There are many “gedanken” experiments that one can do in the comfort of one’s easy chair to prove that hot water CANNOT under any circumstances freeze faster than cold water. I should leave it as an exercise to you people to come up with some yourselves.
But I’ll start out with two:
Lets suppose that the converse occurs, hot water freezes first. Then at some point in the process, the “hot”: water will have “passed” the cold water in its race toward freezing (it freezes first by hypothesis). But wait…, now the cold water is hotter, so now it must freeze first. Since it freezes first, it must start cooling faster than the other, so it passes the previous hotter water in its race to freezing… but wait, now the other one is hotter, oh the hell with it. By the way, how does the first cold water know that it has been passed in temperature and must speed up? Oh the hell with it again.
Number two–Try this thought experiment…
Take a containers of water of temperature “high”. Put it in a perfectly functioning freezer. (This must be stated because halfwits will say… "Yes but, what if the freezer doesn’t work right, or what if it is full of warm meat…) So, to continue…This container of water will freeze after a certain period of time say “x” minutes.
Now, before it freezes, after some arbitrary interval less than “x”, say, “y” minutes (y<x), it will be at some lower temperature . Lets call that temperature “low” (it is in the perfectly functioning freezer remember). This temperature after time “x-y”, “low”, is less than the starting temperature of value “high” the temperature of the water the instant it was placed in the freezer.
Prepare a container of water identical in all respects to the first container. (This is legal in a thougth experiment.) It has a temperature “high” which is higher than the current value of the first container, now of value “low”. Put it in the freezer. It will freeze in “x” minutes. “X” > "X-Y for all positive values of “y”
The vogue of thinking hot water freezes first is popular among scientific illiterates. Even the mainstream media falls for this. There was an article in the Detroit Free Press a few years back about the Zamboni Ice machines (the weird contraptions seen between hockey periods which clean up the ice). The article stated that hot water was used because it froze faster than cold water. Of course a clear impossibility. But it is common for people to think this. The “shock” of the hot water causes the faster freezing is the usual reason given. Where this scientific “shock principle” came from eludes me. Anyway, why is hot water used in zambonis? Anyone who ice skates knows the answer. Cold water will freeze too FAST!!! It will not have the opportunity to melt imperfections in the ice (skate divots, etc.) like hot water will have. Hot water will give a glass surface to the ice, perfect for skating. Cold water may leave skate marks and divots, not pleasing to the eye, and possibly dangerous, especially to on the edge skaters like hocky players.