[Paper Review] Reply to Burridge & Linden: Hot water may freeze sooner than cold

J. I. Katz|arXiv (Cornell University)|Jan 12, 2017

Advanced Thermodynamics and Statistical Mechanics6 references3 citations

TL;DR

This paper refutes Burridge & Linden's dismissal of the Mpemba effect by clarifying it as a freezing phenomenon, not cooling. It argues that initially hot water can freeze faster than cold due to solute concentration via zone refining and freezing point depression in 'hard' water containing Mg/Ca bicarbonates, which precipitate upon heating, and predicts the effect only occurs in such water—offering a testable theoretical framework for future experiments.

ABSTRACT

In a recent paper in Scientific Reports, Burridge \& Linden misinterpret the Mpemba effect as a statement about the rate of cooling of liquid water, when it is in fact a statement about the rate of freezing of water. Debunking an obviously absurd claim about cooling, they miss the significant effect, its only quantitative experimental study and a theoretical argument that explains the effect and predicts that it occurs only for "hard" water (water with significant dissolved Mg and Ca bicarbonates). This prediction remains to be tested.

Motivation & Objective

• To correct the misinterpretation of the Mpemba effect as a cooling phenomenon rather than a freezing one.
• To highlight the only quantitative experimental study of the freezing-based Mpemba effect by Wojciechowski et al. (1988).
• To reiterate and defend the theoretical explanation of the effect based on solute concentration and freezing point depression.
• To predict that the Mpemba effect should only occur in 'hard' water with Mg/Ca bicarbonates, which is experimentally testable.
• To emphasize the lack of water composition reporting in prior studies, hindering reproducibility and validation.

Proposed method

• Uses thermodynamic analysis to show that cooling time from a higher initial temperature must exceed that from a lower one under standard conditions.
• Applies the heat transfer integral equation (eq. 1) to model cooling time dependence on initial temperature.
• Introduces the concept of zone refining during freezing, where solutes are concentrated at the freezing front.
• Applies freezing point depression theory to explain how solute accumulation alters freezing behavior.
• Uses the theoretical framework from Katz (2009) to explain the Mpemba effect via solute redistribution and latent heat dynamics.
• Predicts the Mpemba effect will only occur in 'hard' water due to bicarbonate-to-carbonate precipitation upon heating.

Experimental results

Research questions

• RQ1 Why does initially hot water sometimes freeze before initially cold water, contrary to intuitive expectations?
• RQ2 What physical mechanism could explain the Mpemba effect in freezing, rather than cooling?
• RQ3 Why is the Mpemba effect not observed in all water types, and what water properties are critical?
• RQ4 How does heating water alter its freezing behavior, particularly in the presence of dissolved bicarbonates?
• RQ5 Can the Mpemba effect be reliably predicted and experimentally verified in hard water?

Key findings

• The Mpemba effect is a freezing phenomenon, not a cooling one, and Burridge & Linden incorrectly frame it as a cooling claim.
• The only quantitative experimental study of the freezing-based Mpemba effect (Wojciechowski et al., 1988) found that warmer water froze before cooler water.
• The theoretical explanation by Katz (2009) successfully accounts for the effect via solute concentration and freezing point depression.
• The effect is predicted to occur only in 'hard' water containing Mg/Ca bicarbonates, which precipitate upon boiling.
• Boiling water removes CO2 and converts bicarbonates to carbonates, 'softening' the water and eliminating the conditions for the Mpemba effect.
• The absence of Mpemba effect in Burridge & Linden’s experiments is consistent with their use of boiled water, which was no longer hard.