/sci/ - Science & Math

I pose this question to you. Assume a cup made of a perfect insulator. There is a large amount of water in the cup such that the ratio of water in contact with the cup to water in contact with the cool air is very large. When will the water cool off the fastest? The height of the cup above the surface of the water is the object of our attention here.

When will the water cool off the fastest? When the height is very large, when the height is basically level with the surface of the water, or at some point in between?

This isn't homework; I already know the answer. In fact, the rigorous answer is pretty hard to work out to the point where even physics grad students wouldn't bother unless it was part of their research. But what do you think?