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Photo Source: on a hot summer day in Pixabay, if you are in a hurry to use ice, would you choose to put cold water or hot water in the refrigerator? Common sense tells us to use cold water, of course. Because the cold water is cooler, it freezes more quickly. A few decades ago, however, a teenager found that hot water freezes earlier than cold water in the refrigerator. This has not only subverted people's cognition, but also triggered a debate in academic circles for half a century.

There is an interesting story behind the widely circulated saying that hot water may freeze faster than cold water. In 1963, Erasto Mpamba, a Tanzanian teenager who was still in high school, made ice cream with his classmates. In order to seize the limited refrigerator space, Mpamba did not wait for the milk to cool to room temperature, as other students did, but put the hot milk that had just been boiled directly into the refrigerator. An hour and a half later, he found that his hot milk had frozen into ice cream, but the cold milk put in the refrigerator with the hot milk was still in the state of thick milk. How can hot milk freeze faster than cold milk? Mpamba was so confused that he asked his high school physics teacher, only to be told, "you must have made a mistake. That's not going to happen."

With this doubt in mind, Mpamba waited until physicist Denis Osborne came to Mpamba's high school to sit in on physics classes. Osborne always remembers that the teenager raised his hand and asked, "if you take two beakers and fill them with the same amount of water, but one cup of water is 35 °C and the other is 100 °C. then put the two glasses of water together in the refrigerator, and you will find that the glass of water at 100 °C freezes first. why?" Osborne didn't believe it at first, but out of curiosity, he did the experiment. Osborne then invited Mpamba to the University of Dar es Salaam (University of Dares Salaam) in Tanzania to study the phenomenon and named it the Mpamba effect (Mpemba effect).

Mpamba and Osborne first demonstrated the Mpamba effect when they published an article in the journal Physics Education in 1969. Strangely, however, they were unable to steadily repeat the initial results in subsequent experiments. As a result, there is a great controversy: does the failure of the experiment mean that the Mpamba effect does not exist? Or is it because the experiment is too rough to take into account the effects of unknown variables? In fact, the freezing experiment is so delicate that any small details may affect the freezing process.

In the past few decades, scientists have put forward many theories to explain the Mpamba effect. Some people think that hot water evaporates faster than cold water and is smaller than cold water, so it freezes faster; others think that cold water has more dissolved gas, so the freezing point is lower; others think that external factors are at play: the wall of the cup condenses a layer of frost in the refrigerator, which prevents heat from escaping from the cold water. But hot water will constantly melt the frost, giving off heat and cooling ice more quickly.

However, there is a premise to these explanations-the Mpamba effect is real, and hot water does freeze faster than cold water. But not everyone agrees with this premise.

Source: in Pixabay2016, physicist Henry Burridge of Imperial College London (Imperial College London) and mathematician Paul Linden of University of Cambridge tested the Mpamba effect. Unable to observe the freezing process directly, Burridge and Linden instead measured the time it took for the water temperature to drop from its initial temperature to 0 ℃. They were surprised to find that the result depended on where the thermometer was placed in the water: if the thermometer was placed at the same depth, there would be no Mpamba effect between hot and cold water; but if the thermometer was placed at a depth of even a centimeter, it may mistakenly "confirm" the Mpamba effect.

The results of Burridge and Linden's experiment reflect the high sensitivity of the freezing experiment, although it is not clear whether the Mpamba effect exists or not. but it reveals the key reason why the effect is so unstable: a glass of water is an unstable non-equilibrium system in the process of rapid cooling.

For comparison, water at room temperature is a system in thermal equilibrium, which can be described by three parameters: temperature, volume and number of molecules. If you put this cup of water in the refrigerator, you can imagine that the water molecules on the outside near the wall of the cup are cold, but the water molecules inside the cup remain warm. At this point, the liquid in the cup can no longer be clearly described by parameters such as temperature and pressure, because all the parameters are constantly changing, it becomes an unstable non-equilibrium system. For a long time, physicists know little about non-equilibrium systems.

A strange "shortcut" Zhiyue Lu, an assistant professor of chemistry at the University of North Carolina (University of North Carolina), became curious when he read about the Mpamba effect when he was young. In graduate school, after studying non-equilibrium thermodynamics, he began to design experiments to verify the Mpamba effect. Lu later met Oren Raz, who studied non-equilibrium statistical physics at the Weizmann Institute of Science (Weizmann Institute of Science) in Israel, and together they designed a theoretical framework for the study of the Mpamba effect.

In 2017, Lu and Raz published an article in the Proceedings of the National Academy of Sciences (Proceedings of the National Academy of Sciences). Through random particle dynamics simulations, they found that both the Mpamba effect and the inverse Mpamba effect (such as cold water heating up faster than hot water) may occur under certain conditions. The results show that particles in hotter systems have more energy, so they can try more paths to temperature changes, including a "shortcut": during cooling, the heating system can surpass the cold system through shortcuts to reach the final state faster.

"We all take it for granted that temperature changes are linear-either increasing or decreasing," Raz said. "the system always goes from a higher temperature to an intermediate temperature to a lower temperature. but it is a fallacy for non-equilibrium systems to be described as temperature. in this way, it is not surprising that there are 'strange shortcuts'."

Source: Pixabay2019 year, statistical physicist Maria Wucelia (Marija Vucelja) and Raz et al of the University of Virginia (University of Virginia) theoretically predicted that the Mpamba effect could occur in most disordered materials (aperiodic arrangement of molecules in materials), such as glass. The prediction of this theory covers a wide range of materials, but water is not a disordered material and is not within the scope of this theory.

To test these theoretical predictions, Raz and Lu found experimental physicist John Beschhoff (John Bechhoefer). Beishhoff and his collaborator, Avinash Kumar (Avinash Kumar), came up with an ingenious experimental scheme. They used tiny glass beads (visible only under a microscope) to replace the microscopic particles in the system and used lasers to create a W-shaped "energy landscape" (energy landscape). The deeper valley in the W shape represents the final stable equilibrium state of the system, while the other shallow valley represents a metastable state closer to the final equilibrium state of the system, because the particles may fall into it, but are more likely to fall into the deeper valley eventually.

Source: Merrill Sherman / Quanta Magazine they put the "energy landscape" into the water, and the glass beads can get rid of gravity and move freely. They then placed the glass bead in different positions in the energy landscape, repeated a thousand experiments, and superimposed the results of a thousand observations. So a system of a thousand individual particles is equivalent to a system of a thousand particles.

The researchers placed glass beads anywhere in the energy landscape to simulate the initial hotter system. Because the thermal system contains more energy, particles can move around and explore more actively in the energy landscape. When simulating a colder system, the initial position of the glass beads needs to be limited to the area near the deep valley. When simulating the cooling process, the glass beads will first sink into one of the valleys, and then jump back and forth between the two valleys under the disturbance of water molecules. When the proportion of the length of stay of the glass bead in each valley is stable, it can be judged that the cooling process has been completed. According to the difference of the water temperature and energy landscape of the environment in which the glass beads are located, the criteria for determining whether the cooling is completed are also different. For example, it can be determined that the particle has completed cooling according to 20% of the time it falls into metastability and 80% of the time it falls into the steady state.

Image source: Pixabay under some initial conditions, the heating system cools more slowly than the cold system, which is in line with our intuition. But sometimes particles in the thermal system sink into the valley more quickly. When the experimental parameters are properly adjusted, the particles of the thermal system almost immediately reach the required cooling completion state, much faster than the cold system-a phenomenon that Raz, Wucelia and others have predicted and named the Chompamba effect. They published the results in the journal Nature in 2020. At the beginning of this year, they published an experimental study on the inverse Mpamba effect in the Proceedings of the National Academy of Sciences.

"the results are clear," said Ra ú l Rica Alarc Alarcon of the University of Granada in Spain, who is experimenting with the Mpamba effect. "these studies show that systems farther away from the target state are more likely to reach the target state more quickly."

The unresolved Beschhoff experiment provides an explanation that the Mpamba effect may occur in systems with metastable states. But is it the only explanation? How do other substances undergo non-equilibrium heating and cooling processes, and will there be Mpamba effect? These questions are still unsolved. Even whether there is a Mpamba effect in water is still an open question.

"it is very important to understand the process of relaxation from a non-equilibrium state to an equilibrium state. But frankly speaking, we do not have a good theoretical system so far." Raz said. Judging which systems may operate counterintuitively, like the Mpamba effect, "will help us better understand the relaxation process of the system."

Reference article:

Https://www.quantamagazine.org/does-hot-water-freeze-faster-than-cold-physicists-keep-asking-20220629/

Https://mp.weixin.qq.com/s/BoGfkfl4xRFzo0WEk38IuQ

Links to papers:

Https://www.nature.com/articles/s41586-020-2560-x

Https://www.pnas.org/doi/abs/10.1073/pnas.2118484119

This article comes from the official account of Wechat: global Science (ID:huanqiukexue), written by Adaman (Adam Mann), compiled by: not weekly revision: Bai Defan

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