freezing hot water and cold water experiment

New Research

The Physics of Why Hot Water Sometimes Freezes Faster Than Cold Water

For decades, physicists have debated whether the phenomenon exists and how to study it

Theresa Machemer

Correspondent

The story goes that in 1963, Tanzanian high school student Erasto Mpemba was making ice cream with his class when he impatiently put his sugar and milk concoction into the ice cream churner when it was still hot, instead of letting it cool first. To his surprise, the confection cooled faster than his classmates’ had.

With the help of a physics professor, Mpemba performed additional experiments by putting two glasses of water, one just-boiled and one warm, in a freezer, and seeing which one reached the freezing finish line first. Often, the water with a higher starting temperature was the first to freeze. Their observations set off a decades-long discussion over the existence and details of the counterintuitive phenomenon, now called the Mpemba effect.

Now, new research published on August 5 in the journal Nature not only shows that the Mpemba effect does exist, but also sheds light on how it occurs, Emily Conover reports for Science News .

Rather than experiment on freezing water, which is surprisingly complicated to study, physicists Avinash Kumar and John Bechhofer of Simon Fraser University focused their sights—and lasers—on microscopic glass beads. They measured how the glass beads moved under very specific conditions in water and saw that in some circumstances, beads that started off very hot cooled faster than those that didn’t.

“It’s one of these very simple setups, and it already is rich enough to show this effect.” University of Virginia theoretical physicist Marija Vucelja tells Science News . The experiment also suggests that the effect might show up in materials other than water and glass beads. Vucelja says, “I would imagine that this effect appears quite generically in nature elsewhere, just we haven’t paid attention to it.”

If the freezing point is the finish line, then the initial temperature is like the starting point. So it would make sense if a lower initial temperature, with less distance to the finish line, is always the first to reach it. With the Mpemba effect, sometimes the hotter water reaches the finish line first.

But it gets more complicated. For one thing, water usually has other stuff, like minerals, mixed in. And physicists have disagreed over the what exactly the finish line is: is it when the water in a container reaches the freezing temperature, begins to solidify, or completely solidifies? These details make the phenomenon hard to study directly, Anna Demming writes for Physics World .

The new experiment does away with the details that make the Mpemba effect so murky. In each test, they dropped one microscopic glass bead into a small well of water. There, they used a laser to exert controlled forces on the bead, and they measured the bead’s temperature, per Science News . They repeated the test over 1,000 times, dropping the beads in different wells and starting at different temperatures.

Under certain forces from the laser, the hottest beads cooled faster than the lower temperature beads. The research suggests that the longer path from a higher temperature to the freezing point might create shortcuts so that the hot bead’s temperature can reach the finish line before the cooler bead.

Bechhoefer describes the experimental system as an “abstract” and “almost geometrical” way to picture the Mpemba effect to Physics World . But using the system, he and Kumar identified the optimal “initial temperatures” for a Mpemba cooling effect.

“It sort of suggested that all the peculiarities of water and ice – all the things that made the original effect so hard to study – might be in a way peripheral,” Bechhoefer tells Physics World .

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Theresa Machemer | READ MORE

Theresa Machemer is a freelance writer based in Washington DC. Her work has also appeared in National Geographic and SciShow. Website: tkmach.com

The Mpemba Effect: Does Hot Water Really Freeze Faster Than Cold Water?

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Key Takeaways

The Mpemba effect suggests hot water can freeze faster than cold water under certain conditions, a phenomenon first observed by Aristotle.
Erasto B. Mpemba, a Tanzanian student, rediscovered this effect in 1963 while making ice cream, providing the first documented instance that led to further scientific investigation.
Although still debated among scientists, recent studies suggest the Mpemba effect may occur due to differences in how hot and cold water reach thermal equilibrium.

For centuries, observant scientists from Aristotle to Descartes have harbored a suspicion that — contrary to all conventional wisdom — hot water can somehow freeze faster than cold water. But there was no scientific consensus that this conjecture was actually true.

In 1963, a Tanzanian physics student named Erasto B. Mpemba (pronounced em- pem -ba) rekindled the idea via a fluke accident that occurred when he was making ice cream at his school. He seemed to prove what Aristotle and Descartes had suspected: Hot water reaches a freezing point faster than cold water does. He wrote about his observations in a 1969 paper , titled simply "Cool?" which gave rise to the term "Mpemba effect." But was Erasto Mpemba correct? Does hot water really freeze faster than cold water?

What Is the Mpemba Effect?

Understanding the freezing process, how can hot water freeze faster than cold water, the study that may prove the mpemba effect, is the mpemba effect a proven scientific fact, the mpemba effect in context.

The Mpemba effect is a physics concept that postulates that when hot water and cold water are placed in the identical freezing environment, the hot water will freeze faster than the cold water.

Erasto Mpemba noted that when his class was making ice cream, he placed a near-boiling blend of sugar and milk (which is mostly water) into a freezer, and it froze before other mixtures which had been cooled to room temperature before freezing.

Mpemba's extrapolation from this observation was that when identical volumes of water — one at 212 degrees Fahrenheit (100 degrees Celsius) and the other at 95 degrees Fahrenheit (35 degrees Celsius ) — were placed in identical beakers and put in a freezer, the 212 degree water would turn to ice faster. Mpemba's ice cream observation and water postulation aligned him with many centuries of scientists who had also suspected this unusual property of water.

When water freezes into ice, it undergoes a phase change; it turns from a liquid into a solid. Physicists traditionally declare the phase of a substance when it's at equilibrium . This means the substance is in a stable state, and significant amounts of energy are not flowing from one region to another. It also means that its volume and temperature remain steady. When a substance is not at equilibrium, its energy levels fluctuate, and so does (potentially) its state of matter.

For water to freeze and stay frozen, individual water particles have to reach equilibrium. If too much energy surges through nonequilibrium water, it will fluctuate between solid and liquid (at low temperatures) or liquid and gas (at higher temperatures). The sooner that water particles reach equilibrium at low energy levels, the sooner they can freeze.

Physicists are still debating whether hot water consistently freezes faster than cold water. When it does happen, certain conditions have to be met.

When a vessel of water is submerged in a freezing environment, different parts of the water reach equilibrium at different times. Water around the outskirts of the vessel gets colder faster, which means that it may freeze while water in the middle of the vessel stays liquid. And when you specifically place a vessel of hot water in a freezer (like the 212 degree boiling water described by Mpemba), it is also releasing steam from the top of the vessel, and this decreases the total volume of water that needs to freeze.

Furthermore, cold water (or even room temperature water) often develops a layer of frost on its surface as part of the freezing process. Ironically, this frost temporarily insulates the water (kind of like how an ice igloo insulates its inhabitants against cold air), which can slow down the overall freezing process. Hot water, at least in the early stages, blocks the formation of frost, which allows cold air to penetrate deeper into the vessel.

These are some of the ways that hot water can engender freezing faster than cold water can. But remember that for water to freeze and stay frozen, it must achieve a state of equilibrium.

If there's proof that the Mpemba effect is real and consistent, it comes from a 2020 study by John Bechhoefer and Avinash Kumar. Published in the journal Nature , the study subjected microscopic glass beads to what they called an "energy landscape" controlled by lasers. The researchers heated beads to different temperatures. They then observed which of the beads first reached a state of equilibrium within that energy landscape.

Bechhoefer and Kumar observed that microscopic beads that started at high temperatures reached equilibrium faster than those that started at lower temperatures. That's interesting enough, but how does reaching equilibrium relate to freezing?

The connection comes from prior work done by Zhiyue Lu of the University of North Carolina and Oren Raz of the Weizmann Institute of Science in Israel. Their paper, " Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse ," published in Proceedings of the National Academy of Sciences (PNAS) and described by Quanta Magazine , postulates that hotter systems of matter may be able to skip ahead in the process of reaching equilibrium, thus reaching a stable state faster than a colder system.

If relaxing toward equilibrium is a critical benchmark in the freezing process of water, then the combined work of Bechhoefer and Kumar along with Lu and Raz might prove the existence of a Mpemba effect.

The Mpemba effect is not uniformly accepted as a proven scientific phenomenon. However, centuries of observation, plus recent work by Bechhoefer, Kumar, Lu, and Raz have convinced many physicists that under the right circumstances, hot water really can reach a freezing point faster than cold water.

Some scientists, like Harry Burridge and Paul Linden, remain skeptical. They acknowledge that while some vessels of hot water can freeze faster than equal-sized vessels of cold water, even the slightest shift in conditions erases the effect. Burridge and Linden's own 2016 study, " Questioning the Mpemba effect: hot water does not cool more quickly than cold ," found that any proof of a Mpemba effect depended on the size of a water vessel and the placement of a thermometer. In a separate study, researcher James Brownridge found that impurities in a vessel of water (such as those in Mpemba's ice cream concoction) will alter the liquid's freezing point . While acknowledging there are times when hot water freezes faster than cold water, these scientists argue the phenomenon does not uniformly apply in nature.

However other physicists, like Raúl Rica Alarcón of Spain’s University of Granada, believe these new datasets, such as those offered by Bechhoefer and Kumar, are significant. "My view is that the Mpemba effect can take place under some special circumstances," says Rica Alarcón, "but we are still trying to figure out what are the minimal conditions for this to happen."

Rica Alarcón notes that observances of the Mpemba Effect always involve drastic differences in temperature between a vessel of water and its surrounding environment. And, he adds, you can observe equally intriguing phenomena when you reverse the temperatures and place frozen ice into a hot environment.

The Mpemba Effect, says Rica Alarcón, "seems to be one of a large group of anomalous thermalization effects, which take place when a system is suddenly put in contact with a thermal bath at a different temperature." The Mpemba Effect describes a hot-to-cold phase change like "when you take a hot cup and you put it in the fridge or in the freezer." But cold-to-hot phase changes also invoke unusual results. "Interesting effects take place when you perform temperature quenches from cold to hot," says Rica Alarcón, "like when you put an ice cube into boiling water."

We know that many generations of scientists have observed hot water freeze with surprising speed. Rica Alarcón urges us to regard this process more holistically, and think about the Mpemba Effect as part of a broader phenomenon. "Thermalization," he explains, "can follow counterintuitive paths due to the fact that the processes take place out of equilibrium."

Just like fresh water, ocean water can freeze — it just does it at a lower temperature. Sea water freezes at about 28.4 degrees Fahrenheit (minus 2 degrees Celsius) because of its salt content, while fresh water freezes at 32 degrees Fahrenheit (0 degrees Celsius).

Ask An Engineer

Does hot water freeze faster than cold water?

It’s an age-old question with a simple answer: no.

Since the time of Aristotle, researchers and amateur scientists alike have batted about the counterintuitive theory that hot water freezes faster than cold. The notion even has a name: the Mpemba effect, named for a Tanzanian schoolboy who in 1963 noticed that the ice cream he and his classmates made from warm milk froze quicker than that made from cool milk.

“No matter what the initial temperature of water is, it must be brought to the freezing point before it will change state and become ice,” says Prakash Govindan, a postdoctoral associate in MIT’s mechanical engineering department. It will actually take more time and/or energy to freeze hot water because it must be brought down further in temperature until it reaches the freezing point, about 0 ° C.

Govindan suggests conducting a simple experiment to demonstrate that hot and cold water will behave as logic predicts. “Fill two identical containers with hot and cold tap water from the kitchen sink and see which freezes first,” he says. Interestingly, he points out, the rates of change in this experiment will not be the same. “When you set them in the freezer, the freezer will work harder to bring the temperature of the hot water down, so initially the rate of heat transfer will be faster in the hot water.” However, the other container will be cooling at the same time (if not at quite the same rate).

When the temperature of the water in each container reaches just about 0 ° C it will undergo the same changes as it moves from a liquid to a solid, and it will take the same amount of time to begin forming tiny ice crystals. At that point, each mixture of liquid and ice will be at a uniform temperature, and as more heat is taken from the mixtures, the thermodynamic principle of latent heat kicks in: The water continues to convert to a solid state, but no longer changes in temperature. “As long as you have a mixture of liquid water and solid ice, the temperature will remain at 0 until all the water is frozen,” says Govindan.

It’s never been convincingly proven than hot water and cold water behave differently from each other at any step of the freezing process, despite the ongoing fascination with the Mpemba effect. In early 2013, Europe’s Royal Society of Chemistry even held a competition for the best explanation of the theory. The winner speculated that hot water indeed freezes more quickly if the cold water is first supercooled. But logic triumphs when it comes the plain ordinary water that comes from the household faucet. Most likely to impact the freezing point of water is the presence of impurities such as salt, dissolved solids and gases — and the ingredients of homemade ice cream.

Thanks to Khubaib Mukhtar of Pakistan for this question.

April 30, 2013

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Science project, does hot water freeze faster than cold water.

freezing hot water and cold water experiment

Have you ever refilled the ice cube tray in your freezer after using the last ice cube in your cup of juice? You probably automatically poured cold water in the ice cube tray without asking the question, "Does hot water freeze faster than cold water?"

It makes sense to believe that cold water would turn to ice before hot water because the hot water would need to cool first before it could freeze; but how do you know if that idea is correct? Test this theory —untested idea—will tell you whether cold water actually freezes faster than hot water.

Does temperature affect how quickly water freezes?

3 bowls of equal size and shape
Sticky labels
Measuring cup
Thermometer
Clear enough room in your freezer for the three bowls. You need to be able to put them in the freezer at exactly the same time, so you don't want to be moving your frozen food and drinks around later.
Think about what you know about ice. What temperature is water right before it freezes? You probably usually take baths in warm water. How quickly does the water turn cold when you're in the tub?
After considering different temperatures of water and ice, make a guess—called a hypothesis —answering the question: Does hot water freeze faster than cold water?
Write your hypothesis in your notebook, including whether you think the hot, warm, or cold water would freeze first and why .
Using your marker, write Hot on one of your sticky labels. Repeat with labels for Warm and Cold.
Place the sticky labels on each of the three bowls, using one per bowl. The labels will help you keep track of which bowl holds which temperature of water.
With your pencil, draw three columns in your notebook. Label the first column Hot, the second one Warm and the third Cold.
With the help of an adult, heat 1 cup of water to 100 degrees Fahrenheit. Pour it into the Hot bowl, being careful not to burn yourself.
Heat 1 cup of water to 70 degrees Fahrenheit, and pour it into the Warm bowl.
Fill the Cold bowl with water that's 40 degrees Fahrenheit.
Immediately place all three bowls in the freezer.
Record the starting temperatures in the correct columns of your notebook.
Open the freezer door every 10 minutes and take the temperature of the water in each bowl with a thermometer. Record the temperature in your notebook.
Repeat Step 13 until all three bowls have frozen over.
Compare the information in each of the three columns in your notebook. Was your hypothesis correct?

The bowls that contain the hot and warm water will freezer faster than the bowl that is filled with cold water.

Hot water freezing more quickly than cold water is known as the Mpemba effect . So, why does the Mpemba effect occur?

First, all water evaporates , which means that the liquid (water) "disappears" and becomes a vapor , or gas. Hot water evaporates at a much faster rate than cold water. This means that the bowl with hot water actually had less water than the bowl with cold water, which helped it freeze more quickly.

Second, convection (the transfer of heat within the water as it moves around) plays a part in helping hot water freeze more quickly than the bowl of cold water. The hot water has more convection currents than cold water, causing it to cool down much more quickly. That's why your bath water always seems to get cold much faster than you'd like!

Now that you know about freezing water at different temperatures, keep the science going by testing other liquids, such as milk or apple juice. Will warm milk freeze faster than cold milk? Or, switch up the project altogether! Does milk freeze faster than water at the same temperature? Science is all about guessing what will happen, then testing to see if you're right. You now know that hot water freezes faster than cold water, so brainstorm a new project that you're interested in. By constantly changing your experiments, you'll continue learning new things—and become a science whiz!

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October 21, 1998

Is It True that Hot Water Freezes Faster than Cold Water or that Cold Water Boils Faster than Hot Water?

It seems hard tobelieve, but some people swear that it is so

A woman tosses hot water into the freezing cold air.

Ismail Kaplan Getty Images

This seemingly simple question continues to generate considerable controversy. Takamasa Takahashi, a physicist at St. Norbert College in De Pere, Wis., attempts a definitive answer:

"Cold water does not boil faster than hot water. The rate of heating of a liquid depends on the magnitude of the temperature difference between the liquid and its surroundings (the flame on the stove, for instance). As a result, cold water will be absorbing heat faster while it is still cold; once it gets up to the temperature of hot water, the heating rate slows down and from there it takes just as long to bring it to a boil as the water that was hot to begin with. Because it takes cold water some time to reach the temperature of hot water, cold water clearly takes longer to boil than hot water does. There may be some psychological effect at play; cold water starts boiling sooner than one might expect because of the aforementioned greater heat absorption rate when water is colder.

"To the first part of the question--'Does hot water freeze faster than cold water?'--the answer is 'Not usually, but possibly under certain conditions.' It takes 540 calories to vaporize one gram of water, whereas it takes 100 calories to bring one gram of liquid water from 0 degrees Celsius to 100 degrees C. When water is hotter than 80 degrees C, the rate of cooling by rapid vaporization is very high because each evaporating gram draws at least 540 calories from the water left behind. This is a very large amount of heat compared with the one calorie per Celsius degree that is drawn from each gram of water that cools by regular thermal conduction.

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"It all depends on how fast the cooling occurs, and it turns out that hot water will not freeze before cold water but will freeze before lukewarm water. Water at 100 degrees C, for example, will freeze before water warmer than 60 degrees C but not before water cooler than 60 degrees C. This phenomenon is particularly evident when the surface area that cools by rapid evaporation is large compared with the amount of water involved, such as when you wash a car with hot water on a cold winter day. [For reference, look at Conceptual Physics, by Paul G. Hewitt (HarperCollins, 1993).]

"Another situation in which hot water may freeze faster is when a pan of cold water and a pan of hot water of equal mass are placed in a freezer compartment. There is the effect of evaporation mentioned above, and also the thermal contact with the freezer shelf will cool the bottom part of the body of water. If water is cold enough, close to four degrees C (the temperature at which water is densest), then near-freezing water at the bottom will rise to the top. Convection currents will continue until the entire body of water is 0 degrees C, at which point all the water finally freezes. If the water is initially hot, cooled water at the bottom is denser than the hot water at the top, so no convection will occur and the bottom part will start freezing while the top is still warm. This effect, combined with the evaporation effect, may make hot water freeze faster than cold water in some cases. In this case, of course, the freezer will have worked harder during the given amount of time, extracting more heat from hot water."

Robert Ehrlich of George Mason University, in Fairfax, Va., adds to some of the points made by Takahashi:

"There are two ways in which hot water could freeze faster than cold water. One way [described in Jearl Walker's book The Flying Circus of Physics (Wiley, 1975)] depends on the fact that hot water evaporates faster, so that if you started with equal masses of hot and cold water, there would soon be less of the hot water to freeze, and hence it would overtake the cold water and freeze first, because the lesser the mass, the shorter the freezing time. The other way it could happen (in the case of a flat-bottomed dish of water placed in a freezer) is if the hot water melts the ice under the bottom of the dish, leading to a better thermal contact when it refreezes." �

Still feeling skeptical? Fred W. Decker, a meteorologist at Oregon State University in Corvallis, encourages readers to settle the question for themselves:

"You can readily set up an experiment to learn which freezes earlier: water that is initially hot, or water that is initially cold. Use a given setting on an electric hot plate and clock the time between start and boiling for a given pot containing, say, one quart of water; first start with the water as cold as the tap will provide and then repeat it with the hottest water available from that tap. I'd wager the quart of water initially hot will come to a boil in much less time than the quart of water initially cold.

"The freezing experiment is harder to perform, because it ideally requires a walk-in cold storage chamber that is set to a temperature below freezing. Take into the chamber two quart-volume milk bottles filled with water, one from a hot tap and the other from a cold tap outside the chamber. Time them to freezing, and I would wager again that the initially colder water will freeze sooner than the initially hot water."

[We would add that, if you don't want to suffer in a walk-in freezer, you can conduct a reasonably good version of the above experiment in the freezer compartment of your refrigerator; just don't check the water too often-in which case it will never freeze-or too infrequently, in which case you may miss the moment when one container is frozen but not the other.]

Decker concludes that "much folklore results from trying to answer such a question under conditions that do not make 'all other things equal,' which the foregoing experiments do.

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Controversy Continues Over Whether Hot Water Freezes Faster Than Cold

June 29, 2022

Whether hot or cold water freezes faster remains unknown.

Francis Chee / SPL / Science Source

Introduction

It sounds like one of the easiest experiments possible: Take two cups of water, one hot, one cold. Place both in a freezer and note which one freezes first. Common sense suggests that the colder water will. But luminaries including Aristotle, Rene Descartes and Sir Francis Bacon have all observed that hot water may actually cool more quickly. Likewise, plumbers report hot water pipes bursting in subzero weather while cold ones remain intact. Yet for more than half a century, physicists have been arguing about whether something like this really occurs.

The modern term for hot water freezing faster than cold water is the Mpemba effect, named after Erasto Mpemba, a Tanzanian teenager who, along with the physicist Denis Osborne, conducted the first systematic, scientific studies of it in the 1960s. While they were able to observe the effect, follow-up experiments have failed to consistently replicate that result. Precision experiments to investigate freezing can be influenced by many subtle details, and researchers often have trouble determining if they have accounted for all confounding variables.

Over the past few years, as the controversy continues about whether the Mpemba effect occurs in water, the phenomenon has been spotted in other substances — crystalline polymers , icelike solids called clathrate hydrates , and manganite minerals cooling in a magnetic field. These new directions are helping researchers peek into the complicated dynamics of systems that are out of thermodynamic equilibrium. A contingent of physicists modeling out-of-equilibrium systems has predicted the Mpemba effect should occur in a wide variety of materials (along with its inverse, in which a cold substance heats up faster than a warm one). Recent experiments appear to confirm these ideas.

Yet the most familiar substance of all, water, is proving to be the slipperiest.

“A glass of water stuck in a freezer seems simple,” said John Bechhoefer , a physicist at Simon Fraser University in Canada whose recent experiments are the most solid observations of the Mpemba effect to date. “But it’s actually not so simple once you start thinking about it.”

‘That Cannot Happen’

“My name is Erasto B. Mpemba, and I am going to tell you about my discovery, which was due to misusing a refrigerator.” Thus begins a 1969 paper in the journal Physics Education in which Mpemba described an incident at Magamba Secondary School in Tanzania when he and his classmates were making ice cream.

A middle-aged man in a suit holding an ice cube in his palm

The late Erasto Mpemba initiated decades of research into whether hot water freezes faster than cold water.

PA Images / Alamy Stock Photo

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.

A photo of a school auditorium with blue walls and rows of empty wooden desks.

Mpemba first observed the alleged effect that bears his name in the 1960s as a student at Magamba Secondary School in Tanzania. The school’s auditorium is shown in 2009.

imageBROKER / Alamy Stock Photo

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.

A pair of portraits of men looking at the camera.

Zhiyue Lu of the University of North Carolina (top) and Oren Raz of the Weizmann Institute of Science in Israel have shown that hot liquids may find “strange shortcuts” to their freezing points.

Robert Filcsik (top); Itai Belson / Weizmann Institute of Science

Zhiyue Lu of the University of North Carolina (left) and Oren Raz of the Weizmann Institute of Science in Israel have shown that hot liquids may find “strange shortcuts” to their freezing points.

Robert Filcsik (left); Itai Belson / Weizmann Institute of Science

Lu met Oren Raz , who now studies nonequilibrium statistical mechanics at the Weizmann Institute of Science in Israel, and they began developing a framework to investigate the Mpemba effect generally, not just in water. Their 2017 paper in the Proceedings of the National Academy of Sciences modeled the random dynamics of particles, showing that in principle there are nonequilibrium conditions under which the Mpemba effect and its inverse could occur. The abstract findings suggested that the components of a hotter system, by virtue of having more energy, are able to explore more possible configurations and therefore discover states that act as a sort of bypass, allowing the hot system to overtake a cool one as both dropped toward a colder final state.

“We all have this naive picture that says temperature should change monotonically,” said Raz. “You start at a high temperature, then a medium temperature, and go to a low temperature.” But for something driven out of equilibrium, “it’s not really true to say that the system has a temperature,” and “since that’s the case you can have strange shortcuts.”

The thought-provoking work drew the interest of others, including a Spanish group that began simulating what are known as granular fluids — collections of rigid particles that can flow like liquids, such as sand or seeds — and showed that these, too, can have Mpemba-like effects. Statistical physicist Marija Vucelja of the University of Virginia started wondering how common the phenomenon might be. “Is this like is a needle in a haystack, or could it be useful for optimal heating or cooling protocols?” she asked. In a 2019 study , she, Raz, and two co-authors found that the Mpemba effect could appear in a significant fraction of disordered materials, such as glass. While water is not such a system, the findings covered an enormous variety of possible materials.

To investigate whether these theoretical hunches had any real-world basis, Raz and Lu approached Bechhoefer, an experimentalist. “Literally, they kind of grabbed me after a talk and said, ‘Hey, we’ve got something we want you to hear about,’” Bechhoefer recalled.

Exploring the Landscape

The experimental setup Bechhoefer and his collaborator Avinash Kumar came up with offers a highly conceptual, stripped-down look at a collection of particles under the influence of different forces. A microscopic glass bead representing a particle is placed in a W-shaped “energy landscape,” created using lasers. The deeper of the two valleys in this landscape is a stable resting place. The shallower valley is a “metastable” state — a particle can fall into it but may eventually get knocked into the deeper well. The scientists submerged this landscape in water and used optical tweezers to position the glass bead within it 1,000 different times; collectively, the trials are equivalent to a system with 1,000 particles.

Merrill Sherman/Quanta Magazine; source: Nature

An initially “hot” system was one where the glass bead could be placed anywhere, since hotter systems have more energy and can therefore explore more of the landscape. In a “warm” system, the starting position was confined to a smaller area close to the valleys. During the cooling process, the glass bead first settled into one of the two wells, then spent a longer period jumping back and forth between them, buffeted by water molecules. Cooling was considered complete when the glass bead stabilized into spending specific amounts of time in each well, such as 20% of its time in the metastable one and 80% in the stable one. (These ratios depended on the water’s initial temperature and the valleys’ sizes.)

For certain initial conditions, the hot system took longer to settle into a final configuration than the warm system, matching our intuitions. But sometimes the particles in the hot system settled into the wells more quickly. When the experimental parameters were tuned just right, the hot system’s particles almost immediately found their final configuration, cooling exponentially faster than the warm system — a situation that Raz, Vucelja and colleagues had predicted and named the strong Mpemba effect. They reported the results in a 2020 Nature paper and published similar experiments showing the inverse Mpemba effect in PNAS earlier this year.

“The results are clear,” said Raúl Rica Alarcón of the University of Granada in Spain, who is working on independent experiments related to the Mpemba effect. “They show that a system that is farther away from the target can reach this target faster than another one that is closer to the target.”

A pair of portraits of men standing next to lab equipment.

Recent experiments with lasers and glass beads by Avinash Kumar (top) and John Bechhoefer of Simon Fraser University indicate that hot liquids can indeed relax to equilibrium faster than cold liquids.

Simon Fraser University (top); Dianne Mar-Nicolle

Recent experiments with lasers and glass beads by Avinash Kumar (left) and John Bechhoefer of Simon Fraser University indicate that hot liquids can indeed relax to equilibrium faster than cold liquids.

Simon Fraser University (left); Dianne Mar-Nicolle

Yet not everyone is entirely persuaded that the Mpemba effect has been demonstrated in any system. “I always read these experiments and I’m not impressed by the write-up,” said Burridge. “I never find a clear physical explanation, and I feel that leaves us with an interesting question as to whether Mpemba-like effects exist in a meaningful way.”

Bechhoefer’s trials appear to offer some insight into how the Mpemba effect could arise in systems with metastable states, but whether it is the only mechanism or how any particular substance undergoes such out-of-equilibrium heating or cooling is unknown.

Determining if the phenomenon occurs in water remains another open question. In April, Raz and his graduate student Roi Holtzman posted a paper showing that the Mpemba effect could happen through a related mechanism that Raz has previously described with Lu in systems that undergo a second-order phase transition, meaning that their solid and liquid forms can’t coexist at the same temperature. Water is not such a system (it has first-order phase transitions), but Bechhoefer described the work as gradually sneaking up on an answer for water.

If nothing else, the theoretical and experimental work on the Mpemba effect has started giving physicists a handhold into nonequilibrium systems that they otherwise lack. “Relaxation towards equilibrium is an important question that, frankly, we don’t have a good theory [for],” said Raz. Identifying which systems might behave in strange and counterintuitive ways “would give us a much better picture of how systems relax towards equilibrium.”

After igniting a decades-long controversy with his teenage interrogations, Mpemba himself went on to study wildlife management, becoming a principal game officer in Tanzania’s Ministry of Natural Resources and Tourism before retiring. According to Christine Osborne, the widow of Denis Osborne, Mpemba passed away around 2020. Science continues to spring from his insistence about the effect that bears his name. Osborne, discussing the results of their investigations together, took a lesson from the initial skepticism and dismissal that the schoolboy’s counterintuitive claim had faced: “It points to the danger of an authoritarian physics.”

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Original by Monwhea Jeng (Momo), Department of Physics, University of California, 1998.

Can hot water freeze faster than cold water?

Yes—a general explanation.

Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real. It has been seen and studied in numerous experiments . Although this phenomenon has been known for centuries, and was described by Aristotle, Bacon, and Descartes [1–3] , it was not introduced to the modern scientific community until 1969, by a Tanzanian high school pupil named Mpemba. Both the early scientific history of this effect, and the story of Mpemba's rediscovery of it, are interesting in their own right — Mpemba's story in particular providing a dramatic parable against making snap judgements about what is impossible. This is described separately below.

The phenomenon that hot water may freeze faster than cold is often called the Mpemba effect. Because, no doubt, most readers are extremely skeptical at this point, we should begin by stating precisely what we mean by the Mpemba effect. We start with two containers of water, which are identical in shape, and which hold identical amounts of water. The only difference between the two is that the water in one is at a higher (uniform) temperature than the water in the other. Now we cool both containers, using the exact same cooling process for each container. Under some conditions the initially warmer water will freeze first. If this occurs, we have seen the Mpemba effect. Of course, the initially warmer water will not freeze before the initially cooler water for all initial conditions. If the hot water starts at 99.9°C, and the cold water at 0.01°C, then clearly under those circumstances, the initially cooler water will freeze first. But under some conditions the initially warmer water will freeze first: if that happens, you have seen the Mpemba effect. But you will not see the Mpemba effect for just any initial temperatures, container shapes, or cooling conditions.

This seems impossible, right? Many sharp readers may have already come up with a common proof that the Mpemba effect is impossible. The proof usually goes something like this. Say that the initially cooler water starts at 30°C and takes 10 minutes to freeze, while the initially warmer water starts out at 70°C. Now the initially warmer water has to spend some time cooling to get to get down to 30°C, and after that, it's going to take 10 more minutes to freeze. So since the initially warmer water has to do everything that the initially cooler water has to do, plus a little more, it will take at least a little longer, right? What can be wrong with this proof?

What's wrong with this proof is that it implicitly assumes that the water is characterized solely by a single number — its average temperature. But if other factors besides the average temperature are important, then when the initially warmer water has cooled to an average temperature of 30°C, it may look very different than the initially cooler water (at a uniform 30°C) did at the start. Why? Because the water may have changed when it cooled down from a uniform 70°C to an average 30°C. It could have less mass, less dissolved gas, or convection currents producing a non-uniform temperature distribution. Or it could have changed the environment around the container in the refrigerator. All four of these changes are conceivably important, and each will be considered separately below. So the impossibility proof given above doesn't work. And in fact the Mpemba effect has been observed in a number of controlled experiments [5,7–14]

It is still not known exactly why this happens. A number of possible explanations for the effect have been proposed, but so far the experiments do not show clearly which, if any, of the proposed mechanisms is the most important one. While you will often hear confident claims that X is the cause of the Mpemba effect, such claims are usually based on guesswork, or on looking at the evidence in only a few papers and ignoring the rest. Of course, there is nothing wrong with informed theoretical guesswork or being selective in which experimental results you trust; the problem is that different people make different claims as to what X is.

Why hasn't modern science answered this seemingly simple question about cooling water? The main problem is that the time it takes water to freeze is highly sensitive to a number of details in the experimental setup, such as the shape and size of the container, the shape and size of the refrigeration unit, the gas and impurity content of the water, how the time of freezing is defined, and so on. Because of this sensitivity, while experiments have generally agreed that the Mpemba effect occurs, they disagree over the conditions under which it occurs, and thus about why it occurs. As Firth [7] wrote "There is a wealth of experimental variation in the problem so that any laboratory undertaking such investigations is guaranteed different results from all others."

Finally, supercooling may be important to the effect. Supercooling occurs when the water freezes not at 0°C, but at some lower temperature. One experiment [12] found that its initially hot water supercooled less than its initially cold water. This would mean that the initially warmer water might freeze first because it would freeze at a higher temperature than the initially cooler water. If true, this would not fully explain the Mpemba effect, because we would still need to explain why initially warmer water supercools less than initially cooler water.

In short, hot water does freeze sooner than cold water under a wide range of circumstances. It is not impossible, and has been seen to occur in a number of experiments. But despite claims often made by one source or another, there is no well-agreed explanation for how this phenomenon occurs. Different mechanisms have been proposed, but the experimental evidence is inconclusive. For those wishing to read more on the subject, Jearl Walker's article in Scientific American [13] is very readable and has suggestions on how to do home experiments on the Mpemba effect, while the articles by Auerbach [12] and Wojciechowski [14] are two of the more modern papers on the effect.

History of the Mpemba Effect

The fact that hot water freezes faster than cold has been known for many centuries. The earliest reference to this phenomenon dates back to Aristotle in 300 B.C. The phenomenon was later discussed in the medieval era, as European physicists struggled to come up with a theory of heat. But by the 20th century the phenomenon was only known as common folklore, until it was reintroduced to the scientific community in 1969 by Mpemba, a Tanzanian high school pupil. Since then, numerous experiments have confirmed the existence of the "Mpemba effect", but have not settled on any single explanation.

The earliest known reference to this phenomenon is by Aristotle, who wrote:

"The fact that water has previously been warmed contributes to its freezing quickly; for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun. . ." [1,4]

He wrote these words in support of a mistaken idea which he called antiperistasis. Antiperistasis is defined as "the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality, for instance, the sudden heating of a warm body when surrounded by cold" [4] .

Medieval scientists believed in Aristotle's theory of antiperistasis, and also sought to explain it. Not surprisingly, scientists in the 1400s had trouble explaining how it worked, and could not even decide whether (as Aristotle claimed in support of antiperistasis), human bodies and bodies of water were hotter in the winter than in the summer [4] . Around 1461, the physicist Giovanni Marliani, in a debate over how objects cooled, said that he had confirmed that hot water froze faster than cold. He said that he had taken four ounces of boiling water, and four ounces of non-heated water, placed them outside in similar containers on a cold winter day, and observed that the boiled water froze first. Marliani was, however, unable to explain this occurrence [4] .

Later, in the 1600s, it was apparently common knowledge that hot water would freeze faster than cold. In 1620 Bacon wrote "Water slightly warm is more easily frozen than quite cold" [2] , while a little later Descartes claimed "Experience shows that water that has been kept for a long time on the fire freezes sooner than other water" [3] .

In time, a modern theory of heat was developed, and the earlier observations of Aristotle, Marliani, and others were forgotten, perhaps because they seemed so contradictory to modern concepts of heat. But it was still known as folklore among many non-scientists in Canada [11] , England [15–21] , the food processing industry [23] , and elsewhere.

It was not reintroduced to the scientific community until 1969, 500 years after Marliani's experiment, and more than two millennia after Aristotle's "Meteorologica I" [1] . The story of its rediscovery by a Tanzanian high school pupil named Mpemba is written up in the New Scientist [4] . The story provides a dramatic parable cautioning scientists and teachers against dismissing the observations of non-scientists and against making quick judgements about what is impossible.

In 1963, Mpemba was making ice cream at school, which he did by mixing boiling milk with sugar. He was supposed to wait for the milk to cool before placing it the refrigerator, but in a rush to get scarce refrigerator space, put his milk in without cooling it. To his surprise, he found that his hot milk froze into ice cream before that of other pupils. He asked his physics teacher for an explanation, but was told that he must have been confused, since his observation was impossible.

Mpemba believed his teacher at the time. But later that year he met a friend of his who made and sold ice cream in Tanga town. His friend told Mpemba that when making ice cream, he put the hot liquids in the refrigerator to make them freeze faster. Mpemba found that other ice cream sellers in Tanga had the same practice.

Later, when in high school, Mpemba learned Newton's law of cooling, that describes how hot bodies are supposed to cool (under certain simplifying assumptions). Mpemba asked his teacher why hot milk froze before cold milk when he put them in the freezer. The teacher answered that Mpemba must have been confused. When Mpemba kept arguing, the teacher said "All I can say is that is Mpemba's physics and not the universal physics" and from then on, the teacher and the class would criticize Mpemba's mistakes in mathematics and physics by saying "That is Mpemba's mathematics" or "That is Mpemba's physics." But when Mpemba later tried the experiment with hot and cold water in the biology laboratory of his school, he again found that the hot water froze sooner.

Earlier, Dr Osborne, a professor of physics, had visited Mpemba's high school. Mpemba had asked him to explain why hot water would freeze before cold water. Dr Osborne said that he could not think of any explanation, but would try the experiment later. When back in his laboratory, he asked a young technician to test Mpemba's claim. The technician later reported that the hot water froze first, and said "But we'll keep on repeating the experiment until we get the right result." But repeated tests gave the same result, and in 1969 Mpemba and Osborne wrote up their results [5] .

In the same year, in one of the coincidences so common in science, Dr Kell independently wrote a paper on hot water freezing sooner than cold water. Kell showed that if one assumed that the water cooled primarily by evaporation, and maintained a uniform temperature, the hot water would lose enough mass to freeze first [11] . Kell thus argued that the phenomenon (then a common urban legend in Canada) was real and could be explained by evaporation. But he was unaware of Osborne's experiments, which had measured the mass lost to evaporation and found it insufficient to explain the effect. Subsequent experiments were done with water in a closed container, eliminating the effects of evaporation, and still found that the hot water froze first [14] .

Subsequent discussion of the effect has been inconclusive. While quite a few experiments have replicated the effect [4,6–13] , there has been no consensus on what causes the effect. The different possible explanations are discussed above . The effect has repeatedly a topic of heated discussion in the "New Scientist", a popular science magazine. The letters have revealed that the effect was known by laypeople around the world long before 1969. Today, there is still no well-agreed explanation of the Mpemba effect.

Evaporation

One explanation of the effect is that as the hot water cools, it loses mass to evaporation. With less mass, the liquid has to lose less heat to cool, and so it cools faster. With this explanation, the hot water freezes first, but only because there's less of it to freeze. Calculations done by Kell in 1969 [11] showed that if the water cooled solely by evaporation, and maintained a uniform temperature, the warmer water would freeze before the cooler water.

This explanation is solid, intuitive, and undoubtedly contributes to the Mpemba effect in most physical situations. But many people have incorrectly assumed that it is therefore "the" explanation for the Mpemba effect. That is, they assume that the only reason hot water can freeze faster than cold is because of evaporation, and that all experimental results can be explained by the calculations in Kell's article. But the experiments currently do not bear this belief out. While experiments show evaporation to be important [13] , they do not show that it is the only mechanism behind the Mpemba effect. A number of experimenters have argued that evaporation alone is insufficient to explain their results [5,9,12] ; in particular, the original experiment by Mpemba and Osborne measured the mass lost to evaporation, and found it substantially less that the amount predicted by Kell's calculations [5,9] . And most convincingly, an experiment by Wojciechowski observed the Mpemba effect in a closed container, where no mass was lost to evaporation.

Dissolved Gasses

Another explanation argues that the dissolved gas usually present in water is expelled from the initially hot water, and that this changes the properties of the water in some way that explains the effect. It has been argued that the lack of dissolved gas may change the ability of the water to conduct heat, or change the amount of heat needed to freeze a unit mass of water, or change the freezing point of the water by some significant amount. It is certainly true that hot water holds less dissolved gas than cold water, and that boiled water expels most dissolved gas. The question is whether this can significantly affect the properties of water in a way that explains the Mpemba effect. As far as I know, there is no theoretical work supporting this explanation for the Mpemba effect.

Indirect support can be found in two experiments that saw the Mpemba effect in normal water which held dissolved gasses, but failed to see it when using degassed water [10,14] . But an attempt to measure the dependence of the enthalpy of freezing on the initial temperature and gas content of the water was inconclusive [14] .

One problem with this explanation is that many experiments pre-boiled both the initially hot and initially cold water, precisely to eliminate the effect of dissolved gasses, and yet they still saw the effect [5,13] . Two somewhat unsystematic experiments found that varying the gas content of the water made no substantial difference to the Mpemba effect [9,12] .

It has also been proposed that the Mpemba effect can be explained by the fact that the temperature of the water becomes non-uniform. As the water cools, temperature gradients and convection currents will develop. For most temperatures, the density of water decreases as the temperature increases. So over time, as water cools we will develop a "hot top" — the surface of the water will be warmer than the average temperature of the water, or the water at the bottom of the container. If the water loses heat primarily through the surface, then this means that the water should lose heat faster than one would expect based just on looking at the average temperature of the water. And for a given average temperature, the heat loss should be greater the more inhomogenous the temperature distribution is (that is, the greater the range of the temperatures seen as we go from the top to the bottom).

How does this explain the Mpemba effect? Well, the initially hot water will cool rapidly, and quickly develop convection currents and so the temperature of the water will vary greatly from the top of the water to the bottom. On the other hand, the initially cool water will have a slower rate of cooling, and will thus be slower to develop significant convection currents. Thus, if we compare the initially hot water and initially cold water at the same average temperature, it seems reasonable to believe that the initially hot water will have greater convection currents, and thus have a faster rate of cooling. To consider a concrete example, suppose that the initially hot water starts at 70°C, and the initially cold water starts at 30°C. When the initially cold water is at an average 30°C, it is also a uniform 30°C. But when the initially hot water reaches an average 30°C, the surface of the water is probably much warmer than 30°C, and it will thus lose heat faster than the initially cold water for the same average temperature. Got that? This explanation is pretty confusing, so you might want to go back and read the last two paragraphs again, paying careful attention to the difference between initial temperature, average temperature, and surface temperature.

At any rate, if the above argument is right, then when we plot the average temperature versus time for both the initially hot and initially cold water, then for some average temperatures the initially hot water will be cooling faster than the initially cold water. So the cooling curve of the initially hot water will not simply reproduce the cooling curve of the initially cold water, but will drop faster when in the same temperature range.

This shows that the initially hot water goes faster, but of course it also has farther to go. So whether it actually finishes first (that is, reaches 0°C first), is not clear from the above discussion. To know which one finishes first would require theoretical modelling of the convection currents (hopefully for a range of container shapes and sizes), which has not been done. So convection alone may be able to explain the Mpemba effect, but whether it actually does is not currently known. Experiments on the Mpemba effect have often reported a "hot top" [5,8,10] , as we would expect. Experiments have been done that looked at the convection currents of freezing water [27,28] , but their implications for the Mpemba effect are not entirely clear.

It should also be noted that the density of water reaches a maximum at four° C. So below four°C, the density of water actually decreases with decreasing temperature, and we will get a "cold top." This makes the situation even more complicated.

Surroundings

The initially hot water may change the environment around it in some way that makes it cool faster later on. One experiment reported significant changes in the data simply upon changing the size of the freezer that the container sat in [7] . So conceivably it is important not just to know about the water and the container, but about the environment around it.

For example, one explanation for the Mpemba effect is that if the container is resting on a thin layer of frost, than the container holding the cold water will simply sit on the surface of the frost, while the container with the hot water will melt the frost, and then be sitting on the bottom of the freezer. The hot water will then have better thermal contact with the cooling systems. If the melted frost refreezes into an ice bridge between the freezer and the container, the thermal contact may be even better.

Obviously, even if this argument is true, it has fairly limited utility, since most scientific experiments are careful enough not to rest the container on a layer of frost in a freezer, but instead place the container on a thermal insulator, or in a cooling bath. So while this proposed mechanism may or may not have some relevance to some home experiments, it's irrelevant for most published results.

Supercooling

Finally, supercooling may be important to the effect. Supercooling occurs when water freezes not at 0°C, but at some lower temperature. This happens because the statement that "water freezes at 0°C" is a statement about the lowest energy state of the water: at less than 0°C, the water molecules "want" to be arranged as an ice crystal. This means that they will stop zooming around randomly as a liquid, and instead form a solid ice lattice. But they don't know how to form themselves into an ice lattice, but need some small irregularity or nucleation site to tell them how to arrange themselves. Sometimes, when water is cooled below 0°C, the molecules will not see a nucleation site for some time, and then water will cool below 0°C without freezing. This happens quite often. One experiment found that initially hot water would supercool only a little (say to about −2°C), while initially cold water would supercool more (to around −8°C) [12] . If true, this could explain the Mpemba effect because the initially cold water would need to "do more work"; — that is, get colder — to freeze.

But this also cannot be considered "the" sole explanation of the Mpemba effect. First of all, as far as I know, this result has not been independently confirmed. The experiment described above [12] only had a limited number of trials, so the results found could have been a statistical fluke.

Second, even if the results are true, they do not fully explain the Mpemba effect, but replace one mystery with another. Why should initially hot water supercool less than initially cold water? After all, once the water has cooled to the lower temperature, one would generally expect that the water would not "remember" what temperature it used to be. One explanation is that the initially hot water has less dissolved gas than the initially cold water, and that this affects its supercooling properties (see Dissolved Gasses for more on this). The problem with this explanation is that one would expect that since the hot water has less dissolved gas, and thus fewer nucleation sites, it would supercool more, not less. Another explanation is that when the initially hot water has cooled down to 0°C (or less), its temperature distribution throughout the container varies more than the initially cold water (see Convection for more on this). Since temperature shear induces freezing [26] , the initially hot water supercools less, and thus freezes sooner.

Third, this explanation cannot work in all of the experiments, because many of the experimenters chose to look not at the time to form a complete block of ice, but the time for some part of the water to reach 0°C [7,10,13] (or perhaps the time for a thin layer of frost to form on the top [17] ). While [12] says that it is only a "true Mpemba effect" if the hot water freezes entirely first, other papers have defined the Mpemba effect differently. Since the precise time of supercooling is inherently unpredictable (see e.g. [26] ), many experiments have chosen to measure not the time for the sample to actually become ice, but the time for which the sample's equilibrium ground state is ice; that is, the time when the top of the sample reached 0°C [7,10,13] . The supercooling argument does not apply to these experiments.

Experiments on the Mpemba Effect

General discussion on the mpemba effect, related articles.

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Does hot water freeze faster than cold water?

August 22, 2024 By Emma Vanstone Leave a Comment

It sounds completely counterintuitive, but whether hot water freezes faster than cold water has been debated for centuries.

The Mpemba Effect

The Mpemba effect is the term used for hot water freezing faster than cold water after a Tanzanian student named Erasto Mpemba found that his mixture of hot milk and sugar froze faster than his classmate’s mixtures that had been left to cool before freezing.

You can test to see if the Mpemba Effect occurs by placing two equal amounts of water in a freezer to investigate which freezes first. One sample should be at room temperature, and the second should be hot or boiling water.

If you’re interested in the quite complex science behind the Mpemba effect, How Stuff Works has a great article explaining it.

Last Updated on August 23, 2024 by Emma Vanstone

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Reader Interactions

Is it true that hot water makes ice cubes faster than cold water?

Asks porterhouse from brooklyn, new york, greg soltis • september 22, 2008.

Does ice freeze more quickly if you start with hot water? <br> [Credit: Molika Ashford]

Does ice freeze more quickly if you start with hot water? [Credit: Molika Ashford]

Should i be scared of my tap water, melissa mahony • july 19, 2006.

Is it true that some frogs can survive being frozen?

Rachel Mahan • June 23, 2008

Deciphering bacteria’s defenses, one gene at a time, adam t. hadhazy • august 27, 2008.

Determining whether or not hot water can freeze faster than cold water may seem like a no-brainer. After all, water freezes at zero degrees Celsius. And wouldn’t water hot enough to kill E. coli bacteria (about 120 degrees Fahrenheit or 50 degrees Celsius) take a longer path than cooler water at a fall New England beach (about 60 degrees Fahrenheit or 15 degrees Celsius) towards a frigid future as ice? While a logical assumption, it turns out that hot water can freeze before cooler water under certain conditions.

This apparent quirk of nature is the “ Mpemba effect ,” named after the Tanzanian high school student, Erasto Mpemba, who first observed it in 1963. The Mpemba effect occurs when two bodies of water with different temperatures are exposed to the same subzero surroundings and the hotter water freezes first. Mpemba’s observations confirmed the hunches of some of history’s most revered thinkers, like Aristotle, Rene Descartes and Francis Bacon, who also thought that hot water froze faster than cold water

Evaporation is the strongest candidate to explain the Mpemba effect . As hot water placed in an open container begins to cool, the overall mass decreases as some of the water evaporates. With less water to freeze, the process can take less time. But this doesn’t always work, especially when using closed containers that prevent evaporated water from escaping.

And evaporation may not be the only reason the water can freeze more quickly. There may be less dissolved gas in the warmer water, which can reduce its ability to conduct heat, allowing it to cool faster. However, Polish physicists in the 1980s were unable to conclusively demonstrate this relationship.

A non-uniform temperature distribution in the water may also explain the Mpemba effect. Hot water rises to the top of a container before it escapes, displacing the cold water beneath it and creating a “hot top.” This movement of hot water up and cold water down is called a convection current. These currents are a popular form of heat transfer in liquids and gases, occurring in the ocean and radiators that warm a chilly room. With the cooler water at the bottom, this uneven temperature distribution creates convection currents that accelerate the cooling process. Even with more ground to cover to freeze, the temperature of the hotter water can drop at a faster rate than the cooler water.

So the next time you refill your ice cube tray, try using warmer water. You might have ice cubes to cool your drink even sooner.

Also on Scienceline :

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Deciphering bacteria’s defenses , one gene at a time.

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18 comments.

The negative consequences of your tongue-in-cheek closing sentence gave me pause. Can you imagine the enormous amount of fresh water wasted (the cost of which is already skyrocketing in the US) should any sizeable portion of the populace begin running their taps until hot water pours out just to obtain “warmer (than tap water temp) water” for slightly faster ice cube formation? Add to that the wasted energy caused by heating the water only to cool it down again. Comparing/quantifying the inputs and savings – fresh water costs + energy cost of heating a volume of water – energy saved by not running the freezer compressor quite as long to cool it down again gives me a slurpee-like “brain freeze”!

Oh, it would be terrible! with americans making ice cubes constantly as we all do, it would virtually eliminate all water from the planet in a matter of days! I brushed my teeth this morning, I left the faucet on too. I got news for you, there is no more or less water on the planet now as there was this morning or there will be tomorrow.

Just want to say- I live in an area that has very cold winter temperatures, and the hot water pipes ALWAYS freeze before the cold water pipes.

Ed is correct, the hot water will cause global warming and then we won’t have any ice. I’m totally serial.

A coworker who tried the warm-water method for making ice noted that the ice had absorbed smells/taste from other food in the freezer.

Learned this awhile ago while working as a chef’s assistant. Hot water freezes faster and COLDER water boils faster.

Making water warmer would not make it feeze faster, it has to be boiling. I once left bowls of hot, warm and cold water out in freezing temperatures and found that the hot water froze first, the cold water second and the warm water last.

Hi – I always thought that the hot water ice blocks froze first because of the extent of the difference in temperature between the water and the surrounding cold air, with the freezing being caused by the rapid osmosis – in the same way that evaporation causes cooling.

However, I was wondering, does this just effect the outside edges of the ice-block? If so, how does this effect the time it takes for the whole ice-block to freeze – right through to the core of the block?

Great goods from you, man. I have understand your stuff previous to and you are just extremely wonderful.

This is the most idiotic post and comment thread (aside from the tongue in cheek ones) that I have ever read.

I would like to know about logical difference between ice cold water and simple cold water?

Has anyone thought I how gross the inside of a hot water tank is… I wouldn’t drink or eat anything that comes from a hot water tank. I have seen it it’s not safe to drink… Why make ice cubes from it?!

very nice blog

My never images are never as good :(

I guess the majority of people did not take physics or even simple science in high school. This has been taught for decades. Ha.

wow I never knew this, got landed to this page while searching for something similar on goolge :) will try and compare and come back to post if this is right !!

Back when I worked as a bartender the notion was that making ice using hot water resulted in clearer ice cubes than using cold water.

I have observed this to be true, the cloudiness in conventional ice cubes appears to be trapped and compressed dissolved gasses in the water. Heating the water expels the gasses, so the ice freezes clear.

The rate at which ice cubes melt is faster with hot water. However, whether they freeze faster overall I am going to see for myself. Time for some good old fashioned expiriementation.

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It's True: Hot Water Really Can Freeze Faster Than Cold Water

Hot water really can freeze faster than cold water, a new study finds. Sometimes. Under extremely specific conditions. With carefully chosen samples of water.

That’s what Brownridge has done. One of his experiments, presented online, repeatedly froze a sample of hot water faster than a similar sample of cool water.

Note the word similar. In order for the experiment to work, the cool water had to be distilled, and the hot water had to come from the tap.

Brownridge heated the tap water to about 100° C, while the distilled water was cooled to 25° C or lower. When both samples were put into the freezer, the hot water froze before the cold water. Brownridge then thawed the samples and repeated the experiment 27 times. Each time, the hot tap water froze first.

Physical chemist Christoph Salzmann of the University of Durham in England says he’s not convinced the Mpemba effect really exists, because there are innumerable things that influence the timing of freezing, making it impossible to completely control.

Image: Kenn Wilson /flickr

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Does hot water freeze faster than cold water?

Is it true that hot water freezes faster than cold water and if so, what practical applications have there been found for this phenomenon?

2 I know it does because Peggy Knapp did it on Newton's Apple . That was a great program. – mmyers Commented May 19, 2011 at 15:54
3 I tried this by putting two glasses with the same volume of water in the freezer, one glass had room temperature water the other had hotter, recently boiled water. My outcome was that the cold water froze first as you'd expect. It is a well documented effect though and I'd be interested to know why my experiment gave a negative result. – Stephen Paulger Commented May 20, 2011 at 14:31
3 If evaporation is a key factor, then the surface area will be important for the experiment. Two glasses of water in a freezer will not yield the same result as two shallow amounts of water spread over a square foot each. The hot water will evaporate much faster when it is very shallow and spread out. It has less total mass to retain heat and a lot more surface area to cool it and evaporate it. The hot water will evaporate reducing mass and will then freeze faster than the cold water. The relative humidity in the air will also be a variable to consider. – user2952 Commented May 20, 2011 at 14:51
3 I once heard a rebuttal to this by claiming that hot water must become cold water before it could become frozen water. I find that a good example of completely missing the point. – MrHen Commented May 20, 2011 at 19:42
Related. physics.stackexchange.com/questions/122742/… – Takahiro Waki Commented Jan 17, 2018 at 6:01

4 Answers 4

In certain settings, cold water freezers slower than hot water. This is called the Mpemba effect .

The Mpemba effect is the observation that warmer water sometimes freezes faster than colder water. Although the observation has been verified, there is no single scientific explanation for the effect.

Can hot water freeze faster than cold water? , Monwhea Jeng, University of California, 1998

Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real. It has been seen and studied in numerous experiments. While this phenomenon has been known for centuries, and was described by Aristotle, Bacon, and Descartes [1—3], it was not introduced to the modern scientific community until 1969, by a Tanzanian high school student named Mpemba.

Some suggested reasons given in the paper:

Evaporation — As the initially warmer water cools to the initial temperature of the initially cooler water, it may lose significant amounts of water to evaporation. The reduced mass will make it easier for the water to cool and freeze. Then the initially warmer water can freeze before the initially cooler water, but will make less ice. [...] Dissolved Gasses — Hot water can hold less dissolved gas than cold water, and large amounts of gas escape upon boiling. So the initially warmer water may have less dissolved gas than the initially cooler water. [...]

2 I think it is worth giving at least some of the suggested reasons here (e.g. more evaporation of the hot water means less water to freeze). – Oddthinking ♦ Commented May 19, 2011 at 7:07
7 Wouldn't these theories, particularly the evaporation theory easily be tested??? For example measure how much ice is in each sample after the experiment??? – kralco626 Commented May 19, 2011 at 10:33
5 @mplungjan That's actually a different phenomenon called supercooling, where a liquid is cooled to below it's freezing point without it actually freezing (because it lacks a nucleus point from where the freezing should start), and freezes instantly upon applying a shock, or something that makes it non-homogenous. Check out wikipedia for more info: en.wikipedia.org/wiki/Supercooling – Andrei Fierbinteanu Commented May 19, 2011 at 11:15
3 One plausible explanation is that the warmer water has a stronger convection current when cooling. The angular momentum of the convection current sustains the current after dropping to a lower temperature, and so the water cools throughout more rapidly. – Richard Gadsden Commented Jul 1, 2012 at 17:42
5 Interesting answer is at MIT web: Does hot water freeze faster than cold water? Their conclusion is no . – Palec Commented Nov 25, 2013 at 3:58

This was, actually, my 6 th 5 th grade Science Fair experiment. :)

And I'd never heard of this effect before; it was a random experiment I thought of and tried.

My answer: it depends on what you mean by "freeze" .

Cold water starts freezing sooner (entering 0 degrees C), but hot water finishes freezing sooner (leaving 0 degrees C). I measured this with a digital thermometer.

No idea why, but I'm darn sure my experiment was accurate.

I found the data!

I blurred out the years to avoid carbon dating myself. ;)

3 This post does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. – Larian LeQuella Commented Jan 13, 2012 at 21:17
15 @LarianLeQuella: Does original research count? – user541686 Commented Jan 13, 2012 at 21:20
57 Does "publication" and "peer review" at a science fair count for nothing these days? ;p BTW, did you win anything? – Dan Moulding Commented Mar 1, 2012 at 12:51
9 Bravo! Anyway, the fact that you, at age ten, had access to a computer for analysis already partially carbon dates you. :) – JasonSmith Commented Jan 7, 2015 at 14:40
12 Yeah, I guess I silicon-dated myself :) – user541686 Commented Jan 30, 2017 at 0:13

A new paper on this phenomenon has been published recently. It offers yet another explanation and has even caught the attention of popular media.

doi:10.1038/srep03005

arXiv:1310.6514v2 [physics.chem-ph]

They say the interaction between the hydrogen bonds and the stronger bonds that hold the hydrogen and oxygen atoms in each molecule together, known as covalent bonds, is what causes the effect. Normally when a liquid is heated, the covalent bonds between atoms stretch and store energy. The scientists argue that in water, the hydrogen bonds produce an unusual effect that causes the covalent bonds to shorten and store energy when heated. This they say leads to the bonds to release their energy in an exponential way compared to the initial amount stored when they are cooled in a freezer. So hot water will lose more energy faster than cool water. Dr Changqing said: “Heating stores energy by shortening and stiffening the H-O covalent bond. “Cooling in a refrigerator, the H-O bond releases its energy at a rate that depends exponentially on the initially stored energy, and therefore, Mpemba effect happens.” The Royal Society of Chemistry received more than 22,000 responses to its call for a solution to the Mpemba effect and it is still receiving theories despite the competition closing a year ago.

Quoted from Telegraph.co.uk .

It is true, in proper circumstances.

The Scientific explanation for that relates to the fact the freezing temperature may increase with the pressure.

The Mpemba effect is about freezing hot samples faster than cold which may not represent a substantial difference with small pressure variations but phenomenons like supercooling and superheating do have practical applications such as better preservation of organs in medical refrigerators and superconductivity in electrical devices.

You can find more about this in: The Mpemba effect: why hot water can sometimes freeze faster than cold .

6 The freezing temperature actually decreases when the pressure increases... (see the phase diagram of water : 1.bp.blogspot.com/_Ukz5Qzczfbc/TVEUPJxtDfI/AAAAAAAAB54/… ) – Jules Olléon Commented May 20, 2011 at 14:21

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What Freezes first… Hot or Cold Water?

Follow FizzicsEd 150 Science Experiments:

You Will Need:

One cup of cold water, 100mL in volume
One cup of hot water, 100mL in volume
One Stopwatch
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A pen and paper

What freezes first, hot or cold water Science Experiment - setupmaterials

Instruction

What freezes first, hot or cold water Science Experiment - end results

Stir both water cups the same amount of time. Place both cups of water inside your freezer and start the timer.

Keep checking at 5 minute intervals to see which freezes first.

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Record your observations. What happened?

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Why Does This Happen:

Hmmmm, you’ve completed an experiment whose results are quite tricky to explain. Did you find that the hot water froze first? Under some conditions this can happen…

We started with two containers of water, which were identical in shape and held identical amounts of water. The only difference between the two was that the water in one was at a higher (uniform) temperature than the water in the other. Of course, if the hot water had started at 99.9° C, and the cold water at 0.01° C, then clearly under those circumstances, the initially cooler water would have frozen first. However, under some conditions the initially warmer water will freeze first — if that happens, you have seen the Mpemba effect which describes the phenomenon.

How does it work you might ask? Several ideas have been put forward and no-one really is sure as to which effect plays the biggest role:

1. As the initially warmer water cools to the freezer temperature, it may lose significant amounts of water to evaporation. The reduced mass will make it easier for the warmer water to cool and freeze than the colder water.

2. A convection current may have been setup in the warmer water. As the warmer water cooled it lost heat primarily through the surface of the liquid faster than the colder water. This is due to a great temperature difference between the cold freezer air and the warm water. The water from the bottom of the cup then rose to the water surface, bringing more heat energy to the cold freezer air. As the current is greater in the warmer water than the cold water, a greater amount of liquid got exposed to the cold freezer air. Think of a fan forced oven, circulating the hot air through the oven heats the oven faster than just allowing the air to sit still… bakers have known this over a thousand of years!

More on temperature and water rising or falling 3. The surrounding air around the cups may have more movement around the warmer cup, therefore drawing heat energy away from the warmer cup more effectively.

4. Warm water holds less dissolved gas than cold water. There have been some suggestions that the presence of dissolved gases impede the production of convection currents in the colder water.

5. The cold water may have supercooled , therefore not forming a solid as quick as the hot water.

Quote: “I often put boiling water in the freezer. Then whenever I need boiling water, I simply defrost it.” -Gracie Allen.

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28 thoughts on “ What Freezes first… Hot or Cold Water? ”

Very helpful and useful for kids and everyone and it’s easy to understand.

Thanks Amal, we’re glad that you’ve been using these science activities!

can you please answer these 2 questions: What’s the independent, dependent & controlled variable of this experiment? And what equipments have you used for this experiment?

The independent variable for this experiment was the temperature of the water (this was the variable that we could manipulate). The dependent variable was the time it took for the water to change from liquid to solid (as this depends on the initial temperature of the water). The controlled variables were the freezer temperature, the cup size, the volume of the water used in each test and the amount of stirring in each cup. More details on variable testing here

You can find the details on the materials needed at the top of this page. Have fun with this experiment!

what are some risks that can take place when doing this experiment

If the water is close to boiling you really need to be careful. Also, water spills are a slipping hazard.

Is this an actual good experiment that will work in class

Hi Ben, give it go and see what happens! All the best.

is it ok to do in school

Sure thing, just check with your teacher first and let them handle the hot water. Have fun!

i don’t have it yet,but it sounds like its super fun! : )

Its an interesting experiment! Please let us know what your results were… do they conform to the theory above? Have fun!

How hot should the hot water be?

Hi! Try cups with different amounts of heat – you might find that there is a particular temperature where the result can be opposite 🙂 We like to use near-boiling vs room temperature, but you could try every temperature as a series of tests (as long as you’re safe with water over 55 degrees celsius). Have fun!

Hi, can you please describe the science involved in this investigation

Hi Jae! This is based on the Mpemba effect. Check out further details here

The cold water froze first for me, why?

This has been a tough one for us to reproduce too! We’ve found that there can be slight differences within the freezer itself, whereby placement of the cups in relation to the vents being a crucial factor. Did you try it again?

wow, this experiment was really surprising at first but now that I have read the science behind it, it makes a lot more sense.

Great to hear that you were able to confirm this experiment! It’s a strange one to observe 🙂

Just did the experiment with my son. I was fully expecting the hot water to freeze first, but it ended up being the cold water that froze. Cold started to freeze after 20 minutes. At 40 minutes cold is solid and hot is probably a third of the way frozen. Disappointed that the results didn’t turn out as described in the experiment. Maybe there needs to be more controls included in the experiment. I made sure to use the same cup and I put the cups in the same spot of the freezer. It would be good to have a suggested temperature for both.

Hi Alisa, I’m glad to hear you and your son have tried this experiment! Freezing water may seem commonplace, so you’d think that scientists would have this all figured out…but in fact, the Mpemba Effect is still being researched and redefined! From fancy labs where things are monitored and controlled down to the molecular level to high school classrooms, scientists see different results. This is because the effect is only sometimes observed under “some conditions”, as we have stated in the experiment description. The latest research suggests that convection currents, nucleation sites, supercooling and dissolved gases/ions all might play a part, and have complex interactions. This means that even though you have used the same cup and put it in the same spot in the freezer (great variable control, by the way!), our freezers at home may still introduce inconsistencies as it cycles on and off to maintain temperature (usually -10 to -18 degrees Celcius), or have the cooling vent in a location which favours the cold or hot sample (top or bottom may influence the outcome). How we pour the water into the cup and walk it over to the freezer and place it might make a difference. One scientist even wrote that “two samples of water taken from the same bottle may differ significantly”! While these are factors that are very hard to control at home, this is such an interesting experiment to attempt because this is not an experiment where it will “work” or “fail”. At Fizzics we don’t always get the same results either, but we love figuring out why we see each observation! The authors of this article had some success with around 50 degrees Celcius difference in sample temperatures. Fizzics scientists have observed the effect in the past with nearly boiling (80-100 degrees) vs. cold tap water.

I loved this experiment

Glad that you enjoyed it!

Hi this is perfect for my students because I looked it up on Google and it was perfect and like to say thank you guys for putting this up because I need to show it to my students and I love how it’s very good experience

Hi this is perfect for my students

Fantastic! Please let us know how you go 🙂

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Does hot or cold water freeze first?

Part of the show national science and engineering week, snowflake2.jpg.

If you put some hot water and some cold water in the freezer, which one freezes first?

There's convection currents going on inside the water...

If you've got something warm, it's less dense so it rises upwards and the cooler stuff sinks. This creates a turning circulation.

If you put that in the freezer, because the water is stirred up by the heat, the water will start moving and it will carry on moving for quite some time and this will keep mixing the water enabling it after its cooled down to keep loosing heat more quickly than cold water because that's more static and doesn't move so much to start with.

Therefore the cold water will be overtaken on the freezing process, possibly by the hot water.

The obvious thing would be that the cold water would freeze first, because its got less energy to lose but I have heard that the hot water would freeze sooner but I've not looked in to it in detail. The convection currents helping the water water freeze first make sense though.

The other thing is if you heat up water and boil it you drive off all the gases dissolved in it, and those gases might be reducing the freezing point.

So, if you did the experiment fairly and used distilled water or something, it would be an accurate way of testing.

Previous Do swallows roll 360 degrees?
Next Why can you see vapour trails only sometimes?

The Claim Hot Water Freezes Faster Than Cold Water Is Even Weirder Than You Think

Despite sounding like the most egregious contradiction in physics, hot water appears to freeze faster than cold water under certain circumstances. The phenomenon can be traced back to Aristotle himself , but after centuries of experiments demonstrating this phenomenon, no one's been able to explain it.

Now physicists are pointing to strange properties of hydrogen bonds as the solution to one of the oldest mysteries in physics - but others are claiming the so-called Mpemba effect doesn't even exist at all.

For a bit of background into the Mpemba effect , this phenomenon has been confounding physicists since Aristotle first noticed it more than 2,000 years ago.

After similar accounts from the likes of Francis Bacon and René Descartes , the possibility of hot water freezing faster than cold water finally gained widespread acceptance in the 1960s, thanks to a Tanzanian schoolboy who noticed the effect when making ice cream.

Erasto Mpemba and his schoolmates often made ice cream by boiling milk and mixing it with sugar, and letting it cool before placing it in the freezer.

One day, Mpemba grew impatient , and instead of letting his mix cool before placing it in the freezer, he put his still-boiling milk in anyway, and hoped for the best.

To everyone's surprise, his ice cream set quicker than his peers', and in 1969, Mpemba teamed up with a physics professor to publish a paper describing the apparent phenomenon.

But there's a big problem with the Mpemba effect. While it's been more or less accepted as fact, physicists can't agree on how exactly it works, because how can hot water hit freezing point faster than cold water, when cold water already has a massive head-start?

There's also the lingering problem of replication.

Attempts to replicate the Mpemba effect in a foolproof, consistent manner have failed, but there's enough inconsistent evidence out there to prevent it from being debunked altogether.

Back in 2012, the Royal Society of Chemistry ran a competition asking scientists to explain the phenomenon, and despite receiving some 22,000 papers from all over the world, none of the explanations were convincing enough on their own to draw widespread consensus.

As Signe Dean reported for us last year :

"The most commonly proposed hypothesis … is that hot water evaporates more quickly, losing mass and therefore needing to lose less heat in order to freeze. However, scientists have also demonstrated the Mpemba effect with closed containers where evaporation doesn't take place. Another theoretical speculation is that water develops convection currents and temperature gradients as it cools. A rapidly cooling glass of hot water will have greater temperature differences throughout, and lose heat more quickly from the surface, whereas a uniformly cool glass of water has less of a temperature difference, and there's less convection to accelerate the process. But this idea has not been entirely verified either."

So after centuries of experiments, we're still looking for answers.

Now researchers from the Southern Methodist University in Dallas and Nanjing University in China think they might have a solution - strange properties of bonds formed between hydrogen and oxygen atoms in water molecules could be the key to explaining the elusive Mpemba effect.

Simulations of water molecule clusters revealed that the strength of hydrogen bonds (H-bonds) in a given water molecule depends on the arrangements of neighbouring water molecules.

"As water is heated, weaker bonds break, and groups of molecules form into fragments that can realign to form the crystalline structure of ice, serving as a starting point for the freezing process," Emily Conover reports for Science News.

"For cold water to rearrange in this way, weak hydrogen bonds first have to be broken."

In other words, we find a higher percentage of strong hydrogen bonds in warm water than cold, because the weaker ones were broken as the temperatures increased.

As the team concludes in their paper:

"The analysis … leads us to propose a molecular explanation for the Mpemba effect. In warm water, the weaker H-bonds with predominantly electrostatic contributions are broken, and smaller water clusters with … strong H-bonding arrangements exist that accelerate the nucleation process that leads to the hexagonal lattice of solid ice. Therefore, water freezes faster than cold water in which the transformation from a randomly-arranged water clusters costs time and energy."

But as with all the explanations that have come before this one, we're going to need to see more proof before we can know for sure that this - or a combination of factors - is truly at play in the Mpemba effect.

While some put the replication problem down to several factors coming together in different ways to achieve the phenomenon - including convection, evaporation, and supercooling - and the fact that freezing is a gradual, not instantaneous, process, others say the Mpemba effect is nothing more than an incredibly persistent myth.

Another recent paper by a team from Imperial College London monitored the time it took for hot and cold water samples to drop to freezing point (0 degrees Celsius).

"No matter what we did, we could not observe anything akin to the Mpemba effect," one of the researchers, Henry Burridge, told Science News.

So what's actually going on here? We'll have to wait and see which conclusion - if any - bears out with further research, but one thing's for sure when it comes to water - it's still surprising us , even after all these years.

The hydrogen bonds paper has been published in the Journal of Chemical Theory and Computation , and the debunking paper has been published in Scientific Reports .

Water Freezing Point - Including Saltwater Tests

Posted by Admin / in Matter Experiments

It is well-known that the freezing temperature of water is 0°C or 32°F. Is there any way to change the freezing temperature of water? By performing this simple 30 minute experiment you will find out. Freezing temperature of water is tested by mixing water with some different materials and then performing freezing tests.

Materials Needed

Clean tap water
Cold Outside Temperature or a Freezer
Thermometer (liquid) - Optional
Thermometer - (atmosphere) or smart phone

EXPERIMENT STEPS

Step 1: Fill 3 small containers with water. Each container must have about the same amount of water. Do not fill the containers too full because they will need to be moved. Place a thermometer in one of the water containers and take a reading of the plain water termperature. The three liquid containers will all have the same starting temperature.

Step 2: Make a table salt (sodium Chloride) and water solution. The maximum amount of salt that typical tap water can hold until saturation is about one part salt and three parts water. We will not use this much because it takes too long to stir in the salt to get it to completely solution. Instead, we are using small containers so we only used about 2 teaspoons. Mix in all of the salt until there are no more crystals at the bottom. It will take a few minutes.

Mix a solution of table salt and water

Step 3: Next make an epsom salt (magnesium sulfate) and water solution. Epsom salt is much easier to mix with water. Again, we only used a few teaspoons full of epsom salt with our small containers.

Mix a solution of epsom salt (magnesium sulfate) and water

Step 4: Place all three containers outside or in a freezer. The outside temperature must be lower than freezing for this experiment to work. Start a stopwatch timer to begin tracking the amount of time it takes for the water samples to freeze.

Set the timer to see how long it takes for each of the water solutions to freeze

Step 5: Measure and record the starting temperature of the air outside or in the freezer.

Measure the air temperature (or freezer temperature)

Step 6: Observe the mixtures and record the time when each of the water samples freeze. This is the time when the top of the sample freezes. It will take much longer for the entire sample to freeze. We will understand the results by only observing a freezing of the surface.

Observe the solutions and record how long it takes for the water, epsom saltwater and table saltwater to freeze

Step 7: Take a measurement of the air temperature at the end of the experiment to make sure it has not changed much.

SCIENCE LEARNED

What results were observed during your experiment? You probably saw that pure water froze first, followed closely by the epsom salt solution. Saltwater takes a little longer thant the other samples to freeze, but if it is cold enough, saltwater will freeze. In general, water freezes at 0°C (32°F) and ocean saltwater freezes at 28.4°F (-1.9°C), but there are some additional factors that effect the temperature and how long each of the samples take to freeze. Here are some factors that will change either the temperature or the amount of time the samples take to freeze (or both):

Starting Temperature of the Samples
The air temperature
Atmosphere - Elevation and Atmospheric Pressure
Amount of salt or epsom salt in each solution
Contaminants in the water
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Hot and Cold Water Density

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Experiment to show all the phases of the water cycle.

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Open access
Published: 24 November 2016

Questioning the Mpemba effect: hot water does not cool more quickly than cold

Henry C. Burridge 1 , 2 &
Paul F. Linden 1

Scientific Reports volume 6 , Article number: 37665 ( 2016 ) Cite this article

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Fluid dynamics
Thermodynamics

The Mpemba effect is the name given to the assertion that it is quicker to cool water to a given temperature when the initial temperature is higher. This assertion seems counter-intuitive and yet references to the effect go back at least to the writings of Aristotle. Indeed, at first thought one might consider the effect to breach fundamental thermodynamic laws, but we show that this is not the case. We go on to examine the available evidence for the Mpemba effect and carry out our own experiments by cooling water in carefully controlled conditions. We conclude, somewhat sadly, that there is no evidence to support meaningful observations of the Mpemba effect.

Increasing trends in regional heatwaves

Increasing heat and rainfall extremes now far outside the historical climate

Physical interpretation of entropy, Boltzmann constant, and temperature

Introduction.

The statement “hot water does not cool more quickly than cold” is vague and imprecise; hot water can be made to cool more quickly than cold by supplying more energy to the cooling of hot water, but it is under such a non-specific premise that the Mpemba effect has become an artefact in popular science. More precisely, we show that for two samples of water, identical except for a difference in initial temperature, cooled under the same conditions to a prescribed temperature (for example, the freezing temperature of water) the initially hotter sample will take longer to cool — contrary to the assertion of the Mpemba effect. Despite the non-specific nature of the effect, the Mpemba effect has been the subject of numerous articles in international broadsheet newspapers (e.g. refs 1 , 2 , 3 ) and was the focus of a competition organised in 2012 by the Royal Society of Chemistry (RSC) which received substantial publicity, for example a special report on the BBC’s Newsnight programme. As such the Mpemba effect cannot simply be disregarded. Moreover, both The Telegraph 2 and The Daily Mail 4 have reported that the scientific work of a group of chemists working in Singapore 5 provides a molecular mechanism to explain the effect. These findings, and those of ref. 6 , concern the molecular interactions and hydrogen bonding within liquid water. While the findings of these studies are of great interest in their own right, we note that small-scale molecular effects are parameterised within the thermal and fluid properties of water — properties which are known to a reasonable degree of accuracy and do indeed vary with temperature. Such findings therefore offer a route to explaining the Mpemba effect only if they result in a meaningful hysteresis in the thermal or fluid properties of water. A model exhibiting a hysteresis in the cooling of water is presented by ref. 5 which is compared to an observation of the Mpemba effect documented as part of a popular science competition organised by the RSC 7 — we include the experimental observations by ref. 7 within the data analysed in the present study. It is our aim to present an investigation of the history behind the Mpemba effect, examine the scientific evidence for it, consider the underlying physical mechanisms for the effect and determine whether the effect actually exists in any meaningful manner.

There is no clear universally accepted scientific definition of the ‘Mpemba effect’. Mpemba & Osborne 8 document the time for freezing to commence while others include the freezing process (for example see ref. 9 ). This lack of clarity is reflected by the level of discrepancies in the literature, which offers a number of different explanations. Broadly speaking, when two samples of water are cooled to the same temperature, in the same manner with the two samples being identical except for their initial temperature, and the initially hotter sample cools in less time, one can consider the Mpemba effect to have been observed. The temperature at which cooling times are compared has often been chosen to be 0 °C (or below) making careful measurements more difficult because of the phase change that occurs as water freezes.

Observations of hot water freezing in less time than cold water date back to classical science. Aristotle 10 noted that the ancient Greeks of Pontus exploited the effects when they encamped on the ice to fish, and similar observations have been repeated by Bacon 11 and Descartes 12 . More modern awareness of this apparent anomaly range from the accidental experiments of the Tanzanian school boy, Mpemba (after whom the phenomenon is popularly known 8 ), to the competition calling for explanations of the phenomenon by the RSC.

The Mpemba effect is an oft cited scientific anomaly and has been widely used in high-school and undergraduate physics projects 13 , 14 . The effect may appear anomalous since on first consideration one might regard the first law of thermodynamics to be breached. An interpretation of the first law is that the change in the internal energy of a closed system is equal to the amount of heat supplied (accounting for any work done on or by the system). Thus, in the absence of work, for a constant heat flux one naturally expects hot water to take longer to cool to freezing than cooler water. However, typically the cooling does not occur in environments which can be regarded as inducing a constant heat flux, instead most cooling occurs in (near) constant temperature environments. One example of this being the widespread domestic formation of ice-cubes within ice-trays, for which the ice-trays typically sit on a cold plate within a freezer and are cooled by the thermostatically controlled freezer which acts to maintain an approximately constant temperature. Hence, an ice-tray filled with warm water experiences a larger temperature difference and, therefore, a larger initial heat flux compared with an ice-tray filled with cooler water. Moreover, in the presence of an initially hot sample the freezer may remain on, and doing work, to drive the cooling for longer. This, however, by no means explains the Mpemba effect — the hot water must take some time to cool to the initial temperature of the cooler sample of water, after which all else being equal one would expect the further cooling of the warm sample to take the same time as the cooling of the colder sample. Hence the warm water, in total, would take longer to cool. Thus for the Mpemba effect to be observed there must be some difference in the chemistry of the samples or the physics of their cooling either initially or when at equivalent temperatures — understanding and examining the various mechanisms that might give rise to such differences remains the focus of scientific debate.

The winning entry to the RSC competition, for example, cites four factors as possibly contributing to the Mpemba effect, namely: (a) evaporation, (b) dissolved gases, (c) mixing by convective currents, and (d) supercooling 7 . No doubt all four processes affect the cooling rate of water, albeit to differing extents, and crucially their effects may be strongly coupled. For example, in two volumes of water, only differing in initial temperature and then cooled in identical conditions, one would expect that different convective currents might develop. Therefore, for significantly different initial temperatures the characteristic times that a given water particle remains in contact with an imperfection in the container or impurity within the water (e.g. dissolved gases) would vary between the two samples and so the level of supercooling required to form ice crystals would vary also. Thus it can be reasoned that the observed variations in the extent to which supercooling occurs must arise, at least in part, due to differences in convective currents and the relative levels of dissolved gases (further affected if evaporation occurs). Hence all the factors which have been proposed to individually cause the Mpemba effect may alter the extent of supercooling required to cause water to freeze.

A reasonable start to analysing the problem is to consider the process in two stages; first, cooling the water to an average temperature of 0 °C (or enthalpy equivalent thereof), and second, freezing the water to form solid ice. In so doing any effects associated with the supercooling of water are entirely contained within the second stage. We restrict our definition of the Mpemba effect to the first stage of the process, i.e. the process of cooling a sample of warm water to 0 °C in less time than it takes to cool a sample of water, which is notionally identical except that it is initially at a lower temperature, to 0 °C.

Three widely cited historical references to Mpemba-like effects in water

The cooling and freezing of water has intrigued some great scientific minds. Aristotle, Sir Francis Bacon and René Descartes have all been credited with consideration of the Mpemba effect 15 and, although this list is by no means comprehensive, it is worth documenting the precise observations of these three renowned scientists.

In his treatise on earth sciences (therein “Meteorology”) Aristotle 10 , book I part 12 is concerned with the freezing of water and contains the following text: The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun. So the inhabitants of Pontus when they encamp on the ice to fish ( they cut a hole in the ice and then fish ) pour warm water round their reeds that it may freeze the quicker, for they use the ice like lead to fix the reeds.

The reference to ice as ‘like lead’ in connection to fishing potentially raises confusion since the use of lead to weight fishing lines is widespread in traditional fishing; ice being less dense than water clearly makes it unsuitable for weighting fishing lines. It is our interpretation of the description ‘like lead to fix the reeds’ that it refers to the stiffening of the reeds by the formation of ice so that the reeds can be plunged beneath the water, hence avoiding the need to weight the reeds so that they might sink. It would, therefore, seem that Aristotle and the peoples of ancient Greece believed that warming water did make it freeze faster.

The second book (section L in ref. 11 ) of Sir Francis Bacon’s “Aphorisms on the interpretation of nature or on the kingdom of man”, includes a lengthy discourse regarding “Mans works on natural bodies” including a discussion of heat and cold; within which, while concerned with matters of medicine, he states: We should also deal with the preparation of substances to receive cold: for example, slightly warm water will freeze more easily than water which is altogether cold, and so on.

No further discussion nor details are provided. Indeed, it is not clear whether any of Bacon’s experiments actually concerned the freezing of water 16 and hence the observations leading to, or the source of, his stated belief that warm water cools faster than cold is also unclear.

In his essay on Meteorology, near the end of his first discourse, René Descartes 12 describes some experiments in which both hot and cold water are frozen within a beaker and states: we can also see by experiment that water which has been kept hot for a long time freezes faster than any other sort, because those of its parts which can least cease to bend evaporate while it is being heated.

The ‘bending’ which he describes, refers to his hypothesis for the motion of particles and although he credits evaporation for hot water freezing faster, his description of the experimental beaker indicates it has a long thin neck (which aided his observations of the expansion and contraction of water as it was heated and cooled) but would have restricted the area of the free-surface and hence evaporation. It is, therefore, unlikely that evaporation was the dominant physical effect leading to Descartes’ observation. However, like Aristotle and Bacon, Descartes does seem to document observations or convictions that can be fairly described as indicating that they would have supported assertions that the ‘Mpemba effect’ is genuine.

More recent scientific investigations of the Mpemba effect

The, now popular, adoption of the name ‘Mpemba effect’ is owed to the lack of freezer space at a Tanzanian school. While making ice-cream one pupil placed his mixture of milk and sugar in the freezer without first boiling it; another pupil, Mpemba, worried that he would not find space in the freezer and put his boiling mixture straight into the freezer without first allowing it to cool. Both pupils returned an hour and a half later to find Mpemba’s mixture had frozen while the other had not 8 . Mpemba did not brush this curious observation aside, instead he asked friends (some of whom made a living selling ice-cream and apparently exploited the time saving effects of this anomalous behaviour) and teachers to explain his observations but to no avail. Mpemba eventually asked a visiting lecturer from the University of Dar es Salaam to explain his observations. The open-minded Dr Osborne was intrigued by Mpemba’s observation and later began investigating the effect with his students, ultimately publishing a scientific paper with Mpemba on the observed effect 8 . The ‘Mpemba effect’ also appears to be widely accepted in the Northern Americas 17 . In the same month that Mpemba & Osborne 8 published their findings a chemist working in Canada 18 published an article on the very same subject. In his article, Kell describes centuries-old Canadian ‘folklore’ of wooden pails being left out to freeze, and the pails containing the hot water freezing fastest.

Certain subsequent studies report being unable to observe the effect, for example, Ahtee 19 who examined the fraction of ice formed and Hsu 9 who considered the time taken for the samples to form solid ice. However, other studies report being able to reproduce the effect, typically, using domestic style ice formation. Numerous differences exist between the experimental conditions of these various studies. These variations include: altering the nature of the cooling supplied, e.g. insulating the base 8 , 20 , submerging samples in cooling baths (for example 21 , 22 ) and radiative cooling 23 ; degassing or deionising the samples (for example see refs 14 and 24 ); the addition of dissolved gases 25 and controlling or monitoring evaporation from the sample (see ref. 23 ). Despite this wealth of experimental data, detailed analysis is typically lacking; for example, almost all studies present the absolute sample temperature rather than the sample temperature relative to the cooling environment and typically no consideration is given to the volume (mass) of water being cooled nor the geometry of the cooling vessel. A notable exception is the study of Maciejewski 17 who analysed his data in terms of nondimensional parameters, the Grashof ( Gr ), Prandtl ( Pr ) and Rayleigh ( Ra ) numbers, concluding that the key parameter is GrPr 3 and that the Mpemba effect may be driven by convection.

A number of studies have proposed physical models for the freezing of water in connection with the Mpemba effect. Katz 26 developed a freezing front model based on a ‘Stefan problem’ with a moving boundary condition which is unable to predict the effect, while the models of Kell 18 , Vynnycky and co-workers 27 , 28 consider the effects of evaporative cooling, suggesting that evaporation alone is sufficient to observe the Mpemba effect. Vynnycky and co-workers include an experimental observation of the Mpemba effect based on temperature measurements near the water surface. However, they also note that different cooling curves were obtained for samples with identical initial temperatures and that they had difficulty in repeatedly reproducing any observations of the Mpemba effect, citing uncontrollable “micro-physical processes” as the cause of such variations. Vynnycky and Kimura 29 present results from a detailed experimental examination, and a theoretical model, for the cooling of water in the context of the Mpemba effect. Their experimental results reporting the time at which solidification begins, show no evidence to support the Mpemba effect. However, their data reporting results for the time at which the layer of ice had grown to a particular thickness (therein 25 mm) “hinted at a freezing time inversion, and hence the Mpemba effect”. They attribute such effects to supercooling and they go on to suggest that their experimental data indicates that supercooling is more likely to occur with lower initial temperatures — a suggestion that would promote Mpemba-like effects in water.

Recent advances in the understanding of the bonding of water molecules have been suggested as a potential route to explaining the Mpemba effect which requires a hysteresis within the molecular interactions dependent on the initial temperature. A model accounting for the relaxation dynamics of the hydrogen bonds in liquid water has been proposed 5 in which a ‘cell’ of water is considered to comprise of the ‘bulk’ (90% of its volume) and the ‘skin’ (10% of its volume). For selected values of the ratio of thermal diffusivity between the skin and bulk (approximately a 50% difference in diffusivity), termed ‘skin supersolidity’, the model exhibits cooling akin to the Mpemba effect. The results of the model are qualitatively compared to an experimental observation of the Mpemba effect documented as part of the 2012 competition organised by the RSC 7 . Through an experimental investigation of the behaviour during cooling of tetrahydrofuran hydrate (a clathrate hydrate) 30 , it is reported that the “formation kinetics of [tetrahydrofuran] hydrate therefore might depend on its initial temperature” and suggest this is Mpemba-like behaviour. The advances in the understanding of the molecular interactions within water, and clathrate hydrates, may be of some significance in understanding the Mpemba effect. However, for this to be the case it would require that the bulk thermal and/or fluid properties of water are significantly influenced by the initial, i.e. the history of the, temperature of the water — it is not yet clear that this is the case. Should it be shown to be necessary it would, indeed, be a result of real significance; for example, standard reference tables for the properties of water would need to be updated to account for not only the current temperature but also the route to the said temperature.

Analysis of our ‘Mpemba style’ data and the data from other studies

Figure 1 plots the variation in the time t 0 , to cool samples to 0 °C, with the initial temperature from a variety of studies including our ‘Mpemba-type’ experiments. We have attempted to represent a broad selection of published experimental data regarding the Mpemba effect. We note that the data from the careful experiments of 29 reporting the time to cool to 0 °C (their Fig. 5), which exhibited no evidence of the Mpemba effect, could not be included due to difficulties in accurately obtaining data from their printed figure. Their results for the time to for the ice layer to grow to a depth of 25 mm cannot be fairly included in our analysis, since we exclude the freezing process; however, we discuss these results when drawing our conclusions. The mass of water, the geometry of its container and indeed the nature of the cooling varied widely between the different datasets and this variation is reflected in the spread of the data. From Fig. 1 it is difficult to draw any conclusions from the data, except that broadly speaking the cooling time increases with initial temperature. The only exception, which reports data (across a broad range of temperatures) that exhibit a decreasing trend in cooling time with increasing initial temperature, is that of Mpemba & Osborne 8 .

The time t 0 to cool to 0 °C, plotted against the initial temperature, T i for the ‘Mpemba-type’ experiments.

The data show a broad trend of increasing cooling time with increasing initial temperature, with the notable exception being the data of Mpemba & Osborne 8 .

Figure 2 shows the variation in the cooling time t 0 , scaled by the convective time scale, with the temperature averaged Rayleigh number from the various studies detailed in Fig. 1 (for details of the convective time scale and the temperature averaged Rayleigh number see the Methods section). Some of the studies included in Fig. 2 did not explicitly provide all the details required to scale the data, and in such cases we made reasonable estimates based on the information provided (details of which are also provided in our Methods section). The experimental conditions vary widely between the eight independent studies from which data are included within the figure. There is no obvious systematic bias for the cooling times based on the geometry of the cooling vessel, despite the aspect ratio of width to height, D/H , varying by a factor of fifteen and the depth of water being cooled varying by a factor of eight within the data — indicating that the geometry may be appropriately reflected by the length scales within the temperature averaged Rayleigh number Ra T . There is, however, an obvious bias in the cooling times based on the nature of the cooling and we broadly split the data into two datasets. The first set we describe as ‘convectively dominated’ data (marked by the solid symbols in Fig. 2 ) which broadly consists of samples where the base was insulated or cooling from below was inhibited in some manner (see the legend in Fig. 2 for details). In such cases there is no direct heat transfer between the freezer base (or cooling plate) and the sample of water is predominately cooled through the sides or top of the sample and unstable density stratifications are promoted. In such cases, the heat transfer is inhibited by the addition of insulation and hence the cooling times are typically increased, despite the increased role of convection. The second dataset we describe as ‘stably cooled’ (marked by the blue hollow symbols in Fig. 2 ) which consists of data for which the heat flux through the base of the sample is expected to have been significant (e.g. where the sample was placed directly on a cooling plate), and the cooling is expect to have promoted stably stratified sample of water (at least above 4 °C).

The data from Fig. 1 scaled to show variation of t 0 / t conv (the time to cool to 0 °C in units of the convective time scale) with Rayleigh number, Ra T = t cond / t conv .

The ‘stably cooled’ data are marked by blue open symbols and ‘convectively dominated’ data are marked by solid symbols. The black solid line marks the scaling for high-Rayleigh number convective cooling, (5).

We note that we scaled the data in Fig. 1 using a number of alternative definitions for the Rayleigh number, for example taking all parameters at the initial conditions or combining individually temperature-averaged parameters to form the Rayleigh number, cf. Equation (7) . The different definitions of the Rayleigh number that we tested all resulted in the various datasets exhibiting trends well approximated by (1).

Considerations of high Rayleigh number convection, in which the assumption that the heat flux is independent of the depth of the fluid, imply that

(for example, see ref. 31 ) where Nu = Q /( κ Δ T/H ) is the Nusselt number, with κ the thermal diffusivity of the fluid, Q being proportional to the flux of heat and Δ T being a characteristic temperature difference between the fluid and the cooled surface. The time rate of change of temperature for a given sample is then proportional to the heat flux, i.e. Q , and given that Ra ∼ β Δ TgH 3 /( κv ), from equation (2) we can write

where β and v are the coefficient of thermal expansion and the kinematic viscosity of the fluid, and A is the cooled surface area of the fluid. Hence

We note that crucially, in deriving (5) we assumed that the convection exhibited behaviour associated with that of asymptotically high Rayleigh number convection. The data investigating the Mpemba effect, plotted in Fig. 2 (obtained at initial Rayleigh numbers up to O (10 10 )), fits well with the trend predicted by (5) suggesting that the experimental data can be regarded as high Rayleigh number. As such, if the data plotted in Fig. 2 are shown not to exhibit the Mpemba effect, as indeed we go on to argue, then one must expect that data obtained at higher Rayleigh numbers would also not exhibit the Mpemba effect.

Analysis of the occurrence of the Mpemba effect

The above analysis, although informative as to the physics of cooling water, does not explicitly address when the Mpemba effect has been observed. In order to establish a single observation of the Mpemba effect, one must compare two experiments which are identical in every manner except for a difference in the initial temperatures of the water samples. One can then state that the Mpemba effect may be regarded to have been observed if the sample of water initially at the higher temperature reaches the desired cooling temperature first. To illustrate when the Mpemba effect may be reported to have been observed we consider the average rate at which heat is transferred Q from the initially hot Q H and initially cold Q C samples, where for a given sample Q = Δ E/t 0 = ( E i − E 0 )/ t 0 ∝ Δ T/t 0 = ( T i − T 0 )/ t 0 with E i and E 0 denoting the initial and final enthalpy of the samples, respectively.

The Mpemba effect can be reported as having been observed when the inequality Q H / Q C > Δ E H /Δ E C is satisfied, since Q H / Q C > Δ E H /Δ E C ⇒ t c > t H , where t c and t H denote the cooling time of the cold and hot samples, respectively. Figure 3(a) plots the variation in the ratio Q H / Q C with Δ E H /Δ E C (or equivalently Δ T H /Δ T C ) for the various pairs of data shown in Fig. 1 and the results of our experiments of the ‘second-type’ (see the Methods section). Figure 3(b) highlights the results of our experiments of the ‘second-type’, with an allowance for spatial variation in the temperature measurements. The relationship Q H / Q C = Δ E H /Δ E C is marked by solid black lines within Fig. 3 . Hence, any data lying above this line may be reasonably reported as an observation of the Mpemba effect.

The variation in the ratio of mean heat transfer rates with initial temperature (or equivalently enthalpy) for pairs of otherwise identical samples of hot and cold water.

We have made efforts to contact both of the authors, Mr Erasto B. Mpemba and Dr Denis Osborne. In our attempts to contact Dr Osborne we were saddened to be informed of his death in September 2014. It seems that throughout his life, Dr Osborne continued to make extremely positive contributions to both science and politics. We have so far failed in our attempt to contact Mr Mpemba although we understand he was the principal game officer in the Tanzanian Ministry of Natural Resources and Tourism, Wildlife Division (he is now retired). We have been unable to deduce the source of any systematic error in the experimental procedure or experimental set-up of Mpemba & Osborne 8 that could feasibly have led to such extreme data being recorded.

Discussion and Conclusions

We conclude that despite our best efforts, we were not able to make observations of any physical effects which could reasonably be described as the Mpemba effect. Moreover, we have shown that all data (with the only exceptions coming from a single study) reporting to be observations of the Mpemba effect within existing studies fall just above the Mpemba effect line, i.e. the difference in the cooling times between the hot and cold samples is marginal. We have shown ( Fig. 3 ) that much of the data reporting to be observations of the Mpemba effect were from studies not reporting the height at which temperatures were measured 7 , 14 , 20 , 21 , 22 , 23 and that the conclusions drawn from these data could have been altered by simply recording temperatures without precisely monitoring the height. Indeed, all the data which lie just above the Mpemba effect line in Fig. 3 (including data for which the temperautre measurement height was carefully monitored and reported 17 , 24 , 28 ) are, by the very nature of experiments, subject to some degree of uncertainty which may ultimately affect whether the observed results are recorded as an apparent observation of the Mpemba effect or not. To be precise regarding our meaning by this statement, let us now consider the reported observations of the Mpemba effect from, arguably, the two most careful sets of experiments within the literature 28 , 29 . The study 28 does present data for one observation of the Mpemba effect but also reports obtaining “different cooling curves even if the initial temperatures were identical”, furthermore they state “[c]areful and precise experiments to probe the Mpemba effect can be tried by cooling hot and cool water in two similar containers simultaneously, but it is extremely difficult to obtain scientifically meaningful and reproducible results”. The study 29 shows a potential observation of the Mpemba effect (in the times for the ice layer to grow to a thickness of 25 mm, their figure 19) for a single pair of initial temperatures (from a possible 21 initial temperature pairings), namely the pair of initial temperatures 10 °C and 15 °C. From data recorded at a fixed height (for example, 5 mm) the samples cooling from 15 °C exhibit a mean cooling time of approximately 95 minutes while those cooling from 10 °C the mean is approximately 105 minutes — hence in taking only the mean of the data for this particular temperature pairing one could describe the Mpemba effect as having been observed. However, the variation in notionally identical experiments is significant. At the same recording height, for samples cooling from 15 °C the recorded time spans the range 95–105 minutes while for samples cooling from 10 °C the recorded time spans the range 100–110 minutes. As such, the variation in notionally identical experiments is at least large enough to render any conclusion that the Mpemba effect has been observed in the mean data as highly questionable, and so this cannot be regarded as a meaningful observation of the effect.

The only exception to our above statements, the single study in which some data is reported that shows dramatically warmer samples cooling in substantially less time (i.e. data points that are far above the line Q H / Qc = Δ T H /Δ Tc in Fig. 3 ) is the data reported by Mpemba & Osborne 8 . If these data could be reproduced in a repeatable fashion and the underlying mechanism understood then it would be of real significance to a multitude of applications relying on the transfer of heat. For example ref. 8 , report cooling a sample from 90 °C to freezing point in 30 minutes while a sample at 20 °C took 100 minutes to cool to freezing point, i.e. the average heat transfer rate during cooling was observed to increase by a factor of 15 by simply increasing the initial temperature of the sample. With the use of modern heat-exchangers such a result would have profound implications for the efficiency of any number of common industrial processes. However, over the subsequent 47 years, numerous studies have attempted to demonstrate the ‘effect’ on a scale comparable to that reported by Mpemba & Osborne. Despite these efforts, including our own, none have succeeded. We must therefore assert that this particular dataset may be fundamentally flawed and thus, unless it can be shown to be reproducible and repeatable, this dataset must be regarded as erroneous.

We must highlight that our primary focus has been to examine the cooling of water to the freezing point (observed under standard atmospheric conditions), i.e. an enthalpy equivalent of 0 °C. In so doing we have been able to show that much of the published experimental data exhibit a scaling behaviour associated with asymptotically high Rayleigh number convection. Thus one cannot expect to observe samples of hot water cooling to 0 °C faster than colder samples by carrying out experiments at higher Rayleigh numbers. Under our definition of the Mpemba effect, akin to the definition in the ‘original’ paper by Mpemba & Osborne 8 (in which they documented “the time for water to start freezing”) we are forced to conclude that the ‘Mpemba effect’ is not a genuine physical effect and is a scientific fallacy.

If one extends the definition of the Mpemba effect to include the freezing process then one can examine the experimental evidence presented by a number of scientific studies which have sought to include the effect of freezing, e.g. refs 9 , 21 , 22 , 28 and 29 . The freezing of water to ice is a thermodynamically intensive process. For example, the energy required to change the phase of a given mass of water at 0 °C, into ice at 0 °C is approximately equal to the energy required to cool the same mass of water from 80 °C to 0 °C in the liquid state. Intuition, therefore, guides one to expect the time to completely freeze a sample of water could depend only weakly on the initial water temperature. Moreover, freezing is initiated by a nucleation process and as such it is susceptible to variations at the smallest physical scales, e.g. imperfections in the surface of containers or impurities within the water samples — the physical scales of which are extremely difficult to control in even the most precise experiments. Such intuition is entirely born out in the experimental evidence, with no single study able to report repeatable observations of the Mpemba effect when the freezing process is included 9 , 21 , 22 , 28 , 29 . Experimental observations of a particular example of warm water cooling and freezing in less time than a particular example of initially cooler water have been made — what is yet to be reported is any experimental evidence that samples of water can be consistently cooled and frozen in less time (the time being less by a repeatable and statistically significant amount) by simply initiating the cooling from a higher temperature. As such we can conclude that even with the freezing process included within the definition of the Mpemba effect, the Mpemba effect is not observable in any meaningful way.

We are not gladdened by such a conclusion, indeed quite the opposite. The Mpemba effect has proved to be a wonderful puzzle with which to engage and interest people of all ages and backgrounds in the pursuit of scientific understanding. However, the role of scientists is to objectively examine facts and further knowledge by reporting the conclusions, and as such we feel compelled to disseminate our findings. Finally, we want to give hope to the educators who may have previously relied on the Mpemba effect as a useful tool with which to inspire their students. There are numerous genuine artefacts of science which can continue to provide such inspiration. For example, try filling two identical glasses, one with fresh water and one with salty water (both of equal temperature), place a few cubes of ice in each and observe which melts first — many students will be surprised by the result, finding it counter to their experience and intuition. Equally one could try placing a thin sheet of card on top of a glass of water, turn the glass upside down and then remove your hand from the card — watch as the atmospheric air pressure allows the water to be held in the glass — repeat this, replacing the card by just a rigid gauze with holes of up to a few millimetres and still the water will be held within the glass 32 . We hope that these examples serve to act as catalysts for those seeking other examples of genuine science and that these help to inspire scientific interest within future generations.

Dimensional considerations

The physics of cooling water within a regular three dimensional vessel, all surfaces of which are held at a uniform temperature, can be described in the terms of a thermal buoyancy potential g ′, three length scales L x , L y , L Z , and the kinematic viscosity v and thermal diffusivity κ for water. It is common in both the practical cooling of water (e.g. the domestic formation of ice-cubes) and the experiments reported in the literature that the two horizontal length scales are of similar magnitude, and herein we assume L x ≈ L y = D (where D is a characteristic width or diameter of the cooling vessel) and denote the vertical length scale L z = H , where H is the depth of water being cooled. As such, the problem can be described by three non-dimensional variables and it is appropriate to select the Grashof number, G r = g ′ H 3 / v 2 (cf. the Reynolds number for inertial flows); Prandtl number, P r = v/κ ; and the aspect ratio D/H . These three non-dimensional parameters can all be combined within a Rayleigh number for the cooling.

Within a fluid heat may be transported either by advection (convection) or thermal diffusion (conduction); the Rayleigh number can be interpreted as a ratio of the time scales for conduction, t cond , and convection, t conv . Suitable length scales for the Rayleigh number can be identified by consideration of these time scales. Conduction, or thermal diffusion, acts to distribute heat in all directions and so t cond ∝ L 2 / κ ∝ min( H 2 , D 2 )/ κ , as conduction will predominantly occur over the shortest length scale of the cooling vessel (since this must be the direction of the strongest temperature gradients). Convection is generated when thermal effects give rise to gravitationally unstable distributions of density and so it is appropriate to consider only the vertical length scale H in the convective time scale. Hence an appropriate Rayleigh number for the cooling is Ra = g ′ H 3 min(1, D/H ) 2 /( κv ) = G r × P r × min(1, D/H ) 2 .

A suitable representation for the thermal buoyancy potential g ′ is worthy of consideration. It is natural to define the buoyancy as the gravitational acceleration scaled by the normalised density difference between two relevant fluids. One might argue that it is appropriate to take the difference between the density of water at the initial temperature and at some other temperature, e.g. 0 °C (see the definition of the Grashof number in ref. 17 ); however, so doing highlights two particular issues. First, the buoyancy can only ever be an indicative scale of the driving cooling potential since one would not expect that, within a given sample, water still at the initial temperature would directly interact with water at 0 °C. Second, such a definition does not account for the differences in the cooling times that one would expect if the same sample were placed in a cooling environment held at 0 °C or in an environment at a far lower temperature, e.g. −50 °C. Consequently, it is more appropriate to accept g ′ as an indicative scale for the driving cooling potential and, as such, define the thermal buoyancy potential by

where T f is the temperature of the cooling environment, T is the characteristic instantaneous temperature of the water being cooled, and β = β(T ) is the coefficient of thermal expansion for water at the temperature T . Given the density maximum of water at about 4 °C, over the relevant temperature range, 0 °C ≤ T ≤ 100 °C, the coefficient of thermal expansion and hence the buoyancy will change sign if a given sample cools below 4 °C. Furthermore, both the kinematic viscosity and thermal diffusivity of water vary with temperature, in the case of the viscosity by factor of six over the temperature range of cooling 33 . In order to account for varying physical properties of water as it cools we consider a temperature averaged Rayleigh number, which incorporates values of β(T ) calculated from the variations in the density of water with temperature from 34 , values of κ(T ) calculated from the density 34 , thermal conductivity 35 and specific heat capacity 36 of water, and v(T ) taken from 33 .

We define the temperature averaged Rayleigh number Ra T , for water cooling from an initial temperature T i to a final temperature T 0 , as

the time scale for conduction as

and maintaining the Rayleigh number as the ratio of times scales for conduction and convection gives the time scale for convection as

Experiments

We carried out two types of experiments: the first was designed to mimic the experiments of Mpemba & Osborne 8 , and the second was designed to avoid any formation of ice, and thereby avoid issues associated with phase change, by keeping the cooling plate at 0.3 °C. For both sets of experiments temperatures were digitally recorded and stored using up to eight thermocouples, with a data-logger connected to a computer running LabVIEW. The thermocouples were calibrated using a refrigerated circulator providing temperatures accurate to within 0.01 °C.

In the first set of experiments, our ‘Mpemba style’ experiments, three samples of water each of mass 400 g (measured to an accuracy of within 0.1%) were placed within glass beakers of approximate diameter D = 9.0 cm; filling the beaker with a water depth of approximately H = 6.3 cm. All the samples of water were boiled, to remove some of the dissolved gases, and then left to cool for varying amounts of time so that the three samples were at different initial temperatures T i = {21.8, 57.3, 84.7} °C, respectively. The samples were then placed on a 5 cm thick sheet of expanded polystyrene sitting inside a standard domestic chest-freezer. All three samples were placed inside the freezer at the same time in order to ensure that the samples were exposed to the same cooling from the thermostatically controlled chest-freezer. The thermostat on the freezer was set to −18 °C. On placing the samples into the freezer the ambient air temperature within was observed to rise but, after approximately 15 minutes, the freezer temperature had cooled back down to −18 °C. Subsequently, the freezer temperature gradually increased (due to the imperfect insulation of the freezer) until it reached approximately −15 °C at which point the thermostat activated the freezer refrigeration unit and the freezer temperature was cooled once again to −18 °C. This periodic cooling and warming of the freezer, in the temperature range −18 °C ≤ T f ≤ −15 °C, continued throughout the experiment. Prior to being placed inside the freezer a thermocouple was located and carefully fixed centrally within each sample of water. The temperature of the thermocouples within each water samples were recorded at 1 second intervals throughout the experiment and the time taken for the temperature of each sample to first fall to 0 °C denoted as t 0 = {6397, 9504, 10812}s, respectively.

In the second set of experiments we filled a perspex tank, of horizontal cross-section 20 cm × 20 cm, with fresh water to a depth of 10 cm. Expanded polystyrene sheets (5 cm thick) were attached to the base and the four sides of the tank to act as insulation. The water was then cooled by carefully suspending a brass cooling plate such that the cooling plate was in direct contact with the upper surface of the water. The cooling plate had been carefully machined so that it contained a continuous channel, entirely housed within the plate except for openings at two of its corners which were connected to insulated pipes. The channel meandered within the plate so that by passing ethylene glycol solutions (continuously cooled by a Thermo Haake refrigerated circulator, Phoenix-line, model PII-C41P) through the channel the entire plate was held at an approximately uniform and constant temperature. The refrigerated circulator included a reservoir containing 15 000 cm 3 of ethylene glycol solution cooled by a refrigeration cycle of power of approximately 1 kW. The circulator passed the solution through insulated pipes and around the machined channel (of cross-section less than 1 cm 2 ) at approximately 400 cm 3 /s.

In these experiments of ‘the second type’, to avoid the formation of ice the cooling plate was held at a temperature of 0.3 °C. Prior to our experiments, seven T-type thermocouples (Omega, HSTC-TT-TI-24 S-5 M) were carefully positioned and clamped in place at specified heights within the tank. The thermocouples had been calibrated, to an accuracy of 0.01 °C using the refrigerated circulator, over a temperature range of −20 °C and 100 °C. Throughout each experiment, temperatures were recorded from each of the thermocouples at a frequency of 1 Hz using a National Instruments 9213 measurement system and digitally stored in csv files for later analysis within Matlab. The characteristic temperature of the water at any instant was determined by spatially averaging the temperatures recorded at the thermocouples positioned at the carefully measured heights. Experiments were run until the water within the tank reached a steady temperature which took approximately one day to occur. Since in these experiments the temperature of the samples were intended to remain above freezing point, we defined the cooling time based on the time taken to cool to 4 °C (this temperature being selected to maximise the role of convection), the times to cool to this temperature were in the range 12–17 hrs. It is important to note that since our experiments of ‘the second type’ were deliberately never cooled to 0 °C data from these experiments cannot be included in Figs 1 or 2 , and is only included in Fig. 3 in which only the relative cooling times of hot and cold samples are compared. As such, our results are not affected by the choice (in our experiments of the second-type) to measure the time to cool to 4 °C — identical trends in our data are observed with any reasonable variation in this choice of the target temperature. During these experiments the initial temperature T i of the fresh water was systematically varied between experiments in the range 18 °C ≤ T i ≤ 75 °C.

Assumptions made in sourcing the data of other studies

In order to be able to scale the data published in other studies it was necessary to have sufficient information in order to be able to calculate the Rayleigh number, i.e. T i , T f , H and D , see equation (7) . For certain studies 9 , 17 , 20 , 28 the required information was explicitly provided. Table 1 provides details of information not explicitly provided by the remaining studies for which we report data. In each case, details of our assumptions and the data on which these assumptions was based is provided. It should be noted that the sensitivity of our results to the assumptions detailed in the table is by no means dramatic. Indeed, any reasonable variations to our assumptions does not alter any of our findings.

Additional Information

How to cite this article : Burridge, H. C. and Linden, P. F. Questioning the Mpemba effect: hot water does not cool more quickly than cold. Sci. Rep. 6 , 37665; doi: 10.1038/srep37665 (2016).

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Acknowledgements

HCB gratefully acknowledges Dr Nick Daish for his encouragement to complete and report this study. In addition, the authors would like to thank Prof. Grae Worster for his insight and advice, and Prof. Graham Hughes for his comments on the high Rayleigh number scaling. The authors further acknowledge the skills and expertise provided by the technical staff at the G. K. Batchelor laboratory. This work was supported, in part, by the Leverhulme Trust Research Programme Grant RP2013-SL-008, and by the Royal Society.

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H.C.B. carried out the experiments, wrote the main manuscript text and prepared the Figures. P.F.L. reviewed and edited the manuscript.

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The hot water will evaporate much faster when it is very shallow and spread out. It has less total mass to retain heat and a lot more surface area to cool it and evaporate it. The hot water will evaporate reducing mass and will then freeze faster than the cold water. The relative humidity in the air will also be a variable to consider.
What Freezes first… Hot or Cold Water?
Of course, if the hot water had started at 99.9° C, and the cold water at 0.01° C, then clearly under those circumstances, the initially cooler water would have frozen first. However, under some conditions the initially warmer water will freeze first — if that happens, you have seen the Mpemba effect which describes the phenomenon.
Does hot or cold water freeze first?
Therefore the cold water will be overtaken on the freezing process, possibly by the hot water. The obvious thing would be that the cold water would freeze first, because its got less energy to lose but I have heard that the hot water would freeze sooner but I've not looked in to it in detail. The convection currents helping the water water ...
The Claim Hot Water Freezes Faster Than Cold Water Is ...
Despite sounding like the most egregious contradiction in physics, hot water appears to freeze faster than cold water under certain circumstances. The phenomenon can be traced back to Aristotle himself, but after centuries of experiments demonstrating this phenomenon, no one's been able to explain it.
Water Freezing Temperature Experiment
It is well-known that the freezing temperature of water is 0°C or 32°F. Is there any way to change the freezing temperature of water? By performing this simple 30 minute experiment you will find out. Freezing temperature of water is tested by mixing water with some different materials and then performing freezing tests.
Questioning the Mpemba effect: hot water does not cool more quickly
Introduction. The statement "hot water does not cool more quickly than cold" is vague and imprecise; hot water can be made to cool more quickly than cold by supplying more energy to the ...

The Physics of Why Hot Water Sometimes Freezes Faster Than Cold Water

The Mpemba Effect: Does Hot Water Really Freeze Faster Than Cold Water?

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It's True: Hot Water Really Can Freeze Faster Than Cold Water

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Does hot water freeze faster than cold water?

4 Answers 4

This was, actually, my 6 th 5 th grade Science Fair experiment. :)

I found the data!

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