THE COFFEE-CREAM PROBLEM

This lab or demo takes about half an hour.

NEWTON S LAW OF COOLING:

The rate of heat conduction is proportional to the temperature difference between an object and its surroundings.

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 quickie 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?

Have the students try to answer this problem for part of their homework assignment the day before the lab. Then they can test their theories in lab.

Use two 250-ml beakers for coffee cups and two 100-ml beakers for creamers. Put 200 ml of water (coffee) in the cups and 40 ml of water (cream) in the creamers. Heat the coffee to boiling (try not to evaporate much).

To one cup add the cream immediately, set both cups on the same table (for the same conductivity and radiation conditions), and record the temperatures in deg C for each cup every 30 seconds for ten minutes.

Then add the cream to the creamless cup, and continue to record temperatures for another two minutes.

Graph the temperature-time curves on the same set of axes, and evaluate the results.

Explain the outcome using Newton's Law of Cooling and Stefan's Law of Radiation.