Hot water freezes faster than cold water - A physics mystery that hasn't been solved after decades

At first glance, the question seems ridiculously simple: "Put two cups of hot and cold water in the freezer, which cup freezes first?"

Common sense says that colder water will freeze faster, yet sages like Aristotle and René Descartes both witnessed and recorded the opposite. In modern times, plumbers have recorded cases where hot water pipes burst in cold weather, while cold water pipes work normally.

Although they were able to observe the phenomenon occurring, subsequent experiments were not able to make a cup of hot water freeze faster than a cup of cold water. Highly accurate tests are affected by many small details, making it difficult for researchers to determine the variables that influence the results.

Over the years, researchers have discovered the Mpemba effect in other compounds, including crystalline polymers, an ice-like solid called clathrate hydrate, and the mineral manganite. cools in a magnetic field. New research directions help scientists gain more data about a complex system, outside the framework of equilibrium rules in thermodynamics.

There are physicists who have tried to build models based on the above unusual rules, predicting that the Mpemba effect will appear in many types of materials; Besides, the opposite effect - that is, cold matter heats up faster than already warm matter - also occurs. Recently conducted experiments have initially verified these assertions.

But the Mpemba effect that takes place in water - the closest, most abundant material we use in experiments - still eludes the eyes of experts.

“A glass of water in the refrigerator sounds simple,” said physicist John Bechhoefer, “but in reality it's not easy at all if you really put your mind to it.” Working at Simon Fraser University, Mr. Bechhoefer is the most experienced individual in Mpemba effect research to date.

When reality goes against common sense

“My name is Erasto B. Mpemba, I will tell you about my discovery, made by abusing the refrigerator.” That was the premise of a scientific report published in 1969 in the journal Physics Education, in which student Mpemba described his and his friends' efforts to make ice cream while studying at Magamba High School in Tanzania.

There was not much space left in the refrigerator, so the Mpemba student had to quickly put his ice cream mixture into the refrigerator. Mpemba ignites the cooling stage of the milk and sugar combination, not waiting for them to come down to room temperature but putting the tray straight into the refrigerator. An hour and a half later, his milk and sugar mixture had turned into ice cream, while his classmates' ice cream was still a thick liquid. When asking a question to the physics teacher, Mpemba received the answer: “You are mistaken. That cannot happen."

Mpemba repeated this question when physicist Osborne visited the school. “If you put two cups of water with equal volumes in the refrigerator, one at a temperature of 35 degrees Celsius and one at a temperature of 100 degrees Celsius, the cup of hot water at 100 degrees Celsius will freeze first. Why?" The laughter of Mpemba's friends and the classroom teacher could not dispel Mr. Osborne's curious thoughts. After testing it himself, a physicist from England discovered the effect described by Mpemba.

However, he still concluded that the experiment was still sketchy and needed more in-depth tests to verify the phenomenon.

As decades passed, scientists published many hypotheses to explain the Mpemba effect. Realizing that water is a strange substance, the solid form is less dense than the liquid form and the two forms can coexist under the same temperature conditions, some experts believe that increasing the temperature can reduce the bonds of the hydrogen network. Amphiphiles are inherently fragile, increasing disorder in the structure, helping to reduce the amount of energy needed for the freezing process.

Another, simpler explanation points out that hot water evaporates faster than cold water, causing the volume to decrease thereby reducing the freezing time. Cold water also contains more dissolved gases, causing a lower freezing point.

Some experts believe that the outer layer of ice becomes a barrier to help the cup not lose heat, while the hot cup will melt the outer layer of ice, causing the hot cup to cool faster.

The above explanations all agree with the assertion that hot water freezes faster than cold water. But the scientific community has not yet found a common voice.

In 2016, physicist Henry Burridge who teaches at Imperial College London and mathematician Paul Linden from the University of Cambridge conducted experiments showing how sensitive the effect is under specific measurements. They observed that hot water formed ice crystals sooner, but took longer to completely freeze. Both phenomena are difficult to measure, so Burridge and Linden measured the amount of time it takes for water to reach 0 degrees Celsius.

They found that the readings were based on where the thermometer was placed. When two glasses of water are placed at the same height, the Mpemba effect will not appear. With just a centimeter difference in distance, the "fake" Mpemba effect will appear. Surveying related literature, Burridge and Linden found that the Mpemba effect only appeared in the first research report by Osborne and Mpemba.

The physicist and mathematician's discovery "shows how sensitive experiments can be, even without recording the freezing process."

Weird shortcuts

The number of scientists who believe in the existence of the Mpemba effect is still large, they believe that at least the effect still appears under certain conditions. As far back as the 4th century BC, the great philosopher Aristotle observed that “when people want to cool water quickly, many people place it in the sun”; It seems that the strange effect was present even before the invention of thermometers. Mpemba also witnessed a similar phenomenon when he was a student, when he compared the freezing speed between his ice cream and that of his classmates.

Still, Burridge and Linden's findings reveal a key reason why the Mpemba effect, whether real or not, is difficult to show in testing: the temperature in a beaker of cooling water rapidly fluctuates. strong when the water is not in a state of balance. Meanwhile, physicists do not have a clear understanding of physical systems that are out of equilibrium.

Once equilibrium occurs, any solution in the bottle can be described by an equation containing three metrics: temperature, volume, and number of molecules. Place the bottle in the refrigerator, and the readings fluctuate uncontrollably, causing inconsistent measurement results. The outermost particles of matter will wander in the cold world, while the matter deep inside the bottle still retains its warmth. Temperature and pressure indicators also fluctuate abnormally.

When assistant professor Lu Zhiyue read about the Mpemba effect while still in school, he snuck into the oil refinery located in Shandong province, where his mother worked, to recreate the experiment. Measuring the temperature change time of freezing water, he was able to bring the water below 0 degrees Celsius without freezing the water (a process called "supercooling", roughly translated as "supercooling" a substance). liquid).

Later, when deeply researching thermodynamics in a non-equilibrium system, he tried the old method of cooling water to recreate the Mpemba effect. He asked the question: “Is there any law of thermodynamics that prohibits the following phenomena from occurring: a [matter that initiates the change process] far from the equilibrium point, reaches the equilibrium point faster than a [matter] closer to the equilibrium point?”

When meeting Oren Raz, a non-equilibrium probabilistic mechanics research expert at the Weizmann Institute of Science, Mr. Zhiyue had the opportunity to develop a model to study the Mpemba effect on many materials other than water. In 2017, they became co-authors of a scientific paper published in the Proceedings of the National Academy of Sciences, describing the stochastic dynamics of particles and showing that in principle, there are certain non-equilibrium conditions that will produces the Mpemba effect and its reverse effect.

The abstract findings show that the elements that make up a system of hot matter (i.e. containing a lot of energy) can produce more feasible mechanisms, one of which allows the matter to gradually cool. takes an unusual shortcut, allowing the hot system to outpace the cold system in a race to the freezing point.

“We all naively think that temperatures will change monotonically. You will start at a high temperature, then go to a medium temperature, then go to a low temperature," said researcher Oren Raz. But with a system that is no longer in equilibrium, “the claim that the system possesses a certain temperature is no longer really true,” and “so shortcuts can appear.”

The curious scientific report has attracted the interest of many researchers, including a group of Spanish scientists who are experimenting with particle solutions - a combination of hard particles that can flow like solution, such as sand grains or tree seeds. Through simulation models, the research team found that the particle solution could also create effects similar to what Mpemba described in the past.

That made probabilistic physicist Marija Vucelja from the University of Virginia wonder how often the Mpemba effect occurs in nature. “Is this a needle in a haystack, or can we take advantage of it to [create] optimal heating or cooling rules?” she wondered. In 2019, she, Oren Raz and two other co-authors discovered that the Mpemba effect can take place in a complex of chaotic substances unlike water, such as glass. The discovery opens up the possibility of the Mpemba effect appearing on many other materials.

To learn more, researchers Lu Zhiyue and Oren Raz met with physicist Bechhoefer, an individual with extensive experience in practical testing.

Explore new limits

The experiment proposed by Bechhoefer and his colleague Avinash Kumar involves lofty concepts, but provides a bare-bones view of a group of particles affected by many different forces. A microscopic-sized glass bead represents a particle of matter placed in an “energy landscape” created by a laser.

The deepest depression in this context is a highly stable rest point, while the shallower depression describes a “metastable” state – a state in which a particle can exist but can still fall. to a more stable area. Scientists submerged this entire energy landscape in water, using optical tweezers to place glass beads at 1,000 different locations; The test would yield similar results with a system consisting of 1,000 particulate matter.

Experiment

Physicists create an artificial energy landscape where the existence of a particle requires different amounts of energy.

They dropped a glass bead into the model, at different positions and at different energy levels (high level makes the bead hot, low level makes the bead cold).

Any particle will move toward equilibrium, moving back and forth between two valleys of a given energy landscape.

Result

The hotter glass bead reached the equilibrium point first.

A high-energy context would be a system that would allow glass beads to be placed anywhere, because a hot system would be energy-rich, allowing for more possibilities. In a warm-only system, the glass bead placement point will be closer to the depression. During the cooling process, the glass beads will settle in one of two hollow areas, then move back and forth between the two areas (also influenced by water molecules).

The cooling process ends when the glass beads stay in a depression for a certain period of time, for example spending 20% ​​of the time in the metastable depression, the remaining 80% in the metastable region. stable depression. This ratio will depend on water temperature and the size of the depressions.

Under certain conditions, a hot system will take longer than a warm system to reach its equilibrium point; That is, a cup of hot water will freeze more slowly than a cup of cold water. But in some cases, the Mpemba phenomenon takes place. Above all, conditions occur where the hot system cools at a noticeably faster rate; Researchers have dubbed this state the “strong Mpemba effect.” The scientific report was published in Nature magazine in 2020.

“The results are clear,” said Raúl Rica Alarcón from the University of Granada in Spain, who is also studying the Mpemba effect. “They successfully described a system that starts far from the equilibrium point, but reaches the target faster than systems located closer.”

In other words, the report confirms the existence of the Mpemba effect, and shows that under certain conditions, the effect will be strongest.

The results have not yet convinced the entire research community that the Mpemba effect can appear on any system. “I read these trials all the time, and I'm not impressed with the way they're presented,” researcher Burridge said. “I still don't see a plausible physical explanation, and I feel like the question lingers whether a phenomenon similar to the Mpemba effect exists in some beneficial way.”

It seems that Bechhoefer's experiment shows that the Mpemba effect can appear in systems containing a metastable state. However, researchers are not sure whether this is the only mechanism causing the Mpemba effect, besides the way particles undergo non-equilibrium heating and cooling is still hidden behind the horizon of discovery.

While nothing has changed, research works related to the Mpemba effect have given physicists a fulcrum in a non-equilibrium system that has many shortcomings. “How [matter particles] approach equilibrium is an important question that, frankly, we still don't have a reasonable theory to explain,” said Mr. Raz. Determining which systems can react in strange ways “will provide a clearer view of how a system approaches equilibrium.”

After sparking a decades-long controversy, Mpemba abandoned physics. He returned to nature through wildlife management, and later became an officer at the Ministry of Tourism and Natural Resources of Tanzania. According to Christine Osborne, the widow of researcher Denis Osborne, Mr. Mpemba passed away in 2022. He left, leaving behind one of the biggest mysteries in science in the form of a strange effect named after him. .