Engines of Our Ingenuity

No. 2100
MPEMBA EFFECT

by John H. Lienhard

Today, another look at an old claim. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

"Hot water freezes faster than cold water." How many times have you heard that, and is it true? Water starts freezing only after its temperature has fallen to its freezing point. Then its huge latent heat must be removed at that temperature. Starting out with hot water means only a little more heat has to be removed.

But the flow of heat from a warm place to a cold one is like the flow of electricity. It depends on the resistance. The filament in your light bulb has a very high resistance, so 110 volts drives a current of only about one amp through it.

To see how the heat flow from water in an ice-cube tray is resisted, it helps to break resistance into two parts, internal and external -- from inside the water to the metal tray, and from the metal tray to the cooled refrigerator shelf.

Starting out with hot water can affect both. First think about internal resistance: Freezing begins as ice whiskers form on the periphery of the water. They can initially form a layer of insulation and slow the heat flow from the bulk of the water. But if the water is hot, convection currents are set up. They can sweep away those first ice
crystals and get all the water down to its freezing temperature more quickly.

If the water is what we call "hard," with calcium and magnesium bicarbonate dissolved in it, something else happens. Those components reduce the freezing temperature only slightly. But as freezing progresses, their concentration in the remaining water increases, and the freezing temperature really drops. If we preheat the water, we drive these components out of solution and leave them behind in our teakettle.

Notice that I betrayed my age a moment ago when I spoke of ice trays. Modern refrigerators no longer have them. We heard a lot more about hot water freezing faster when we used ice trays. That's because of the effect of hot water on external resistance. Slide a tray of hot water onto a frosty shelf, and the frost immediately melts. That removes a huge resistance to cooling, and it can swamp out every other effect.

But there's so little real research behind all this talk. I wouldn't want to try to find the full answer without a grant for several hundred thousand dollars. (And, how badly do I really want a full answer?)

In the 1960s Tanzanian high school student Erasto Mpemba wrote a paper about the effect of preheating on freezing. He'd noticed this odd behavior when he was making ice cream in a cooking class. Now we talk about the Mpemba Effect, although it's been known since Aristotle.

Well, I suppose I'll get mail now that I've brought up this hotly-debated topic. Meanwhile, I leave you with a similar riddle, equally hard to resolve: I'm served a cup of hot coffee that I won't drink until I finish supper. I want it to be hot when I drink it. Should I put the cool cream in now? Or should I wait until I'm ready to drink the coffee?

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


Look up Mpemba Effect on the Internet and you'll get a great deal of material. For a recent article on the subject, see: M. Chown, Why Water Freezes Faster after Heating. New Scientist, 3 June, 2006, pg. 10.

For more on matter of thermal resistance, see: J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook. 3rd ed., Cambridge, MA: Phlogiston Press, 2004, Click here for a free copy. See especially, Chapter 2.


Water cooling in ice
(photo by JHL)

The Engines of Our Ingenuity is Copyright © 1988-2006 by John H. Lienhard.