Yes! If you take an ice cube rack filled with hot water and put it in an iced-up freezer, the ice cubes will form noticably faster than if you use cold water. This phenomenon was first observed by Aristotle:

"Many people, when they want to cool water quickly begin by putting it in the sun. So the inhabitants when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their rods that it may freeze the quicker; for they use ice like lead to fix the rods."

Sir Francis Bacon noticed the same phenomenon when wooden pails were placed on ice. Those with hot water froze faster. There are two major types of explanations for this phenomenon. Either or both may be true, depending on the conditions of the experiment.

Explanation 1: Thermal Contact If you put an ice-cube tray with hot water into a freezer with ice covering the shelf surface, the hot water will melt a little bit of the ice on the shelf. This then refreezes, making better thermal contact between the freezer and the tray. As a result, heat is conducted away more quickly from the water, allowing it to freeze faster.

Explanation 2: Convection It has been noticed that even a metal pail of water suspended in the air on a chilly night will freeze faster if the water is warm. Thermal contact is not the issue here. Instead, it is hypothesized that convection may be the contributing factor. In a pail of cold water, the water is stationary, and freezing begins on the edges of the pail and surface of the water and slowly works its way inside. The core, now insulated by a chamber of ice, freezes more slowly . However, a warm pail of water, when cooled at the edges, will start to churn due to convection. This mixes the water, allowing it to cool more evenly, potentially speeding up the freezing process. The degree of temperature difference determines the amount of convection that occurs.

Obviously, the conditions of the experiment are crucial here. The relative temperature of the water and the environment, the type of container, its size and shape, thermal contact with ice, etc. These all affect the rate of cooling and freezing.

I'm skeptical of this dubious assertion, but I will give it the benefit of my doubt. (Though I really doubt Aristotle had access to a refrigerator) What's more, I will even offer a third hypothesis as to why this might be true.

The heat of fusion for water is 334 J/g. That means for every gram of solid water at 0 degrees Celcius to be turned into liquid water at 0 degrees Celcius (or vice versa) 334 Joules of energy must be absorbed (or radiated) by the water.

So the winner of the race between the hot water and the cold water to the solid state probably depends on the temperature of the hot and cold water. The hot water will be better at melting the surrounding ice. But melting the surrounding ice will require 334 extra Joules of energy that comes right out of the hot water just to get the ice to cross from being solid to being liquid. That might just be enough to drop the temperature of the hot water below the temperature of the water which is considered "cold", so thus the hot water leapfrogs ahead of the cold water in the race to the solid state.

Another factor, it might be only the hot water at the edges of the ice cube tray that experience this benefit of losing the extra 334 Joules/gram of melted refrigerator frost. But, they might form seed crystals of ice sooner, and thus precipitate the freezing of the rest of the water in the ice tray.

I'm not a chemist though, so take all this with a several moles of NaCl, as I suspect that my hypothesis, full of scientific jargon though it may be, is a load of crap.

After thinking about it a bit more, (and reading what's below), of course my hypothesis is a load of crap. BTW, I also tried this with two cups of water (not ice cubes), and when I checked back later, both were frozen solid, so my empirical results are that they both freeze at the same speed. Which is also a load of crap. I always hated chemistry. (Yeah, this probably doesn't count as chemistry, I know.)
Sometimes. If the conditions are right.

However, if you ask the question, "Which gives me the most ice for the water," the answer is cold

Here's the problem with the convection argument above: Why doesn't the hot water reach equilibrium when it reaches 4C? As the water gets cooler, the convection currents become weaker and when it reaches 4 degrees Centigrade the once hotter water would be subjected to the same problems of the cold water. Of course here would be where the conduction argument above would work best, but what if there isn't ice on the shelf? What if I had just defrosted my freezer?

The largest factor in the hot water freezing faster (also known as the Mpemba effect) is, in fact, evaporation. If you put water in the freezer that is 99C and water that is 20C, the hot water will evaporate much of it's volume. With simple math, it's easy to see that less mass of water means faster freezing. When talking about ice cubes in a tray, there is a larger surface area to volume ratio then say, a bucket of water.

There is another factor of impurities in the water. Heating water releases gasses that otherwise lower the freezing point. Cold water retains all of these, and in common experiments can cause inaccurate testing.

But then again, we're talking about making ice cubes.

I suppose if you want to be purely technical, water that is colder will freeze faster - all other things being equal. But if you want to make your ice cubes in a slightly shorter amount of time, put in hot water. But remember - they just might be ice slivers by the time they're done!

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Sort of.

This all depends on your point of view. If you're talking about pure, contaminant-free (this includes air bubbles as well) H2O, then no, hot water does not freeze any faster than cold water. In fact, in this case, it freezes quite a bit slower.

On the other hand, if what we're discussing is straight-from-the-faucet tap water, then it will freeze faster (and stronger, I might add) if it's heated prior to being placed in the freezer. Then again, tap water will also freeze faster if you heat it, let it sit for a while, and then freeze it.

But why, you ask, do these inconsistencies exist? As mentioned in Natrous's writeup, heating water allows gasses to rise to the surface of the water and escape. In fact, these kinds of gasses (and other impurities) are prevalent in all water to some degree or another excluding the Platonic ideal discussed above. These tiny bits of gas act as insulation within the water, much as pockets of air do in foam. Heating the water causes the H2O molecules to move about quite a bit, shaking up these gasses (present even in distilled water, which can trap air bubbles due to being shaken about) which then rise to the surface and escape. The key here is that it isn't the heat that causes the faster freezing time, it's the release of gasses. The water doesn't need to be hot to freeze faster, it needs to have been heated at some point prior to being frozen. Which, of course, is more or less the same thing, but the distinction, however slight, needs to be made.

Boiling the water causes the most satisfactory ice, since the water is at it's most severe state of agitation. In fact, if the water is boiled without heat (such as being placed in a vacuum), the resultant ice will freeze just as fast and strong as if it were boiled using a stove.

This whole mess is due to the human tendency to simplify things, such as Occam's Razor. When people see something heated freezing faster, they naturally assume that it's the heat causing the accelerated freezing. When it was later discovered that boiled water froze faster (this is the version I heard as a child), it was again taken for granted that it was the heat increase responsible, not the boiling action itself. Since heating the water is correlated to a faster freezing time, it can be a tough time convincing someone that heat is not the cause.

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