Archive for December 15, 2015

Why Does Hot Water Freeze Faster Than Cold?

Posted in Biographical, Cute Problems, The Universe and Stuff with tags , , , on December 15, 2015 by telescoper

Many years ago I had to take a day off School to travel down to Cambridge in order to be interviewed for a place on the Natural Sciences Tripos at Magdalene College. One of the questions I was asked was the following:

If you put a bucket of hot water and a bucket of cold water outside on a freezing cold day, which would freeze first?

I think I gave the right answer, which is that it’s not obvious..

My main argument was that evaporation would increase the rate of cooling of the hot water and also mean that when it did get down to freezing point there would be less of it to freeze. I attempted to work something out based on the heat capacity of liquid water versus the latent heat of freezing, but didn’t get very far with that as I couldn’t remember any numbers. I do remember saying that this would also depend on the shape of the bucket, especially on the surface area exposed: water in a flat dish would experience more evaporation than a narrow cylinder.

I only realised later that it wasn’t really the purpose of such questions to arrive at a definite answer, more to give the interviewer an idea of whether the interviewee is capable of thinking on his/her feet. I guess I must have waffled enough to give the misleading impression that I could, and was offered a place.

The reason I am rambling on about this now is that I stumbled across a blog post yesterday about something called the Mpemba Effect from which I quote:

The Mpemba effect is the observation that warm water freezes more quickly than cold water. The effect has been measured on many occasions with many explanations put forward. One idea is that warm containers make better thermal contact with a refrigerator and so conduct heat more efficiently. Hence the faster freezing. Another is that warm water evaporates rapidly and since this is an endothermic process, it cools the water making it freeze more quickly.

None of these explanations are entirely convincing, which is why the true explanation is still up for grabs

It appears that, depending on the circumstances, hot water does indeed freeze faster than cold water but that the reason why is apparently still not obvious.

However, there is a (fairly) recent paper on the arXiv that claims to solve this problem. The abstract reads:

We demonstrate that the Mpemba paradox arises intrinsically from the release rate of energy initially stored in the covalent H-O part of the O:H-O bond in water albeit experimental conditions. Generally, heating raises the energy of a substance by lengthening and softening all bonds involved. However, the O:H nonbond in water follows actively the general rule of thermal expansion and drives the H-O covalent bond to relax oppositely in length and energy because of the inter-electron-electron pair coupling [J Phys Chem Lett 4, 2565 (2013); ibid 4, 3238 (2013)]. Heating stores energy into the H-O bond by shortening and stiffening it. Cooling the water as the source in a refrigerator as a drain, the H-O bond releases its energy at a rate that depends exponentially on the initially storage of energy, and therefore, Mpemba effect happens. This effect is formulated in terms of the relaxation time tau to represent all possible processes of energy loss. Consistency between predictions and measurements revealed that the tau drops exponentially intrinsically with the initial temperature of the water being cooled.

Although I did study chemistry as part of my Natural Sciences degree, I dropped it after the first year and have subsequently forgotten almost everything I learned. I’m therefore not really qualified to judge whether the explanation presented in this paper is reasonable. I would be convinced if the theory could predict other observable outcomes but at the moment it doesn’t seem to.

Any chemists care to comment?