Yes, I can settle your argument... but maybe not as clearly as you might have liked. The answer is that sometimes the cold water freezes faster and sometimes the hot water does. It just depends on the circumstances. For example, it's pretty obvious that if you had a bucket of water that's boiling and one that's at just 1 or 2 degrees Celsius, the cold water would freeze first. And it makes logical sense for the cool water to freeze first, since it has less heat to lose all together.
But it's actually been known since Aristotle was around (~300 B.C.) that sometimes the warmer water freezes first. This eventually came to be called the Mpemba effect, named after a Tanzanian high school student in the 1960's. Unfortunately, though, scientists still haven't agreed on why the Mpemba effect happens. It's probably due to a number of different reasons. Here's just a few:
Evaporation: Hot water evaporates faster than cold water, and as it evaporates, it carries some of the heat (and the water) away. So in the end, there's less water left to cool off.
Dissolved Gases: Hot water has less gases disolved in it than cold water does. Dissolved gases (like dissolved anything) lower the freezing point of water. Now if the surroundings are just a little below the freezing point of water, lowering the freezing point can make in big difference in the freezing time.
Container and Surroundings: Different surroundings will conduct heat differently. For example, if you have two metal buckets of water, it's more likely that the cooler one will freeze first whereas if you have two thermoses with only the lid open, the warmer one may freeze faster. If the surroundings have frost, the warmer water may melt it and leave better contact for heat to flow out than for the cooler water.
Convection: The temperature in the water isn't the same everywhere. As the hot water cools, the hotter parts of the water and the cooler parts of the water actually end up swirling around each other, helping it to cool down. This happens less in the cool water since there's less temperature difference. Of course, this doesn't actually make the warm water freeze first, since once it's cool this effect foes away, but it can reduce the time it takes to get cool, so the other effects can show up more easily.
An interesting example of how this effect is used is in making ice cream. For a long time, many ice cream makers have made their ice cream using warmed milk since it can be made to freeze faster than cold milk.
All this information came from a wonderful (but quite long) article from the Department of Physics at the University of California. This article has all sorts of references to scientific work on this as well as a wonderful history of how the effect was discovered and why it's named after a Tanzanian high school student. So if you're interested in learning more, check it out!
-Tamara (small mods by mw)
p.s. Somebody could figure out the role of these effects with a little effort. For example, evaporation leaves a smaller amount of ice, which should be an easy effect to measure. Dissolved gas lowers the freezing point, something that could be measured using a thermometer. Mike W.
(published on 10/22/2007)