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About the Mpemba Effect

Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real. It has been seen and studied in numerous experiments. While this phenomenon has been known for centuries, and was described by Aristotle, Bacon, and Descartes [1–3], it was not introduced to the modern scientific community until 1969, by a Tanzanian high school pupil named Mpemba.

Both the early scientific history of this effect, and the story of Mpemba’s rediscovery of it, are interesting in their own right — Mpemba’s story in particular providing a dramatic parable against making snap judgements about what is impossible. This is described separately below.The phenomenon that hot water may freeze faster than cold is often called the Mpemba effect. Because, no doubt, most readers are extremely skeptical at this point, we should begin by stating precisely what we mean by the Mpemba effect. We start with two containers of water, which are identical in shape, and which hold identical amounts of water. The only difference between the two is that the water in one is at a higher (uniform) temperature than the water in the other. Now we cool both containers, using the exact same cooling process for each container. Under some conditions the initially warmer water will freeze first.

If this occurs, we have seen the Mpemba effect. Of course, the initially warmer water will not freeze before the initially cooler water for all initial conditions. If the hot water starts at 99.9°C, and the cold water at 0.01°C, then clearly under those circumstances, the initially cooler water will freeze first. However, under some conditions the initially warmer water will freeze first: if that happens, you have seen the Mpemba effect. But you will not see the Mpemba effect for just any initial temperatures, container shapes, or cooling conditions.

This seems impossible, right? Many sharp readers may have already come up with a common proof that the Mpemba effect is impossible. The proof usually goes something like this. Say that the initially cooler water starts at 30°C and takes 10 minutes to freeze, while the initially warmer water starts out at 70°C. Now the initially warmer water has to spend some time cooling to get to get down to 30°C, and after that, it’s going to take 10 more minutes to freeze. So since the initially warmer water has to do everything that the initially cooler water has to do, plus a little more, it will take at least a little longer, right? What can be wrong with this proof? What’s wrong with this proof is that it implicitly assumes that the water is characterized solely by a single number — its average temperature. But if other factors besides the average temperature are important, then when the initially warmer water has cooled to an average temperature of 30°C, it may look very different than the initially cooler water (at a uniform 30°C) did at the start. Why? Because the water may have changed when it cooled down from a uniform 70°C to an average 30°C. It could have less mass, less dissolved gas, or convection currents producing a non-uniform temperature distribution. Or it could have changed the environment around the container in the refrigerator. All four of these changes are conceivably important, and each will be considered separately below. S

o the impossibility proof given above doesn’t work. And in fact the Mpemba effect has been observed in a number of controlled experiments [5,7–14]It is still not known exactly why this happens. A number of possible explanations for the effect have been proposed, but so far the experiments do not show clearly which, if any, of the proposed mechanisms is the most important one. While you will often hear confident claims that X is the cause of the Mpemba effect, such claims are usually based on guesswork, or on looking at the evidence in only a few papers and ignoring the rest.

Of course, there is nothing wrong with informed theoretical guesswork or being selective in which experimental results you trust; the problem is that different people make different claims as to what X is.Why hasn’t modern science answered this seemingly simple question about cooling water? The main problem is that the time it takes water to freeze is highly sensitive to a number of details in the experimental setup, such as the shape and size of the container, the shape and size of the refrigeration unit, the gas and impurity content of the water, how the time of freezing is defined, and so on. Because of this sensitivity, while experiments have generally agreed that the Mpemba effect occurs, they disagree over the conditions under which it occurs, and thus about why it occurs.

As Firth [7] wrote “There is a wealth of experimental variation in the problem so that any laboratory undertaking such investigations is guaranteed different results from all others.”So with the limited number of experiments done, often under very different conditions, none of the proposed mechanisms can be confidently proclaimed as “the” mechanism.

Above we described four ways in which the initially warmer water could have changed upon cooling to the initial temperature of the initially cooler water. What follows below is a short description of the four related mechanisms that have been suggested to explain the Mpemba effect. More ambitious readers can follow the links to more complete explanations of the mechanisms, as well as counter-arguments and experiments that the mechanisms cannot explain. It seems likely that there is no one mechanism that explains the Mpemba effect for all circumstances, but that different mechanisms are important under different conditions.

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