1. Mpeba Effect

People usually think that when a glass of cold water and a glass of hot water are put into the refrigerator at the same time, the cold water freezes quickly. This is not the case. One day in 1963, in a middle school in Tanzania, located in tropical Africa, a group of students wanted to make some frozen food to cool down. A student named Erasto Mpeba added sugar to hot milk and put it in the refrigerator to make ice cream. He thought that if he waited for the hot milk to cool down and put it in the refrigerator, other students would fill up the refrigerator, so he put the hot milk in the refrigerator. Not long after, he opened the refrigerator and took a look. Surprisingly, his cup of ice cream had turned into a cup of delicious ice cream, while the ice cream made by other students with cold water had not yet frozen. His discovery did not attract the attention of his teachers and classmates. On the contrary, it made them laugh. Mpeba told Dr. Osborne, a professor of physics at the University of Dar es Salaam, about this special phenomenon. Osborne was a little surprised after listening to Mpeba's account, but he believed that what Mpeba told must be true. Osborne, who respected science, conducted another experiment, and the results were completely consistent with Mpeba's description. This definitely confirms that in low temperature environments, hot water freezes faster than cold water. Since then, many scientific magazines around the world have introduced this natural phenomenon and named it the "Mpemba Effect".

2. History of the Mpeba Effect

The fact that hot water freezes faster than cold water has been known for many centuries. The earliest mention and documentation of this phenomenon can be traced back to Aristotle in 300 BC, who wrote:

"Previously heated water helps it to Freeze. So when people wanted to cool hot water, they would first put it in the sun..."

But before the 20th century, this phenomenon was regarded only as folklore. It was not until 1969 that Mpemba proposed it again in the scientific community. Since then, many experiments have confirmed the existence of the Mpemba effect, but there is no single explanation.

Around 1461, physicist Giovanni Marliani said in a debate about how objects cooled that he had proven that hot water freezes faster than cold water. He said that he used four ounces of boiling water and four ounces of unheated water, placed in two small containers and placed outside the house in a cold winter, and found that the boiling water froze first. But he was unable to explain this phenomenon.

By the early seventeenth century, this phenomenon seemed to have become common knowledge. In 1620 Bacon wrote that "water, when slightly heated, freezes more readily than cold water." Shortly after, Descartes said, "Experience shows that water which has been kept for some time over a fire freezes more quickly than other waters."

Until 1969, 500 years after Marliani’s experiment, the story of a Tanzanian middle school student named Mpemba rediscovering this phenomenon was published in the magazine New Scientist. This story tells scientists and teachers not to ignore the observations of non-scientists and not to judge prematurely.

In 1963, Mpemba was making ice cream at school, mixing boiling milk and sugar. Originally, he should have waited for the milk to cool before putting it in the refrigerator. But due to lack of space in the refrigerator, he put it in without waiting for the milk to cool down. To his surprise, he found that his hot milk solidified into ice earlier than his classmates'. He asked his physics teacher why, but the teacher said he must have confused it with another student's ice cream because his observation was impossible.

Mpemba believed what his teacher said at the time. But later that year, he met a friend of his who made and sold ice cream in the town of Tanga. He told Mpemba that when he makes ice cream, he puts the hot liquids in the freezer to make them freeze faster. Mpemba discovered that other ice cream sellers in Tanga town had the same practical experience.

Later, Mpemba learned Newton's Law of Cooling, which describes how hot objects become cold (under certain simplified assumptions). Mpemba asked his teacher why hot milk froze before cold milk. The teacher also replied that Mpemba must be confused. As Mpemba continued to argue, the teacher said, "All I can say is that this is your Mpemba's physics, not physics in general." From then on, the teacher and other students used "That's Mpemba's physics." Mathematics" or "That's Mpemba's Physics" to criticize his mistakes. But later, when Mpemba tried experiments with hot and cold water in the school's biology laboratory, he discovered again: the hot water froze first.

Earlier, a physics professor, Dr. Osborne, visited the secondary school in Mpemba. Mpemba asked him this question. Dr Osborne said he could think of no explanation but would try the experiment later. When he returned to his laboratory, he asked a young technician to test Mpemba's experiment. The technician later reported that the hot water froze first, adding: "But we will continue to repeat this experiment until we get the correct result." However, the experiment report gave the same result. In 1969, Mpemba and Osborne reported their results.

In the same year, in one of the most common coincidences in science, Dr. Kell independently wrote an article about hot water freezing before cold water. Kell showed that if it was assumed that water was initially cooled by evaporation and maintained at a uniform temperature, then the hot water would lose enough mass to freeze first. Kell therefore showed that the phenomenon was real (at the time, it was a rumor in Canadian cities) and could be explained by evaporation. However, he was unaware of Osborne's experiments. Osborne measured the lost mass and found that evaporation was not enough to explain the phenomenon. Later experiments using sealed containers, which eliminated the effects of evaporation, still found that hot water froze first.

3. Various explanations for the Mpemba effect

What is the Mpemba effect? There are two cups of the same shape, containing the same volume of water. The only difference is the temperature of the water. Now cool two glasses of water in the same environment. Under certain conditions, water with a higher initial temperature will freeze first, but this is not the case in all cases. For example, hot water at 99.9℃ and cold water at 0.01℃, the cold water will freeze first. The Mpemba effect is not visible under any initial temperature, container shape, and cooling conditions.

Most people will think this seems impossible, and some will try to prove it is impossible. This proof is usually as follows: it takes 10 minutes for water at 30°C to cool down to freeze, and water at 70°C must first take a while to cool down to 30°C, and then spend another 10 minutes cooling down until it freezes. Because what cold water has to do, hot water must do too, so hot water freezes slowly. Is this proof wrong?

This proof is wrong in that it implicitly assumes that the freezing of water is only affected by the average temperature. But in fact, besides average temperature, other factors are also important. A cup of water with an initial uniform temperature of 70°C is cooled to an average temperature of 30°C. The water has changed and is different from the cup of water with an initial uniform temperature of 30°C. The former has less mass, dissolved gases and convection, causing uneven temperature distribution. These factors will change the environment inside the refrigerator and around the container. These four factors will be considered separately below.

1. Evaporation - In the process of hot water cooling to the initial temperature of cold water, the hot water will lose part of the water due to evaporation. Less mass makes water easier to cool and freeze. In this way, hot water may freeze earlier than cold water, but with less ice. If we assume that water only loses heat through evaporation, theoretical calculations can show that evaporation can explain the Mpemba effect. This explanation is credible and intuitive, and evaporation is indeed a very important factor. However, this is not the only mechanism. Evaporation cannot account for experiments done in a closed container, where no water vapor can escape. Many scientists claim that evaporation alone is not enough to explain their experiments.

2. Dissolved gases - Hot water can retain less dissolved gases than cold water. As it boils, a large amount of gases will escape from the water. Dissolved gases change the properties of water. Either make it easier to form convection (and therefore easier to cool), or reduce the amount of heat required to freeze a unit mass of water, or change the boiling point. There is some experimental support for this explanation, but no theoretical calculations.

3. Convection - Due to cooling, water will form convection and uneven temperature distribution. As the temperature rises, the density of water decreases, so the surface of the water is hotter than the bottom of the water—called a "hot top." If water loses heat primarily through the surface, then water in a "hot top" will lose heat faster than at a uniform temperature. When hot water cools to the initial temperature of cold water, it will have a hot top, so it will cool faster than water with the same average temperature but a uniform temperature. Although hot tops and related convection can be seen in experiments, it is still unknown whether convection can explain the Mpemba effect.

4. Surrounding things - the last difference between the two glasses of water has nothing to do with themselves, but to do with the environment around them. Water with a higher initial temperature may change the environment around it in complex ways, affecting the cooling process. For example, if the glass of water is placed on top of a layer of frost, the frost conducts heat poorly. Hot water may melt this layer of frost, creating a better cooling system for itself. Obviously, this explanation is not general enough, and many experiments do not place the container on the frost layer.

Finally, supercooling may be important in this effect. Supercooling is the phenomenon that water only freezes when it is below 0°C. One experiment found that hot water is less likely to be supercooled than cold water. This means that hot water will freeze first because it freezes at a higher temperature. But this doesn't fully explain the Mpemba effect, because we still need to explain why less hot water causes supercooling.

In many cases, hot water freezes before cold water, but this phenomenon is not observed in all experiments. And, while there are many explanations, there is still no one perfect explanation. So, the Mpeba effect remains a mystery.