Science help, heat!!?

Question

You are visiting Iceland. Your best friend is sitting in a thermal spring (temperature 45 degrees C) and you are sitting on a glacier (4 degrees C). Each of you has a metal cup of coffee that is about 60 C. Whose coffee cools at a faster rate? Why?

Answer 1

If the coffee is in styrofoam cups, most of the heat loss will be through the top.  If the air temp. is about the same, cooling would be about the same.  

In metal cups, the one floating in the spring *might* cool faster because more of the cup is in contact with the coolant, where the glacier might only have air for cooling.  

If there are *no* special conditions, the cup in the 4C area will cool faster because heat is lost though a given thickness of insulation (including air layers) at a rate proportional to the temperature *difference*.

Answer 2

It should be obvious to you that the coffee cools faster when you are sitting on a glacier. And you are right if you thought this. The reason is that heat transfer is a function of temperature difference, in fact it is proportional to the gradient (a fancy word for difference  - comes from calculus and means infinitesimally small difference) which is the driving force of the heat exchange. Therefore, the larger the temperature difference, the faster the heat transfer is.