Principle of Heat Exchange    -    The Coffee-Cream Problem

 Newton's law of cooling:   The rate of heat conduction is proportional to the temperature difference between an object and its surroundings.

 The Stefan-Boltzmann law of radiation:  The rate of heat lost by radiation is proportional to the fourth power of the absolute temperature.

 The historic problem: 

            Ah, you see, there is this business man who likes a large amount of cream in his coffee, and he wants the resultant mixture as hot as possible.  (Alas, there is no microwave oven available).

            He has just prepared his boiling coffee when he is called by the boss for a quick conference of ten minutes duration.  The boss tolerates no coffee in his presence.

            What to do?  To keep the coffee as hot as possible should he add the cream now or wait until after the conference?

             Which do you think he should do? _____________________________________

 Using beakers for the coffee cups and water for the coffee and cream, design an experiment to test the problem.  Use the computer and temperature probe to measure the temperature over time.   How would you set up a graph(s) to help prove the best solution.