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An extremely large and valuable diamond has just been reported stolen. A white glove with a large P on it was left at the crime scene, signifying that the culprit was the "Pink Panther", an elusive jewel thief1. Inspector Clouseau has been assigned to the case. Similar gloves had been left at several earlier crime scenes. No one could ever gather any useful evidence from the gloves, but Clouseau, being clumsy yet quite bright, had an idea. He figured that the culprit must keep the glove very close to his or her body (perhaps in a pants pocket) until just before dropping the glove and leaving the scene of the crime. Thus, when the glove is dropped its temperature should be 98 degrees Fahrenheit (roughly body temperature).
Since the crime scene was in a temperature controlled room, where the temperature was held fixed at exactly 70.0262 degrees Fahrenheit, the glove should cool with time. Having had several courses in the physical sciences, Clouseau scratched his head for a moment and thought of the following example, where common sense could fill in the long lost formulas that govern the temperature of cooling objects. He figured that a cup of freshly brewed java (right out of the pot) was about 200 degrees Fahrenheit. After 35 minutes or so (if it wasn't consumed), the temperature would have dropped to about 68 degrees Fahrenheit (the temperature of his kitchen). Clouseau also imagined that at first, when the coffee is much hotter than his kitchen, the temperature of the coffee would fall fast. Later on, as the coffee got closer to the temperature of the room, the drop in the temperature of the coffee would be much slower. A graph of the coffee's temperature (in degrees Fahrenheit versus time) would therefore look something like the plot below, where the line y = 68 has been drawn in as well. |
