February 18, 2008

Can hot water freeze faster than cold water?

Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counter- intuitive, 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, it was not introduced to the modern scientific community until 1969, by a Tanzanian high school student 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 provides 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 -- the 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.

So the impossibility proof given above doesn't work. And in fact the Mpemba effect has been observed in a number of controlled experiments. 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 set- up, 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 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.

Evaporation

As the initially warmer water cools to the initial temperature of the initially cooler water, it may lose significant amounts of water to evaporation. The reduced mass will make it easier for the water to cool and freeze. Then the initially warmer water can freeze before the initially cooler water, but will make less ice. Theoretical calculations have shown that evaporation can explain the Mpemba effect if you assume that the water loses heat solely through evaporation. This explanation is solid, intuitive, and evaporation is undoubtedly important in most situations. However, it is not the only mechanism. Evaporation cannot explain experiments that were done in closed containers, where no mass was lost to evaporation. And many scientists have claimed that evaporation alone is insufficient to explain their results.

Dissolved Gasses

Hot water can hold less dissolved gas than cold water, and large amounts of gas escape upon boiling. So the initially warmer water may have less dissolved gas than the initially cooler water. It has been speculated that this changes the properties of the water in some way, perhaps making it easier to develop convection currents (and thus making it easier to cool), or decreasing the amount of heat required to freeze a unit mass of water, or changing the boiling point. There are some experiments that favor this explanation, but no supporting theoretical calculations.

Convection

As the water cools it will eventually develop convection currents and a nonuniform temperature distribution. At most temperatures, density decreases with increasing temperature, and so the surface of the water will be warmer than the bottom -- this has been called a "hot top." Now if the water loses heat primarily through the surface, then water with a "hot top" will lose heat faster than we would expect based on its average temperature. When the initially warmer water has cooled to an average temperature the same as the initial temperature of the initially cooler water, it will have a "hot top", and thus its rate of cooling will be faster than the rate of cooling of the initially cooler water at the same average temperature. Got all that?

You might want to read this paragraph again, paying careful distinction to the difference between initial temperature, average temperature, and temperature. While experiments have seen the "hot top", and related convection currents, it is unknown whether convection can by itself explain the Mpemba effect.

SurroundingsA final difference between the cooling of the two containers relates not to the water itself, but to the surrounding environment. The initially warmer water may change the environment around it in some complex fashion, and thus affect the cooling process. For example, if the container is sitting on a layer of frost which conducts heat poorly, the hot water may melt that layer of frost, and thus establish a better cooling system in the long run. Obviously explanations like this are not very general, since most experiments are not done with containers sitting on layers of frost.

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4 comments:

erickia said...

hey,nice blog~ok...always stay cool...

profmaster said...

Thanx

matthew said...

You should link to where you copied the text from and also mention that it was written Nov 4, 1998 by Monwhea Jeng (Momo)
Department of Physics, University of California,

Anonymous said...

I totally agree with matthew,
You should link to where you copied the text from and also mention that it was written Nov 4, 1998 by Monwhea Jeng (Momo)
Department of Physics, University of California.

Link to original:
http://math.ucr.edu/home/baez/physics/General/hot_water.html

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