## 18 October 2011

### Hot water CAN freeze more quickly than cold water

I heard that statement years ago and dismissed it, but the subject was brought up recently in a Reddit thread, which linked to an extended explanation by a physicist.  Herewith brief excerpts:
Hot water can in fact freeze faster than cold water for a wide range of experimental conditions.  This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real.  It has been seen and studied in numerous experiments.  While this phenomenon has been known for centuries, and was described by Aristotle, Bacon, and Descartes, it was not introduced to the modern scientific community until 1969, by a Tanzanian high school pupil named Mpemba...

This seems impossible, right?  Many sharp readers may have already come up with a common proof that the Mpemba effect is impossible.  The proof usually goes something like this.  Say that the initially cooler water starts at 30°C and takes 10 minutes to freeze, while the initially warmer water starts out at 70°C.  Now the initially warmer water has to spend some time cooling to get to get down to 30°C, and after that, it's going to take 10 more minutes to freeze.  So since the initially warmer water has to do everything that the initially cooler water has to do, plus a little more, it will take at least a little longer, right?  What can be wrong with this proof?

What's wrong with this proof is that it implicitly assumes that the water is characterized solely by a single number — its average temperature.  But if other factors besides the average temperature are important, then when the initially warmer water has cooled to an average temperature of 30°C, it may look very different than the initially cooler water (at a uniform 30°C) did at the start.  Why?  Because the water may have changed when it cooled down from a uniform 70°C to an average 30°C.  It could have less mass, less dissolved gas, or convection currents producing a non-uniform temperature distribution.  Or it could have changed the environment around the container in the refrigerator.  All four of these changes are conceivably important, and each will be considered separately below...
Prepare to spend some time at the link if you want to understand the details.  I'll accept it on faith now.

1. So the argument is that hot water can freeze faster than cold water ...if the conditions are not the same. Might as well also add that hot water can freeze faster than cold water if the hot water is at -100C, and the cold water is at -5C. Or suppose that the cold water is also full of salt or something.

ALL ELSE BEING EQUAL, cold water freezes faster.

2. That's not what it says. Apparently you haven't even tried to read the article.

EVERYTHING BEING EQUAL, hot water can freeze faster than cold water - but only under certain sets of parameters (which are the SAME for the hot and cold waters).

3. Sorry, Minnesotastan. I still think the implication that hot water can freeze faster than cold water is misleading. What the article points out is that freezing rate depends on lots of factors besides average temperature, and some of these factors can be changed by previous heating. Specifically, the article points out four possibilities: 1) Some of the previously-heated water may have evaporated. Little amounts of water freeze faster. That is hardly equal, and hardly surprising. 2) The previously-heated water will have less dissolved gas, and will freeze faster. OK, fine. But if it's fair to change what is dissolved in the water, why not also posit dissolved salt in one batch of water, or anything else? 3) The previously-heated water will have a non-uniform temperature distribution, such that it can lose heat faster. Yes, fine. That's what evaporation does -- it carries away heat. We all learned that in grade school; it's why we get cold when wet (or sweat). But that's again hardly equal, is it? Why not posit a bright light on one container? 4) Surroundings. Somehow the previously-heated water changed its surroundings. I don't know what this one is talking about. Maybe the freezer burned up and no longer works? Too vague to say much else.

In any case, if you read the article carefully, there are no conditions where the water is THE SAME where warmer water freezes faster. The water still has to always cool before it can freeze. It's why the article keeps using the phrase 'initially warmer'. The only thing that the article supposes it that the RATE OF COOLING can differ.

But we knew that already, right? If something cools faster, it will freeze faster.

We tried it out over a period of days, using the hottest and the coldest water we could get from the tap, putting them in separate ice cube trays in separate (but equally cold) parts of the freezer. The tray with originally-hot water always froze first.

5. The explanation can be [over] simplified as follows: in order for ice to form, that is for freezing to occur, the water molecules have to "bump into each other" in order to "hook up"; in water starting at a lower temperature this bumping occurs at a much lower frequency than it does in warmer water, and thus the opportunities for freezing are greatly reduced as the water continues to cool and molecular motion slows even further. In warmer water the bumping, occurring at a greater rate provides ample opportunity for ice to form.

6. One thing I think we're forgetting to mention here is that the heat from that water has to go somewhere. While it's true that starting conditions have to be perfect for the Mpemba effect to happen, it's ignoring the fact that your freezer will require more energy to pull that heat out of the water. So while it may take less time (under a lot of perfect circumstances) it'll raise your electricity bill and add to um... CO2 emissions & global warming.!? Not to mention the energy it takes to heat the water in the first place.

So really, who cares if that effect is for real, it's going to make what, maybe 2 minutes difference for your typical ice tray.

@ Lynae, I too tried this as a kid for a science fair and found that while the hot water sometimes froze faster- sometimes it didn't. and the net effect was that cold water typically froze faster overall. And the larger the container or size of the "ice block" you were making made the Mpemba effect outright unnoticeable... it really only works with tiny cubes. in other words try it with a gallon of water an see how the effect isn't even a debatable point.

7. Hello Dude,

In hot water there is significant movement at microscopic level, so no surfusion is possible at 0°C, it freezes.
It is possible to prepare cold water in a very quiet place, and then lower the temperature a few degrees below 0°C without the water freezing. Thanks a lot....

8. I don't get why people are still contradicting the fact that Hot water freezes faster than cold water. This has been proven so many times already... A quick search on YouTube shows even students doing experiments :)