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# Sweating

last edited by 5 years, 5 months ago

7.2.P5

This is an estimation problem. Do not use a calculator, and do not look any specific numbers. Instead, approximate to the correct order of magnitude (power of ten) and make estimates of the numbers you need, building from other information in your personal experience.

Heat is generated in the course of maintaining normal human cellular processes and must be constantly removed from the body (to avoid heating up). In normal, resting conditions, the required cooling rate is 90 watts. During exercise, when (thermodynamically inefficient) muscles are being used to move around, the required cooling rate can be as much as one thousand watts. In the Winter Olympics, it is easy to radiate this much heat. In the Summer Olympics, on the other hand, the ambient temperature can be approximately equal to body temperature, and one can no longer cool off by radiating heat. A different, very human, mechanism is required: sweating. For typical Summer Olympics temperatures, vaporizing one gram of water requires about 0.5 kcal. Approximately how many pounds of sweat would one need to produce and evaporate in the course of one hour of steady exercise under these conditions to maintain steady body temperature? Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer.

Bill Dorland 3/1/18