Why hot water can freeze faster than cold
A puzzling phenomenon first noted by Aristotle has finally been solved.
It’s a mystery that has puzzled thinkers since Aristotle mentioned it in the 4th century BCE: sometimes hot water can freeze more quickly than cold.
Now a team of Spanish physicists has worked out how this paradox – known as the Mpemba effect – occurs.
The answer, described in a paper in Physical Review Letters by Antonio Lasanta and colleagues of Charles III University, Madrid, depends on differences in the speed of individual water particles as they scurry in all directions like ants in a nest.
Although the Mpemba effect had been noted over the centuries, including by Rene Descartes and Francis Bacon, it received little serious scholarly attention until the 1960s.
Things changed when a Tanzanian student named Erasto Mpemba noticed a heated ice-cream mixture froze more readily than a cold one. He asked a visiting physicist about it, and together they confirmed the effect was real.
So what is the explanation for the Mpemba effect?
Imagine a beaker of water. The molecules in the water are swarming in all directions. If the water warms up, the molecules move faster; if it cools down they go slower; and if it freezes they wriggle on the spot.
Particles in hotter water move faster than in colder water, so they have more slowing to do to reaching freezing point. So the hotter the liquid, the longer it should take to freeze.
However, the researchers discovered it is not that simple. Temperature only measures the average speed of water particles; it is the number of outliers – stragglers and speedsters – that plays a key role in determining the rate of cooling.
This degree of deviation from the average, a property statisticians call ‘kurtosis’, was neglected in earlier studies.
Plugging kurtosis into the equations was the game-changer in modelling the Mpemba effect.
“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.”