• gram scale,
• clock or timer.

Experimental Procedure

1. Do your background research so that you are knowledgeable about the terms, concepts and questions, above. You should also do as much research as possible on previous experiments related to this phenomenon. The articles by Jeng and Walker (Jeng, 2005; Walker, 1977) are highly recommended.
2. Choose 4 or more initial temperatures to test, and follow the same standard procedure for each initial temperature. For example:
   1. Measure a chosen volume of water (e.g., 50 ml) into a Pyrex beaker.
   2. Cover the beaker so that water vapor will be captured and returned.
   3. Heat the water to the desired initial temperature.
   4. Quickly weigh the beaker and water and then place in the freezer.
   5. Monitor the temperature at regular intervals, and record how long it takes for the temperature to reach 0°C.
   6. Weigh the beaker and water at the end of the experiment to see how much water evaporated while it was in the freezer. (You can let the beaker warm up, so that there is no condensation on it, but keep it covered so that water does not evaporate.)
   7. Repeat the experiment at least three times for each chosen initial temperature.

Variations

There are many possible explanations for the Mpemba effect which you could choose to explore. You can think of your own variation on this experiment, or explore one or more of these variables:

• the method used for freezing, (e.g.: freezer compartment of your refrigerator, rock salt and ice bath, dry ice and alcohol bath, walk-in freezer, outdoors in sub-freezing weather),
• the method used for controlling evaporation, (e.g.: either covering the containers, or adding a layer of oil on top of the water should reduce evaporation),
• container material, size, and shape,
• endpoint of the experiment: wait for freezing solid instead of reaching 0°C.