The mystery began in a student refrigerator, cramped and bustling with the frozen aspirations of young minds. Erasto Mpemba, a student in Tanzania, was in a hurry. Skipping the usual cooling period, he placed his hot mixture of boiled milk and sugar directly into the freezer, aiming for a quick batch of ice cream. To his surprise, and unlike his classmates who patiently waited for their mixtures to cool, Mpemba’s hot concoction froze first. When he sought an explanation from his physics teacher, he was met with disbelief: “You were confused. That cannot happen.”
Years later, during a visit to Mpemba’s high school, Dr. Denis Osborne, a physics professor, encountered the persistent student. Mpemba posed the same intriguing question: “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’s curiosity led him to collaborate with Mpemba at the University College in Dar es Salaam. Working alongside a technician, they conducted experiments that seemed to support Mpemba’s observation, giving rise to what is now known as the Mpemba effect. However, Osborne himself acknowledged the crudeness of their initial tests, suggesting that more rigorous experimentation was needed to truly understand the phenomenon.
Magamba Secondary School auditorium in Tanzania, where Erasto Mpemba first observed the effect of hot water freezing faster than cold water, known as the Mpemba effect.
Mpemba’s initial observation of this peculiar effect occurred in the 1960s while he was a student at Magamba Secondary School in Tanzania. The school’s auditorium stands in 2009, a silent witness to the beginnings of a scientific puzzle.
imageBROKER / Alamy Stock Photo
Over the subsequent decades, scientists have proposed a multitude of theoretical explanations to unravel the Mpemba effect. Water, an anomalous substance, is less dense in its solid form than its liquid state and can exhibit solid and liquid phases simultaneously at the same temperature. One hypothesis suggests that heating water could disrupt the weak hydrogen bonds between water molecules, increasing molecular disorder. This increased disorder, paradoxically, might then require less energy to transition to a frozen state.
Another, more straightforward explanation points to evaporation. Hot water evaporates at a faster rate than cold water. This reduction in volume in the hotter sample could decrease the overall time needed for it to freeze completely. Furthermore, cold water is known to contain a greater amount of dissolved gases, and these dissolved substances can lower its freezing point, potentially delaying the freezing process compared to water that has been heated and lost some of these gases. External factors within the freezer environment could also play a role. A layer of frost, often present in freezers, might act as an insulator, hindering heat dissipation from a cold container. Conversely, a hot container could melt the frost beneath it, establishing better contact with the colder freezer surface and facilitating faster cooling.
However, a fundamental question persists: is the Mpemba effect even real? Not all researchers are convinced that hot water consistently freezes faster than cold water.
In 2016, physicists Henry Burridge from Imperial College London and mathematician Paul Linden from the University of Cambridge conducted meticulous experiments to investigate the Mpemba effect. Their findings, published in Nature, revealed the extreme sensitivity of the effect to measurement conditions. They hypothesized that while hot water might initiate ice crystal formation sooner, the time taken for complete freezing could be longer. Given the difficulty in accurately measuring both the initial crystal formation and complete freezing, Burridge and Linden focused on the time it took for water to reach zero degrees Celsius.
Their research uncovered that temperature readings were significantly influenced by the thermometer’s placement within the water sample. When comparing temperatures at the same height in both hot and cold water containers, the Mpemba effect was not observed. However, even a slight vertical difference of a centimeter in thermometer placement could create what appeared to be evidence of the Mpemba effect. Reviewing existing literature, Burridge and Linden noted that only Mpemba and Osborne’s original study reported an Mpemba effect too significant to be attributed to such measurement errors.
Burridge emphasized the delicate nature of these experiments, stating that their findings “highlight how sensitive these experiments are even when you don’t include the freezing process.”
Strange Shortcuts in Thermodynamics
Despite the skepticism, a significant number of scientists believe that the Mpemba effect can indeed occur, at least under specific circumstances. Historically, Aristotle observed in the fourth century BCE that “many people, when they want to cool water quickly, begin by putting it in the sun,” suggesting an understanding of this principle even before precise temperature measurement tools existed. Similarly, the young Mpemba’s observation of the stark difference between his frozen ice cream and his classmates’ slushy mixtures provided anecdotal evidence.
Burridge and Linden’s work, however, underscores a critical challenge in definitively proving or disproving the Mpemba effect: temperature variations within a rapidly cooling water sample. Water undergoing rapid cooling is in a state of non-equilibrium, a state that is poorly understood by physicists.
In a state of equilibrium, a fluid within a closed system can be described using just a few parameters: temperature, volume, and the number of molecules. But place that system in a freezer, and the simplicity vanishes. The water molecules at the container’s edges are immediately exposed to freezing temperatures, while those deeper inside remain warmer. In such non-equilibrium conditions, fundamental properties like temperature and pressure become ill-defined, fluctuating constantly throughout the system.
Zhiyue Lu, a researcher at the University of North Carolina, was captivated by the Mpemba effect since middle school. Inspired by the puzzle, he even conducted his own experiments at a local oil refinery where his mother worked, utilizing precision lab equipment to measure water temperature changes over time. Later, as a graduate student specializing in non-equilibrium thermodynamics, Lu sought to reframe the approach to the Mpemba effect, questioning the fundamental thermodynamic rules. He pondered, “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?” This question encapsulates the ongoing scientific quest to fully understand the perplexing Mpemba effect and the complex behavior of water in non-equilibrium states.
