The Inverted Freeze
Erasto Mpemba, Denis Osborne, and Non-Equilibrium Thermal Convection
Under Newton's classical law of cooling, the rate at which a body loses heat is strictly proportional to the temperature difference between the body and its surroundings. If beaker A begins with pure water at $90^\circ\text{C}$ and an identical beaker B begins with an equal mass of water at $35^\circ\text{C}$ inside the same freezer, equilibrium thermodynamics dictates that beaker A must first spend time cooling from $90^\circ\text{C}$ down to $35^\circ\text{C}$. From that moment onward, it would seem bound to follow the exact same cooling curve as beaker B. Under that single-variable assumption, it is mathematically impossible for the hotter liquid to freeze first.
Although Aristotle, Francis Bacon, and René Descartes had all recorded observations that previously heated water froze faster than cold water, twentieth-century physics textbooks dismissed those claims as folklore born of faulty thermometers. In 1963, at Magamba Secondary School in Tanganyika, student Erasto Mpemba encountered the anomaly firsthand during an afternoon cooking class. The students were making ice cream by boiling milk with sugar, allowing the mixture to cool to room temperature, and pouring it into ice trays inside a crowded refrigerator. Fearing he would lose the last empty tray, Mpemba poured his boiling-hot milk mixture directly into the freezer beside a friend's tray that had already cooled. When they opened the freezer ninety minutes later, Mpemba's initially boiling mixture was frozen solid. His classmate's pre-cooled mixture remained a thick liquid.
When Mpemba asked his physics teacher how hot milk could overtake cold milk, the teacher replied that Mpemba was confused and mocked the claim before the class as Mpemba's physics. After transferring to Mkwawa High School in Iringa, Mpemba spoke with ice-cream vendors in Tanga who confirmed that they also boiled their mixtures to speed freezing. He then used the high school physics laboratory to test pure water in calibrated beakers. In 1968, when British physicist Denis Osborne from University College Dar es Salaam visited Mkwawa High School to lecture the students, Mpemba raised his hand and reported that water heated to $100^\circ\text{C}$ repeatedly froze before water starting at $35^\circ\text{C}$. Osborne promised to test the claim in his university laboratory, expecting his technician to disprove it that week. Instead, the Dar es Salaam trials confirmed that hot water consistently froze ahead of warm water across a wide band of starting temperatures.
The flaw in the classical textbook proof lay in assuming that a cooling beaker is characterized by a single uniform scalar temperature $T(t)$. When a $90^\circ\text{C}$ beaker cools until its average temperature reaches $35^\circ\text{C}$, it is not in the same physical state as a beaker that started at rest at $35^\circ\text{C}$. Because water has low thermal conductivity, cooling inside a quiescent $35^\circ\text{C}$ vessel is quickly choked by thermal stratification. As the outer walls cool toward $4^\circ\text{C}$ (where water reaches its maximum density) and $0^\circ\text{C}$, stagnant boundary layers insulate the warm core. Conversely, in the $90^\circ\text{C}$ beaker, the steep temperature differential between the hot core and the cold walls drives a high Rayleigh number. That gradient launches vigorous Rayleigh-Bénard buoyancy convection plumes that continuously sweep warm interior fluid to the top surface and walls. Rapid heat transfer continues long after the mean temperature drops past $35^\circ\text{C}$.
Three additional non-equilibrium effects reinforce that convective advantage. First, evaporation from the hot open surface carries away 2,260 kilojoules of latent heat per kilogram of vapor while reducing the remaining liquid mass that must be frozen. Second, boiling expels dissolved oxygen and carbon dioxide gases, altering surface nucleation sites and convective boundary drag. Third, in ordinary domestic freezers, a hot container melts the porous, air-filled frost layer coating the metal cooling shelf beneath it and refreezes that meltwater into a solid ice pad whose thermal conductivity is ten times higher than fluffy frost. Meanwhile, differences in dissolved solutes and convection alter how deeply the liquid supercools below $0^\circ\text{C}$ before dendritic ice crystals nucleate. In 1969, Erasto Mpemba and Denis Osborne published their joint experimental records in Physics Education, demonstrating how convective overturning, evaporative cooling, dissolved gas expulsion, and frost-layer thermal contact allow a hotter liquid to overtake a cooler one on the path to freezing.