A Possible Explanation for the Mpemba Effect

I said this blog would be about everyday science, but I haven't published any posts that really fall into that category yet. So let's fix that.

The Mpemba Effect

Yesterday I heard that a paper had been posted to the arXiv with an explanation for the Mpemba Effect (also called the Mpemba Paradox). As the authors (Zhang et al.) say,

The Mpemba effect…, named after Tanzanian student Erasto Mpemba, is the assertion that warmer water freezes faster than colder water, even though it must pass the lower temperature on the way to freezing.

The story of the Mpemba Effect is a great example of citizen science and of the importance of trusting the evidence. Erasto Mpemba observed that his ice cream froze faster when it went into the freezer hot, than when it had cooled first. He repeated this experiment with beakers of water and found the same result: the hot water froze faster than the cold. He asked his teachers about this and was told he must be confused. Dr. Osborne of the University of Dar es Salaam visited Mpemba's school to give a physics lecture, and Mpemba asked him about the difference in freezing rates. Osborne writes (emphasis mine):

I confess that I thought he was mistaken but fortunately remembered the need to encourage students to develop questioning and critical attitudes. No question should be ridiculed.

Osborne said he didn't know why the hot water froze faster, but he would do some experiments. And he did. He had a technician repeat the experiment, and it became a project for his second year university students. They made several observations about the way that water cools, but they did not have a satisfactory answer to Mpemba's original question. They did get a paper out of it, which I highly recommend. It's an excellent read and not very long.

There have been several hypotheses proposed over the years. Osborne mentions convection effects but calls that explanation only "tentative." Zhang et al. list several others: "evaporation, … frost, supercooling, latent heat of condensation, solutes, thermoconductivity, super cooling [sic], etc." They point out, though, that this effect happens in water, but does not appear to happen in other materials. Apparently ice cream, which is what Mpemba originally used, is sufficiently water-based that they don't consider it another material.

Water is weird

The authors attribute the Mpemba effect to the hydrogen bonds in water. Water is such a neat yet strange molecule. It's really small, but it has properties, like its relatively high boiling point and its reduced density upon freezing, that are unusual for molecules of its size. A lot (dare I say all?) of these weird properties come from the presence and strength of hydrogen bonding. Water is all about the hydrogen bonds. That high boiling point is thanks to fairly strong intermolecular forces. The lower density of ice versus water is due to the cavities that form in the ice crystals when the water molecules arrange themselves with the H's on one molecule attracted to the O's of others. It seems pretty plausible to me that water's amazing hydrogen bonds could explain weird results like the Mpemba effect.

Springy bonds

So the water molecules have H atoms of one molecule tugging on the O of another, making a O:H-O bond. When the water is hot, the H-O bond stiffens:

At cooling, the shorter and stiffer H-O bond will be kicked up in the potential curve by O:H bond contraction, which releases energy to the [freezer] at ice state. The released energy is proportional to the initial temperature of water. This process is like suddenly releasing the compressed spring at different extent of compression with the O:H contraction kicking as an addition of the force propels the energy release. [sic]

So energy is released from the "compressed spring" of the H-O bond (at an exponential rate, no less), and the hotter water freezes faster. Pretty cool.

Other thoughts

The article is a little hard for me to follow in places. For instance, there's so much going on in Figure 2 that I completely misread it to start. (Despite the labels and size differences, I thought it showed a water molecule, i.e. H-O-H not O:H-O, until I took a closer look.) Still, I think it's a neat way to consider the problem, and I wonder if other compounds might have Mpemba effects we haven't noticed yet.

Further reading

  • Zhang, Xi, et al. "O:H-O Bond Anomalous Relaxation Resolving Mpemba Paradox" arXiv:1310.6514 (link)
  • Mpemba, E.B., and D.G. Osborne "Cool?" Phys. Educ. 4 (1969): 172-175. (link)