Saturday, January 2, 2016

Martin Gardner, Jearl Walker, and Coffee Cooling

A note for all you nerds out there---if you are looking for that famous article on coffee cooling, Martin Gardner mentions it but Jearl Walker analyzes it.

Perhaps a little background is in order. Does your coffee stay warmer longer when you add cream? This question isn't as dumb as it sounds. Yes, the cream cools it down, but Newton's Law of Cooling tells us that the rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings. Adding cream reduces T - T_env so dQ/dt will be lower.

I clearly remember reading an detailed article on this topic in Scientific American back in the...well, let's say it was awhile ago. A graph, as I recall, compared theory and experiment. The article also discussed the effects of radiation---the change in color from black to white affects the energy radiated by the body.

But it was in The Amateur Scientist by Jearl Walker, not Martin Gardner's Mathematical Games. Several sources on the Web cite Mr. Gardner for this problem. They mention one of two books: The 2nd Scientific American Book of Mathematical Puzzles & Diversions or its reprint Origami, Eleusis, and the Soma Cuba. I bought both these books and I am here to report that they only give mention to the problem in the article "James Hugh Riley Shows, Inc."

I believe that this is the proper citation for Dr. Walker's article: The Amateur Scientist, Scientific American 237, 152 - 160 (1977). I haven't yet managed to obtain a copy but my search continues.

And why, you ask, do I care about this problem? Heat dissipation is a key problem for modern computers. You may have noticed your laptop warming up when you use it. That effect is peanuts compared to the heat generated by a data center that burns the electricity of a city of 50,000 people. Newton's Law of Cooling is a fundamental concept for computer system designers. And what better way to illustrate the concept, as Mr. Gardner and Dr. Walker so well knew, than with a cup of coffee?

Update:I reproduced Jearl Walker's coffee cooling experiment here.

No comments:

Post a Comment