When does hot water freeze faster then cold water? A search for the Mpemba effect ͒ James D. Brownridgea Department of Physics, Applied Physics, and Astronomy, State University of New York at Binghamton, P.O. Box 6000, Binghamton, New York 13902-6000 ͑Received 24 February 2010; accepted 26 August 2010͒ It is possible to consistently observe hot water freezing faster than cold water under certain conditions. All conditions except the initial temperature of water specimens must be the same and remain so during cooling, and the cold water must supercool to a temperature significantly lower than the temperature to which the hot water supercools. For hot water at an initial temperature of ϾϷ80 °C and cold water at ϽϷ20 °C, the cold water must supercool to a temperature of at least Ϸ5.5 °C, lower than the temperature to which hot water supercools. With these conditions satisfied, we observed initially hot water freezing before the initially cold water 28 times in 28 attempts. If the cold water does not supercool, it will freeze before the hot water because it always cools to 0 °C first regardless of the initial temperatures. © 2011 American Association of Physics Teachers. ͓DOI: 10.1119/1.3490015͔ I. INTRODUCTION obtain reproducible results is because the position of the temperature-measuring device is critical to an accurate deter- Two identical containers with the same amount of water at mination of when all of the water in a container is frozen. different temperatures are placed in a freezer, and the hot Imagine that we have combined the results from many labo- water freezes first. Did you observe the Mpemba effect?1 ratories in which everything was identical except for the po- Since around 300 BCE, the idea that hot water sometimes sitions of the thermocouples in the containers of water, and freezes before cold water has been studied and debated.2,3 we had agreed that when the temperature reached −4 °C, we The reasons why hot water can freeze before cold water would consider the water frozen ͑see Fig. 1͒. In this case, when all conditions are equal are still discussed in the popu- each laboratory would likely report a different time of freez- lar and scientific literature.4–9 ing. These differences were a major barrier in obtaining re- In 1948, Dorsey published data that suggest an answer to producible results during the early phase of this study, and I this question.10 Although he did not specifically address the suggest that it is a universal problem. A difference in position question, the answer is in his data, and my results have con- of only a few millimeters can be significant. The time to firmed several of his findings. Key among them includes that complete solidification varies with the depth of supercooling. “for each sample there are one or more preferred tempera- To avoid this problem, we will define the time of freezing tures at which spontaneous freezing occurs” and “preheating as the time when the latent heat of freezing is released. An the melt produces no certain effect upon it.”10 In other abrupt change in the temperature of the water signals that words, if water in a sealed container is heated and then latent heat has been released. Small volumes of very pure cooled again, it may freeze at a higher, lower, or the same water with no foreign particles in it can be supercooled to as temperature as it would have if it had not been heated. Heat- low as Ϸ−41 °C;11 at this temperature, it is homogeneous ing a container of water does not ensure that it will freeze nucleation that initiates freezing.11,12 Hereafter, we will refer before a cold sample. to foreign particles as “ice nucleation sites.” There is no generally accepted mechanism for the If drinking water is placed in a subzero environment and Mpemba effect. Jeng stated, “Because there are so many fac- not disturbed, it will usually not freeze when its temperature tors that can be varied and the results of the experiments can falls to 0 °C. It will supercool to below 0 °C before hetero- depend sensitively on any of these factors, experimental re- geneous nucleation initiates freezing.11 When freezing is ini- sults are varied and difficult to organize into a consistent tiated by heterogeneous nucleation, the water will not freeze picture.”3 An important factor is the characterization of until its temperature falls to what we call the “ice nucleation freezing—is it the occurrence of the first ice crystal or is it temperature.” We define the latter as the temperature at when all the liquid is solid? Other factors include the posi- which latent heat is released. This temperature varies from tion of the temperature-measuring device in the water ͑see sample to sample and may vary for the same sample. Our Fig. 1͒, the type of container and its shape, and the possible experiments show that many foreign particles are present in loss of water by evaporation. Are all conditions except the every sample of water and that the temperature at which a initial temperature identical and remain so during cooling? particular foreign particle initiates heterogeneous nucleation Does a hot container cause a change in the cooling rate? may be at any temperature between 0 and Ϸ−25 °C. None The aim of this paper is to address each of these factors of the water samples we used supercooled below Ϸ−25 °C. and questions and identify the conditions under which hot water freezes before cold water. Because the question of why II. DATA ACQUISITION hot water sometime freezes faster than cold water has re- mained unanswered for over 2000 years, we will describe in The apparatus consisted of one Omega OMB-DAQ-3000 detail the experiments that led to the identification of the Series 1-MHz, 16-bit USB Data Acquisition module, two conditions under which hot water freezes before cold water. National Instruments PIC-6034E interface cards configured A primary reason why researchers have not been able to to accept eight Type K thermocouples each, two PASCO 78 Am. J. Phys. 79 ͑1͒, January 2011 http://aapt.org/ajp © 2011 American Association of Physics Teachers 78 Fig. 2. Apparatus used to measure the time to freeze. Fig. 1. Illustration of the importance of the position of the temperature- measuring device to accurately determine the time it takes for the water to ing the vial. The mean freezing temperature was completely freeze. The curve with the solid circles represents the tempera- −11.80Ϯ0.17 °C, with a maximum freezing temperature of ture at the top of the container and the curve with the open circles represents −11.2Ϯ0.4 °C and a minimum of −12.8Ϯ0.1 °C. Heating the temperature at the bottom of the container. The unlabeled curves show this sample of water did not reduce the time of freezing. The the temperature gradient from bottom to top as the water cools from time t0 Ϸ hotter the water, the longer it took to cool to 0 °C and ulti- and then freezes to solid ice. At time tm, the water has cooled to 4 °C, the temperature of maximum density, and all eight thermocouples show that the mately freeze from a supercooled state. This experiment was water in the container is at a uniform temperature for the first time since repeated in a completely different setup using hard tap water, cooling began. The water remains at uniform temperature until solid ice and no Mpemba effect was observed. These data show that Ϸ begins to form at the bottom of the container at time tb 7 h. Latent heat each sample of water had a narrow range of ice nucleation Ϸ was released after time tf 3 h. If we had used only one thermocouple near temperatures—the temperature at which latent heat was re- the bottom, we would have erroneously concluded that the water had frozen Ϸ leased. The mean ice nucleation temperature of at time tb. The water did not completely become solid until time ts 17 h Ϯ after cooling began. The correct location for a single temperature-measuring −11.80 0.17 °C was unaffected by heating the water to a device is just below the surface of the water in the center of the container as temperature of Ϸ103 °C as was done 18 times out of the 138 depicted in the inset. freeze/thaw cycles. We conclude that heating water does not cause it to freeze faster. Xplorer GLX with eight temperature probes, two Keithley IV. WHY HOT WATER MAY SOMETIMES FREEZE Instrument Model 155 Null Detector micro voltmeters, three FASTER freezers, and a Lauda RM6-RMS Brinkmann Refrigerating Circulating Bath. The temperature and time data were re- In some cases, hot water freezes sooner because of the corded by a computer usually at a rate of 1 Hz but more higher thermal conductivity between the water container and slowly for cooling rates less than 1 °C/min. We collected the surface of the subzero environment. Two identical copper data for several thousand freeze/thaw cycles because it took cups were placed in a freezer on a bed of frost. The hot cup this many cycles to discover all of the factors that could and caused the frost underneath it to melt forming a pool of liq- did go wrong and to design a set of experiments that met our uid water that soon froze. The cooling conditions were objectives. III. DOES HEATING WATER CAUSE IT TO FREEZE FASTER? To answer this question we flame-sealed 1 ml of distilled water in a small Pyrex test tube, hereafter referred to as a vial.