TS003 – The Mpemba Effect: Mind your variables!

TS003 - The Mpemba Effect: Mind your variables!

In this episode I would like to explain why hot water freezes faster than cold water, when put into the freezer. It is a very counter-intuitive observation, it’s a paradox.

This is called the Mpemba Effect. The effect is named according to Tanzanian high-school student Erasto B. Mpemba who re-discovered the effect while making ice-cream, back in 1963. The Mpemba Effect is a nice example how the change of one variable, the temperature, can have unexpected side effects. Most people assume that the difference between a hot glass of water and a cold glass of water is only the temperature. But this is not the case. Just by heating the water we are introducing a range of other variables that have an unexpected effect on the outcome.

The Mpemba Effect is a very, how shall I say, counter-intuitive observation, it’s a paradox. It is the observation that under certain circumstances, hot water freezes faster than cold water. The effect is named according to Tanzanian high-school student Erasto B. Mpemba who re-discovered the effect while making ice-cream, back in 1963. Aristoteles already described the effect 300BC. So it really is not a new discovery.

The effect occurs only under certain circumstances. You put a glass of hot water into the freezer, next to a glass of cold water. If the conditions are right the hot water will have turned to ice before the cold water. The actual causes of this effect are not fully understood. There seem to be a number of factors responsible, however.

This effect will only work for certain temperatures. If you place water with 99C next to a glass of water with 1C then the 1C water will of course freeze faster. But at other temperatures the issues are different. Let’s assume that 30C water takes, let’s say, 30 minutes to freeze. And let’s also assume that a glass containing 70C water takes 20 minutes to cool to 30C, which is the starting temperature of the first glass. We would conclude that it takes the 70C a total of 50 minutes (20min+30min) to freeze. This is not what we observe, however. And yes, the volume of the water is initially the same for both. The shape and material of the container are also the same.

So why does the hot water freeze faster? We may not even need experiments to determine possible causes for this observation. Most people assume that the difference in temperature of the water is the only variable. But if the observations don’t fit and there was no error in the method, then we may need to question our assumptions.

And in our case we have to question the assumption that the only difference in the two water containers is the temperature. We have to look for other differences that may be responsible for the faster cooling of the initially hot water. Now close your eyes and imagine two glasses of water standing in front of you – one hot and one cold.

The hot water is steaming. The hot water loses volume due to faster evaporation. Water with less volume will cool down faster. And as the water starts to freeze, the volume will increase again. Ice is less dense than liquid water. We would actually see a volume increase in the glass, and would not notice the loss.

There are, however, several other reasons involved as well. The loss of volume of the water actually changes the concentration of minerals in the water. The glass with some evaporated water will have a slightly higher mineral concentration than the glass with the original volume. The salts in the water will not evaporate out. Now, I know that a higher concentration of salt actually lowers the freezing temperature, that’s why we put salt on the roads during winter to prevent ice. So in my view, the higher mineral concentration would actually have the opposite effect. But maybe the cooling due to the loss of volume overcompensates the higher mineral concentration. I honestly don’t know.

And there are yet other factors that I would like to mention. The next time when you heat water, closely observe the pot. You will see many small bubbles forming before the water actually starts to boil. These bubbles are dissolved gases in the water. The heating of the water removes these dissolved gases. So the heating process actually changes the composition of the water as well. The two glasses therefore do not contain the same water. It is interesting to note that water that contains dissolved gases does indeed freeze at a lower temperature, but the temperature difference is very small. It will not contribute much to the Mpemba effect.

I summarize, to keep an overview: The two glasses of water are different not only in temperature but also in volume due to evaporation, and they differ in mineral concentration and also in the concentration of dissolved gases. There are still other differences as well.

The hot water does not cool evenly. The water close to the surface will cool faster than the water in the center. The hot water will tend to rise, while the cold water will move to the bottom of the glass. These are the so-called convection currents. We know that warm air rises due to a lower density, and a similar effect is possible with liquids. Essentially the hot water is “stirring itself“ during the cooling process. And this movement will cause a better mixing of the water and it will therefore cool down faster.

I would guess that the sum of all these effects is rather small, and it is difficult to imagine how they can have such a large influence. As Aristoteles once said: “The whole is more than the sum of its parts”. We do not know how these individual effects interact with each other to produce the observed result. Maybe additional unknown variables are generated by the interaction of these known variables.

I did not tell you my favorite variable yet! I am saving this one for the very end. When you place a hot glass of water into the freezer, then the hot glass will melt the ice beneath it a little. The cold water will of course not do that to the same extent. The melting of the ice will form a thin film of water between the floor of the freezer and the glass of hot water. The glass in now in a much better contact with the cold floor of the freezer. On other words, the water film improves the thermal contact between the glass and the freezer. This glass is therefore capable of cooling down much faster. The hot glass of water has changed its environment!

So, what do we learn from all that? We have to be careful when designing experiments. We should only change one variable at a time. We all agree on that. But sometimes we change more than one variable without knowing it. Just by heating the water we have changed volume, mineral concentration, gas concentration, water movement and the thermal contact with the freezer. And this can lead us to wrong conclusions.

I would like to conclude with a short quote from William Hazlitt (1778-1830), an English essayist: “[Science is] the desire to know causes.”

Questions for Discussion:

  • The purpose of conducting experiments in idealized laboratory situations is to increase the control over the (dependent and controlled) variables. I now claim that the more the experiment is moved into an artificial (lab) environment, the less it will be characteristic of a “real life” observation. To what extent do you agree or disagree?
  • How can we ever be certain that we have identified all the variables that influence the outcome of an experiment? How do we know?

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