The Math of the Mpemba Effect – Hot Water Freezes Faster?

The Mpemba effect: under certain conditions, hot water freezes faster than cold water. First noted by Aristotle, but named after Tanzanian student Erasto Mpemba in 1963. The effect is real but poorly understood – potential explanations include evaporation, convection, supercooling, and hydrogen bonding. Mathematical models (differential equations with non‑linear terms) show that initial temperature affects cooling rate in complex ways. It remains an active research area in thermodynamics and physical chemistry. It reminds us that ‘common sense’ can be wrong, and careful measurement and modelling are essential.