On the Paradox of Chilling Water: Crossover Temperature in the Mpemba Effect

TL;DR

This study quantitatively investigates the Mpemba effect, demonstrating that hot water can cool faster than cold water and identifying specific crossover temperatures under different initial conditions.

Contribution

It provides the first quantitative measurement of crossover temperatures in the Mpemba effect using controlled cooling experiments.

Findings

Warmer water cools faster than colder water under certain conditions.

Crossover temperature varies with initial conditions, found at 2.7°C and -0.07°C.

Empirical evidence confirming the Mpemba effect.

Abstract

Unlike most of the research on the Mpemba effect which has focused on verifying the observation that warm water freezes faster than cold water, our work quantitatively investigates the rates at which hot and cold water cool and the point at which hot water reaches a lower temperature than cold water under a set of external conditions. Using a vacuum pump to cool samples of water initially at different temperatures, we measured reproducible temperature values at which hot and cold water equilibrate. We have confirmed that warmer water indeed cools at a faster rate than colder water and that, surprisingly, this trend continues past the point where the temperatures of the two samples are the same. Our results show that when using optimal initial temperature conditions, the crossover temperature is found to be 2.7 oC whereas our other set of initial conditions gave a crossover temperature of -0.07 oC. These data taken together provide a definite quantitative evidence of the Mpemba effect.