[Physics FAQ] - [Copyright]
updated 11-Jul-1996 by PEG
updated 11-May-1992 by SIC
original by Richard M. Mathews
Many thanks also to David Auerbach for comments which have greatly helped to improve this article.
You put two pails of water outside on a freezing day. One has hot water (95 degrees C) and the other has an equal amount of colder water (50 degrees C). Which freezes first? The hot water freezes first! Why?
It is commonly argued that the hot water will take some time to reach the initial temperature of the cold water, and then follow the same cooling curve. So it seems at first glance difficult to believe that the hot water freezes first. The effect is definitely real and some people claim to have duplicated it in their refrigerator.
This question is a favourite of popular science magazines where it is often referred to as the Mpemba effect after a Tanzanian student who observed it while making ice cream and raised the question in 1969. However, the folklore on this matter may well have started centuries ago when wooden pails were usual. Sir Francis Bacon, Descartes and even Aristotle are said to have remarked on it.
Every "proof" that hot water can't freeze faster assumes that the state of the water can be described by a single number, the temperature, but remember that temperature is a function of position. There are also other factors besides temperature, such as motion of the water, gas content, etc. With these multiple parameters, any argument based on the hot water having to pass through the initial state of the cold water before reaching the freezing point should be examined very carefully.
There are a number of factors which contribute to this effect. Each one of them may have greater or lesser significance depending upon relative temperatures, air conditions, container dimensions and material etc. Here we describe five of the most important factors. In any real situation a combination of these processes and possibly others may be at work. (David Auerbach's article cited below should be consulted for more factors).
Although detailed research has been done on some specific cases where hot water freezes faster than cold, the classic experiment with pails of water has probably not been studied in enough detail to establish the correct conditions for it to happen and the most significant causes of the effect. The answers given here should not be considered definitive without further studies. In principle it should not be difficult to devise the appropriate experiments to test the significance of the factors given, or even to do a good quantitative analysis of each one. If anyone ever does, please send us the results!
The cooling of pails without lids is partly Newtonian and partly by evaporation of the contents. The proportions depend on the walls and on temperature. Evaporation is more important while the temperature is high and there is a large exposed surface area. If equal masses of water are taken at two starting temperatures, more rapid evaporation from the hotter one may diminish its mass enough to compensate for the greater temperature range it must cover to reach freezing. In one experiment, water cooling from 100C lost 16% of its mass by 0C.
The cooling effect of evaporation is twofold. First, mass is carried off so that less needs to be cooled from then on. Also, the temperature drops due to heat lost in causing the phase change from water to vapour (latent heat of evaporation).
Thus experiment and theory agree that hot water freezes faster than cold for sufficiently high starting temperatures, if the cooling is by evaporation. Cooling in a wooden pail or barrel may often be predominantly by evaporation. In fact, a wooden bucket of water starting at 100C would finish freezing in 90% of the time taken by an equal volume starting at room temperature.
When water cools below 0C it does not always freeze. In some conditions it can undergo supercooling, remaining liquid at temperatures below its freezing point. Sometimes it may remain liquid at temperatures as low as -20C.
The reason is that ice crystals require nucleation points to start formation. Nucleation points may be gas bubbles, dust particles or a rough surface. If these are not present in the liquid then supercooling will occur until the temperature goes so low that ice crystals form spontaneously. Once they start to form in a supercooled liquid they will grow rapidly forming a slush which then freezes further to solid ice.
Why is water in the hot bucket more likely to supercool? Firstly, heating the water will remove dissolved gases which would otherwise have formed bubbles as the liquid cools, and which might have acted as nucleation points. In a bucket it is also possible that nucleation will start on the inner bucket surface unless it is very clean and smooth. In the case of wooden buckets the wood itself may retain sufficient heat from the initially hot water to delay nucleation at the sides.
Why does supercooling result in the hotter water freezing faster? First consider the water which started colder and which does not get supercooled. In this case a thin layer of ice is likely to form quickly on the surface. This layer acts as insulation between the water and the cold air and also prevents further evaporation. The rate of ice formation after this initial layer has formed is considerably slower. In the case of the water which started out hot and which is subjected to supercooling, the supercooled water no longer has this protective layer of ice. It loses heat at a much faster rate through its exposed surface. When the supercooling ends and it finally does freeze much more heat will have been lost and more ice will form than in the other bucket.
A considerable amount of experimental support has been offered for the significance of supercooling and some experts now believe that it is the most important factor in the cause of the Mpemba effect. However, most of these experiments have been carried out in rather ideal experiments. For example, sealed glass containers filled with water are plunged into freezing cold liquid. Such experiments are designed to produce supercooling and it is not clear how well they represent the classic case of water in a bucket.
A peculiar property of water is that it is most dense at 4C. If you start with a bucket of water at 4C and place it outside at a lower temperature, the water at the surface will cool rapidly. Because this water is less dense than the water below which remains at 4C, it will stay at the surface forming a thin cold layer. Under such conditions a thin layer of ice will form on the surface after only a short space of time, but this layer will then act as an insulator protecting the water below most of which is still at 4C. Further freezing is then very slow assuming that the bucket itself is made of a good insulating material.
The situation with the hot bucket is rather different. The surface water cools even more rapidly due to evaporation and the large temperature difference. However, the cooled water is now more dense than the hot water below. It sinks, pushing more hot water to the surface. Significant convection currents are driven by the water cooling from the surface and sinking. This circulation of water ensures that the temperature drops rapidly.
But why doesn't it reach a stable state with the water at 4C and then follow the same course as the colder water? This is a very good question! To explain the Mpemba effect through convection alone it would be necessary to show that hot and cold water currents are separated in the process and that convection can continue after the average temperature had dropped below 4C.
However, no experimental evidence has been found to support the hypothesis that cold and hot water are separated by convection in this way. If convection plays any role at all, it is more likely to be in aiding the rapid cooling down to temperatures of 4C.
Water always contains dissolved gases such as oxygen and carbon dioxide. These impurities have the effect of lowering its freezing point. When water is heated, much of these gases are driven out because their solubility in water is less at higher temperatures. When the hot water cools it then has less dissolved gas than water which was not heated so it has a higher freezing point and freezes first. This is often cited as a an important factor but no references to experimental evidence or quantitative analysis have been given.
This final mechanism is more relevant to the case where water is placed in a freezer in small containers. In such circumstances it has been observed that the warmth of the hot water container can melt ice encrusting the surface on which it is placed. When this refreezes it creates a good connection between the container and the surface which allows much better conduction of heat than the frost on which the colder container rests. As a result, heat is drawn out of the warmer container more rapidly.
This factor can be easily tested by setting up the right conditions in a freezer.
"Hot water freezes faster than cold water. Why does it do so?", Jearl Walker in The Amateur Scientist, Scientific American, Vol. 237, No. 3, pp 246-257; September, 1977.
"The Freezing of Hot and Cold Water", G.S. Kell in American Journal of Physics, Vol. 37, No. 5, pp 564-565; May, 1969.
"Supercooling and the Mpemba effect", David Auerbach, in American Journal of Physics, Vol. 63, No. 10, pp 882-885; Oct, 1995.
"The Mpemba effect: The freezing times of hot and cold water", Charles A. Knight, in American Journal of Physics, Vol. 64, No. 5, p 524; May, 1996.
"The Final Word", New Scientist, 2nd December 1995. (see also a letter from Charles Knight in the 26th March 1996 issue)