Space was limited in the students’ refrigerator, and in the rush to nab the last available ice tray, Mpemba opted to skip waiting for his boiled-milk-and-sugar concoction to cool to room temperature like the other students had done. An hour and a half later, his mixture had frozen into ice cream, whereas those of his more patient classmates remained a thick liquid slurry. When Mpemba asked his physics teacher why this occurred, he was told, “You were confused. That cannot happen.”
Later, Osborne came to visit Mpemba’s high school physics class. He recalled the teenager raising his hand and asking, “If you take two beakers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a refrigerator, the one that started at 100°C freezes first. Why?” Intrigued, Osborne invited Mpemba to the University College in Dar es Salaam, where they worked with a technician and found evidence for the effect that bears Mpemba’s name. Still, Osborne concluded that the tests were crude and more sophisticated experiments would be needed to figure out what might be going on.
Over the decades, scientists have offered a wide variety of theoretical explanations to explain the Mpemba effect. Water is a strange substance, less dense when solid than liquid, and with solid and liquid phases that can coexist at the same temperature. Some have suggested that heating water might destroy the loose network of weak polar hydrogen bonds between water molecules in a sample, increasing its disorder, which then lowers the amount of energy it takes to cool the sample. A more mundane explanation is that hot water evaporates faster than cold, decreasing its volume and thus the time it takes to freeze. Cold water also could contain more dissolved gases, which lower its freezing point. Or perhaps external factors come into play: A layer of frost in a freezer can act as an insulator, keeping heat from leaking out of a cold cup, whereas a hot cup will melt the frost and cool faster.
Those explanations all assume that the effect is real — that hot water really does freeze faster than cold. But not everyone is convinced.
In 2016, physicist Henry Burridge of Imperial College London and mathematician Paul Linden of the University of Cambridge did an experiment that showed how sensitive the effect is to the particulars of measurement. They speculated that hot water might form some ice crystals first but take longer to fully freeze. Both of these events are difficult to measure, so Burridge and Linden instead noted how long it took water to reach zero degrees Celsius. They found that the readings depended on where they placed the thermometer. If they compared the temperatures between hot and cold cups at the same height, the Mpemba effect didn’t appear. But if measurements were off by even a centimeter, they could produce false evidence of the Mpemba effect. Surveying the literature, Burridge and Linden found that only Mpemba and Osborne, in their classic study, saw a Mpemba effect too pronounced to attribute to this kind of measurement error.
The findings “highlight how sensitive these experiments are even when you don’t include the freezing process,” said Burridge.
Strange Shortcuts
Yet a good number of researchers think the Mpemba effect can occur, at least under certain conditions. After all, Aristotle wrote in the fourth century BCE that “many people, when they want to cool water quickly, begin by putting it in the sun,” the benefits of which were presumably noticeable even before the invention of sensitive thermometers. School-age Mpemba was similarly able to observe the unsubtle difference between his frozen ice cream and his classmates’ slurry. Still, Burridge and Linden’s findings highlight a key reason why the Mpemba effect, real or not, might be so hard to pin down: Temperature varies throughout a cup of rapidly cooling water because the water is out of equilibrium, and physicists understand very little about out-of-equilibrium systems.
In equilibrium, a fluid in a bottle can be described by an equation with three parameters: its temperature, its volume and the number of molecules. Shove that bottle in a freezer, and all bets are off. The particles at the outer edge will be plunged into an icy environment while those deeper in will remain warm. Labels like temperature and pressure are no longer well defined but instead constantly fluctuate.
When Zhiyue Lu of the University of North Carolina read about the Mpemba effect in middle school, he snuck into an oil refinery in the Shandong province of China where his mother worked and used precision lab equipment to measure temperature as a function of time in a sample of water (he ended up supercooling the water without it freezing). Later, while studying nonequilibrium thermodynamics as a graduate student, he tried to reframe his approach to the Mpemba effect. “Is there any thermodynamic rule that will forbid the following: Something starting further away from the final equilibrium that would approach equilibrium faster than something starting from close?” he asked.
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