Principle of Heat Exchange    -    The Coffee-Cream Problem

  The historic problem:

            Ah, you see, there is this business man (Bob)  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 and why?   (Hint:  you must predict what you think will happen and why before you start the experiment.  Then do not let this change your collection of data and final analysis, especially if you were wrong in your initial prediction).

Some limits (controlled variables): 
a)  use beakers for the coffee cups (unless you can bring two cups from home)
b) use hot water for the coffee and cold water for the cream (no sugar)
c) allow the experiment run over a 12 minute window (for experiment 1:  add cream at beginning and let run for 12 minutes; for experiment 2: let run for 10 minutes, add cream, let run for 2 minutes)
d) amounts of coffee and cream used (what are reasonable amounts of each – may take research)
e) do you stir/swirl?
f) initial temperatures???
g) others???

Need in final report by each student:
a)  graph of entire 12 minute duration with as many data points as possible in the key minutes section of each experiment (i.e., first 4 minutes and last 2 minutes of experiment 1 and then first 2 minutes and last 4 minutes of experiment 2)
b) experimental procedure in outline format
c) list of variables controlled (with method)
d) final result with conclusions as to why it worked the way it did
e) all data in presentation form (from each student)

Some of the science that can be investigated:

 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.