A search for the Mpemba effect: When hot water freezes faster then cold water James D. Brownridge Department of Physics, Applied Physics, and Astronomy, State University of New York at Binghamton, P.O. Box 6000 Binghamton, New York 13902-6000, USA Abstract: An explanation for why hot water will sometime freeze more rapidly than cold water is offered. Two specimens of water from the same source will often have different spontaneous freezing temperatures; that is, the temperature at which freezing begins. When both specimens supercool and the spontaneous freezing temperature of the hot water is higher than that of the cold water, then the hot water will usually freeze first, if all other conditions are equal and remain so during cooling. The probability that the hot water will freeze first if it has the higher spontaneous freezing temperature will be larger for a larger difference in spontaneous freezing temperature. Heating the water may lower, raise or not change the spontaneous freezing temperature. The keys to observing hot water freezing before cold water are supercooling the water and having a significant difference in the spontaneous freezing temperature of the two water specimens. We observed hot water freezing before cold water 28 times in 28 attempts under the conditions described here. I. Introduction Before starting the search for the Mpemba effect, the meaning of freezing Two identical containers holding the faster or freezing first must be same amount of water at different addressed. Does it mean the onset of the temperatures are placed in a freezer, and release of the latent heat of freezing, or you determine that the hot water freezes the appearance of the first ice crystal or first. Did you observe the Mpemba the solidification of the last bit of liquid effect?1 The Mpemba effect describes water? If you selected one of the above the phenomenon of a sample of hot as your answer, how would you observe water freezing faster than a specimen of the time at which that event occurred in cold water. To understand why we ask a specimen of water? For example, in this question, we encourage the reader to Fig. 3, how long did it take for the water read the Monwhea Jeng review paper, to freeze? Now, imagine that we have Hot water can freeze faster than cold, combined the results from eight different for background and perspective.2 In this laboratories in which everything was paper; we will attempt to explain why identical, except for the positions of the hot water can freeze faster than cold thermocouples in the water. In this case, water when all other conditions are each laboratory would report a different identical. We will also demonstrate, by time of freezing. These differences were showing experimental results, why, for a major barrier to obtaining reproducible over 2000 years, it has been so difficult results during the early phase of this to reproduce this result in the same study. A difference in position of only a laboratory, let alone at different few millimeters can be significant laboratories and with different depending on the size of the container. investigators. Because, of the uncertainty in what is meant by “freezing first” or “freezing 1 faster,” we will define the time of years ago. Now, after many years of freezing as the time when the latent heat laboratory work freezing hot and cold of freezing is released. The cooling water, I am prepared to explain why hot curves in this paper clearly show when water will sometimes freeze before cold the latent heat of freezing is released. water when one of two seemingly The exact time when the first ice crystal identical specimens are randomly appears or when the last few molecules selected for heating and both are placed of liquid water become solid ice is not in a cooling environment to freeze. always apparent. However, a sudden rise in temperature from several degrees As it turned out, data suggesting an below 0o C indicates that the latent heat answer to this question was published by of freezing was released as the specimen N. Ernest Dorsey in 1948.6 Although he supercooled, as seen in Fig. 1. In the rare did not specifically address or answer case when a specimen does not the question, the answer is clear in his supercool, the temperature suddenly data. My laboratory results have stops decreasing at 0o C, indicating that confirmed several of his findings. Key the sample is freezing. among them: “…For each specimen there are one or more preferred With the tip of a thermocouple in a temperatures at which spontaneous specimen of water, the time that the freezing occurs…” and “…Preheating latent heat of freezing is released can be the melt produces no certain effect upon determined to within 100 ms as the it …”6 In other words, if a specimen of water supercools a few o C, as seen in water in a sealed container is heated and Fig. 5. then cooled again, it may freeze at a higher, lower or the same temperature as The fact that hot water will sometimes it would have had it not been heated. freeze before cold water has been Heating a specimen of water may or may observed and debated since around 350 not cause it to freeze before a cold BC; see reference 2 and the references specimen. Scientific and popular therein. The question of why hot water literature, as well as anecdotal reports, can freeze before cold water when all confirms this.1-9 other conditions are as equal as possible is still debated in both popular and Dorsey referred to “…preferred scientific literature.1-5 Several good temperature at which spontaneous discussions of the history of the Mpemba freezing occurs” as motes in 1948; they effect and why there is not a generally are now called nucleation sites.6 He accepted answer can be found in purposed that there may be one or more reference 2 and the references therein. motes in a specimen of water and that they each may have a different Several years ago, a colleague asked me spontaneous freezing temperature, which if it was true that hot water could freeze can be changed. before cold water. I answered yes, and he asked why; to make a long story If each nucleation site (mote) in a short, I did not know. However, I specimen of water has a unique assured him that I would have the spontaneous freezing temperature6, then answer soon. That was more than ten a specimen of water should freeze when 2 its temperature reaches the highest one cool, are placed in a different cold spontaneous freezing temperature among environment to freeze. The results of the nucleation sites, which is what we these two experiments are presented in observed. Figs. 1 and 2. This ambiguity in which sample freezes first is typical of A quote from the review paper by published experimental investigations of Monwhea Jeng2 explains why there is the Mpemba effect. The aim of this work not a generally accepted mechanism for is to identify the conditions under which the Mpemba effect. hot water will consistently freeze before cold water. What follows is a “Because there are so many factors that can be description of a set of experiments that varied and the results of the experiments can led to the identification of these depend sensitively on any of these factors, experimental results are varied and difficult to conditions. organize into a consistent picture...” Monwhea Jeng.2 Some of the factors are: The definition of freezing first; is it the first ice crystal or is it when all liquid is solid? The definition of the freezing time. The position of the temperature-measuring device in the water. The container shape. The type of container. Are all conditions except temperature truly identical, and do they remain so during cooling? The loss of water by evaporation. Fig. 1. Cooling curves of hot water and cold Does the hot container cause a change in the water. The same amount of water was added to cooling rate? two glass vials of equal weight. The vials were then suspended inside a freezer and allowed to In this research, we independently air cool. The temperature of the air inside the freezer was -15oC. addressed each of these variables and more. II. The paradox Two “identical” containers holding the same amount of water by weight, one hot and one cold are placed in a cold environment to freeze. The hot water freezes first. Some time later, two Fig. 2. Cooling curves of hot water and cold “identical” containers holding equal water. The same amount of water was added to amounts of water by weight, one hot and two glass vials of equal weight. The vials were then suspended inside a freezer and allowed to 3 air cool. The temperature of the air inside the o freezer was -15 C. IV Experiment 1 Definition of “freezing first” After settling on a definition of “freezing first”, we needed an objective way to determine exactly when a specimen of water was frozen. Because we defined “freezing” as the instant that the latent heat of freezing begins to be released, the experiment was designed to objectively determine this time. In Fig. 4, we show a schematic diagram of the apparatus designed to measure the onset Fig. 3. The signal that latent heat has begun to of the release of the latent heat of flow is independent of the position of the freezing in two simultaneous ways. thermocouple tip in the water (inset (a)). The shape of the cooling curves above freezing and the time to solid ice are, however, very sensitive If a specimen of water supercools, we to the thermocouple position.