It’s a mystery that has puzzled thinkers since Aristotle: under the right circumstances, hot water can freeze more quickly than cold. Now, for the first time, a team of Spanish physicists has worked out how and why this seeming paradox – known as the Mpemba effect – can occur.
The answer, as described in a paper in Physical Review Letters by Antonio Lasanta of Charles III University Madrid and colleagues, depends on the speed of individual water particles as they scurry in all directions like ants in a nest.
Although the Mpemba effect had been noted by many scientists and natural philosophers over the centuries – including Rene Descartes and Francis Bacon – it received little modern study until the 1960s. Things changed when a Tanzanian teenager named Erasto Mpemba noticed an ice-cream mixture that had been heated froze more readily than one that was cold. Mpemba asked a physicist who was visiting his high school about it, and together they confirmed the existence of the effect in the lab.
Since then, various explanations have been proposed for the Mpemba effect: that evaporation from warm water carries heat away more effectively, or unusual flows within the fluid, or even supercooling, in which the water’s temperature falls well below zero before it turns to ice.
None of the explanations have been entirely convincing. Indeed, a recent study concluded “somewhat sadly” that it could find no evidence the effect even exists.
In order to study the problem, the Spanish researchers started by defining it more clearly. Imagine two beakers of water, one hotter and one colder, that are placed in a freezer. If the Mpemba effect applies, the hotter one will reach zero degrees sooner than the colder one.
Inside each beaker, the molecules that make up the water are swarming in all directions. If the water warms up, they move faster; if it cools down they slow to a crawl; and if it freezes they get stuck in place, wriggling feebly on the spot.
Lasanta’s team analysed a simplified version of this situation, in which the particles in the liquid are miniscule spheres that lose a tiny bit of energy each time they collide with one another.
The conventional wisdom is that the time it takes for each beaker of water to freeze depends only on its initial temperature. Particles in the hotter water move faster, which means they have more slowing to do – so the hotter the liquid, the longer it should take.
The researchers discovered, however, that temperature wasn’t the only important factor.
If water particles are like ants running around a nest, the temperature of the entire fluid corresponds to their average speed. So a nest where all the ants are walking at 50 metres an hour looks the same as one where half are doing 50, a quarter are sprinting at 75 and the final quarter are dawdling at 25.
However, the number of outliers – the lazy stragglers and the speed demons – turns out to play a key role in determining the rate of cooling. This degree of deviation from the average, a property known to statisticians as ‘kurtosis’, had been neglected in earlier studies which might account for the poor reproducibility of the Mpemba effect.
Plugging kurtosis into the equations was the game changer. “We can make analytical calculations to know how and when the Mpemba effect will occur,” says Lasanta.
When conditions are just right – if the hot beaker is the right amount hotter than the cold beaker and its molecules are wayward enough to generate high kurtosis – the model simulation shows that the hotter sample will cool faster than the colder one.
“In fact,” says Lasanta, “we find not only that the hottest can cool faster but also the opposite effect: the coldest can heat faster, which would be called the inverse Mpemba effect.”
The next step? Trying to verify the simulations – first in the lab, then in the real world. If it all pans out, the discovery may have applications in refrigeration and cooling.
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