IT IS sometimes said that hot water will freeze faster than cold water. The notion is quite old, and many people in cold places such as Canada wash their car or fill their birdbath with cold water believing that doing so will delay freezing. Is there anything to it? The answer is yes, although this counterintuitive result had little support until Erasto Mpemba, a high school student in Tanzania, rediscovered the effect while making ice cream as a project in physics.

The technique was supposed to be to heat milk, mix in sugar, let the mixture cool to room temperature and then put it in an electric freezer. One day Mpemba and a classmate placed their mixtures in the freezer at the same time, but because they were both in a hurry Mpemba did not bother to cool his mixture and his classmate did not even bother to heat his. Mpemba was surprised to find that his hot mixture froze long before the cool one.

The ice-cream effect gained credibility and fame when Mpemba and D. G. Osborne of University College Dar es Salaam published an account of it in Physics Education. The resulting correspondence in that journal and others was fairly hot and heavy for a while. The scientists who wrote maintained either that the effect was well known or that the observation was in error. The effect is definitely real and can be duplicated in your own kitchen, but the explanation is still the subject of controversy.

One of the first explanations was that the hotter container melted the ice under it and so made better thermal contact with the freezer shelf. The effect is the same, however, when the container is thermally insulated from the freezer shelf, as Mpemba and Osborne's was. Moreover, the explanation would not serve for the examples of washing cars and filling birdbaths or for frost-free freezers where no ice forms on the freezer shelf.

Several factors appear to be involved in the effect. First, in the hotter container the liquid may circulate better, so that the hot water in the central region moves rapidly to the walls of the container or to the top surface of the water. Second, more of the gas dissolved in the water may be released if the water is warmer. Dissolved gas delays cooling, and its elimination before cooling allows the water to reach the freezing point sooner. The hot-water pipes in your home are more likely to freeze than the cold-water pipes because the dissolved gas was eliminated when the water was heated. Third, the warmer water may lose more of its mass and heat to evaporation than the cooler water does. Thus there would be less mass to cool, and the water would reach the freezing point sooner. If there is a significant loss of mass, then (once the freezing point is reached) the initially hot water will certainly freeze faster because there is less mass from which heat must be removed to achieve the transition from liquid water to ice.

Here I shall describe my experiments on freezing water and suggest others that you can do at home, but I have not been able to resolve the controversy. I want to leave that to you. As Ian Firth of the University of St. Andrews put it in one of the most thorough discussions of the subject: "There is a wealth of experimental variation in the problem so that any laboratory undertaking such investigations is guaranteed results different from all others." Your primary difficulty in your own freezing experiments will be to tackle only one variable at a time.

In order to standardize the type of container I did the experiments in ordinary Pyrex beakers with graduated measurements on the side. Pyrex is good for this purpose because it can withstand the rapid temperature change from the stove to the freezer without cracking. A thermocouple probe of the kind described in this department last month was placed below the water level in a beaker and taped in position. The other end of the thermocouple was put in an ice-water bath for a reference temperature, since such a bath is at zero degrees Celsius. Probably most kitchen containers would serve to hold the reference bath, but the most convenient container is a Thermos jug. With it the ice-water bath lasted for several hours. If you dc not want to go to the trouble of setting up the thermocouple, a common thermometer that reads from zero to l00 degrees C. is adequate. Be sure that the mercury reservoir of the thermometer is fully submerged in the water.

To thermally insulate the beaker from the frost on the floor of the freezer I used a cork mat of the kind put under ho dishes. Polystyrene or any thick cloth o pad will work just as well. Without the insulation you might find that the hotter water cools faster partly because it melts itself into the frost better. In frost-free refrigerator no such insulation is needed. The air temperature in my freezer was between-8 and -1 degrees C. To maintain a consistent a temperature be sure to keep the freeze door shut as much as possible.

The beaker should be heated slowly on an electric or gas burner. To guarantee uniform heating of all the water put a flat metal plate over the burner: other wise the thermocouple may be over particularly hot or cool portion of the burner and may give a misleading temperature reading. The beaker should b covered so that the water evaporate during the heating is returned to it. You would do well to work at first with small amount of water, say 50 to 10 milliliters, to hold down the time needed to take the data for several different initial temperatures. The time factor is also a reason why you should have several practice runs before actually taking the data carefully. I began my work with 200 milliliters of water, took data for three days and then found I had not bee careful enough in my procedure. I had to discard all the data.

When the water reaches the desire initial temperature on the stove, it an the attached thermocouple probe must be quickly moved into the freezer because of the rapid cooling of the water in the first several minutes after the beaker is removed from the heat source. You cannot obtain accurate readings by firs 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.

I worked with ordinary tap water that had been boiled to eliminate dissolve gas. After each run I allowed the water to return to room temperature before added water to restore the original volume. By measuring the amount of water needed to restore the original volume in the beaker you measure the amount o water lost through evaporation during cooling. I found that the most accurate and convenient way to replace the water was to squirt it from a hypodermic syringe marked in cubic centimeters.

The thermocouple probe was placed at various depths in the water to monitor the cooling rate at different depths. You should avoid letting the probe become exposed to the air during a run as evaporation lowers the water level, because then it samples only the air temperature With a blower turning on and off in frost-free refrigerator, you then get perplexing oscillation in temperature readings. If you do use a frost-free refrigerator, try to keep the blower either on or off for the entire run. The air cur rent set up by the blower is a significant factor in cooling the beaker.

Instead of measuring the time needed to freeze all the water I stopped each run when the thermocouple reached zero degrees C. By then a thin layer of ice ha usually formed on the outer edge of the surface of the water. One might be able to measure the time of complete freezing by placing the thermocouple in the middle of the sample and waiting until the temperature began to drop below zero degrees C. Not until the water is completely frozen can the temperature be below zero degrees.

The best test for any procedure you devise is repeatability. As repeatable as most of my measurements were, however, I still obtained strange large deviations on some of the runs. I do not know the reason, but I suspect that impurities in the water altered the time needed to cool it.

My first run was with 50 milliliters of water in a small beaker, graduated to 150 milliliters, which had an inside diameter of 5.3 centimeters and a height of 8.1 centimeters. The water in it had a height of about 1.8 centimeters. I used a refrigerator with a freezer that was not frost-free. A plot of the time needed to cool the water to zero degrees C. against the initial temperature of the water showed a steady rise until about 80 degrees for the initial temperature. Thereafter the cooling curve rose less rapidly. Disappointingly, the curve did not bend over in such a way as to show that less time would be needed for a high initial temperature than for a cooler one.

The same amount of water in a larger beaker (graduated to 600 milliliters, diameter 8.2 centimeters, height 12.4 centimeters, water height .9 centimeter) and in the same freezer did give a curve that bent over at an initial temperature of between 60 and 65 degrees C. This result means that water beginning at, say, 99 degrees would reach the freezing point about seven minutes before water beginning at 60 degrees. Presumably if I were to time the process until the water had frozen completely, the bending over of the curve would be even more pronounced if the evaporation of the water was a significant factor. With more evaporation at the higher temperatures, more mass would be lost and less heat would have to be removed from water at zero degrees C. in order to transform it into ice.

The results suggest that evaporation is important. In going from the small beaker to the large one the area of the water surface more than doubled, and the rate of evaporation therefore increased. I do not know, however, how the shortening of the water column affected the convection-current cells in the water. A more important quantity in describing the change between beakers might be the ratio of the surface area to the area of the sides. From the surface the heat loss is primarily by evaporation, whereas through the sides the loss is by convection and radiation. The change in beakers increased this ratio of areas by three times. Evaporation therefore gained an advantage over the heat loss through the sides of the beaker, and that may be why the time curve then bent over.

With the same amount of water in the same beaker but in a frost-free freezer the water cooled in about half the time because of the constant blowing of the air around the beaker. The bend in the curve is still visible and appears at approximately the same temperature. At initial temperatures near the boiling point the curve appears to rise again. Perhaps there the increase in temperature begins to outweigh the loss of mass due to evaporation or the increase in water circulation. You might want to search for such a second rise in your own data; no one has yet reported it.

Increasing the water volume to 100 milliliters in the 600-milliliter beaker and returning to my original refrigerator, I took data with the thermocouple probe near the bottom of the water and then again near the top. The bottom displayed a curve that bent over nicely but with the peak cooling time shifted to a higher initial temperature of about 80 degrees C. Water initially at 95 degrees reached the freezing point about three minutes before water initially at 80 degrees.

To see when initially hot water and initially cooler water reached the same temperature in their race to the freezing point I took temperature measurements about every five minutes during the runs where the thermocouple was near the bottom. Particularly interesting was the minute-by-minute comparison between the water initially at the temperature (81 degrees C.) requiring the most time to reach freezing and the water initially even hotter (95.5 degrees). The initially hotter water reached the same temperature as the water initially at 81 degrees seven or eight minutes after the cooling began. The temperature of the initially hot water then stayed below that of the initially cooler water until the last 15 or 20 minutes before freezing. Just before the initially hot water froze its temperature dropped rapidly to the freezing point, whereas the initially cooler water stayed near one degree C. for several more minutes.

If the cooling rate is exponential, that is, if the temperature of the water depends on an exponential function of the elapsed time, then the data will yield a straight line when they are plotted on semilog paper. Plotting my data in that way, I found that the cooling is rather steep in the first and last few minutes of each run but that straight lines can be fitted through the data points for most of the run. The samples of water starting at 81 degrees C. and at 55 degrees appear to have two regions in their cooling, because for each one I had to use two straight lines with different slopes to fit the data points. Except for the first and last few minutes the curves for the two samples were parallel, suggesting similar cooling mechanisms for each The water beginning at 95.5 degrees C had a much steeper slope in the first half of the run, suggesting an additional mechanism of heat loss that the water at the lower initial temperatures did not have. In other words, above a starting temperature of 81 degrees C. either evaporation loss or circulation suddenly becomes significant and the cooling rate is increased.

The measurements taken near the surface of the water showed a more pronounced bending over of the curve of time needed to reach freezing than the measurements taken near the bottom. The initial temperature requiring the most time to reach freezing appeared to be the same. I reran the surface measurements with the same initial temperature of 70 degrees C. as in a bottom measurement in order to see how the surface and the bottom differed in temperature during a run. Within a few minutes after the beginning of a run the surface was cooler by a few degrees, the difference increasing to three degrees by the middle of the run and then narrowing again until within a few minutes before the surface began to freeze. More measurements such as these would be interesting because the convection-current cells in the water are driven by the difference in temperature between the surface of the water and the bottom. You might want to do more work on this temperature difference in order to determine the possible influence of the convection cells on the freezing effect. I suggest, however, that instead of repeating runs as I have done you lower two thermocouples into the water to take the measurements at the different depths simultaneously.

To decrease the effect of evaporation, at least by eliminating the loss of mass due to evaporation, I repeated the run for 100 milliliters of water in a 600-milliliter beaker with the thermocouple near the bottom, but this time I fastened a plastic food wrapping over the top of the beaker with a rubber band. Evaporation still removed heat from the water but the evaporated mass condensed on the plastic wrapping and dripped back into the beaker. For all the initial temperatures the time needed to reach freezing increased. This result suggests that the loss of mass during evaporation is important.

Measuring the loss of mass in normal runs by finding how much water is needed to refill the beaker to its previous level is not very accurate. Nevertheless, the general result is that more water is lost when the initial temperature is higher. In a theoretical study of the cooling rate in water George S. Kell of the National Research Council of Canada found that water cooling from 100 to zero degrees C. loses about 16 percent of its mass if the primary heat loss is by evaporation. My results appear to be in line with Kell's calculations, again suggesting that the loss of heat and mass by evaporation is important in the paradoxical freezing effect.

The circulation of the cooling water can be examined by squirting a small amount of dye into the beaker of water with a hypodermic syringe. The large-scale motion is a rising in the center and a sinking on the outside edge. The transport of heat by this circulation cell is probably determined in part by the depth of the water, the cross-sectional area of the beaker and the temperature difference between the top and the bottom of the water column. I do not know of any easy calculation to show how these factors influence the heat transport, and so I do not know how much of the freezing effect is due to the circulation of the water.

Much work remains to be done on this effect. How does the surface area influence the time required for freezing? Is there a particularly advantageous ratio of surface area to side area that will enhance the bending of the curves? If you have access to a walk-in freezer, you could measure the loss of mass from the beakers during the cooling by running the experiment on a balance. The relation of mass loss to the temperature of the water as a function of time could be checked against theoretical predictions such as those Kell has made.

An interesting conjecture offered by Kell is that one reason this freezing effect has been largely forgotten in modern times is that the replacement of wood pails by metal ones diminished or eliminated the effect. Faster conduction of heat through the walls and the bottom of the container may diminish the importance of evaporation to the cooling. Firth argues against this conclusion. You can check it by using containers of the same size but made of different materials, such as metal and plastic. You can also work with two Pyrex beakers, putting a layer of thermal insulation around the sides and under one of them.

My results on the mass loss can be improved by cutting off the beakers just above the waterline. When a beaker is thus shortened, none of the evaporated water can collect on it to fall back into the water.

In addition to eliminating the loss of mass by putting a cover on the beaker you might try spreading a thin layer of oil on the surface. If the freezing effect is due to evaporation, the effect should then be lessened. Such thin layers of fluid have been spread on bodies of water in arid regions to decrease evaporation.

One of the major factors in the cooling rate of tap water was eliminated in my experiments, namely the gas dissolved in cold water from the faucet. Although controlling the amount of gas dissolved in the water would be very difficult, you can at least run the experiment under identical conditions except with fresh tap water and with previously boiled water. Does the dissolved gas actually retard the cooling?

You might also investigate how the cooling rate is affected if salt is added to the water to lower the freezing point. The effect might be more pronounced is instead of water you use a fluid (such a alcohol) that evaporates more readily. You will not freeze the alcohol unless you have access to extreme means o cooling, such as with liquid nitrogen, but the time needed to reach zero degrees C. may show the bent curve that is found with water.

Bibliography

COOL? E. B. Mpemba and D. G. Osborne in Physics Education, VOI. 4, NO. 3, pages 172-175; May, 1969.

THE FREEZING OF HOT AND COLD WATER. G. S. Kell in American Journal of Physics, Vol. 37, NO. 5, pages 564-565; May, 1969.

COOLER? Ian Firth in Physics Education, Vol. 6, NO. 1, pages 32-41; January, 1971.

COOLER-LOWER DOWN. Eric Deeson in Physics Education, Vol. 6, NO. 1, pages 42-44 January, 1971.

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