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A jogger generates heat energy at a rate of 834.0 W. If all this energy is removed by sweating, how much water must evaporate from the jogger's skin each hour?

Question

A jogger generates heat energy at a rate of 834.0 W. If all this energy is removed by sweating, how much water must evaporate from the jogger's skin each hour?

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Solution

To solve this problem, we need to know the heat of vaporization of water, which is approximately 2260 kJ/kg. This is the amount of energy required to convert 1 kg of water from a liquid to a gas.

  1. First, convert the power generated by the jogger to kilojoules per hour. There are 3600 seconds in an hour, so the jogger generates 834.0 W * 3600 s/hr = 3002.4 kJ/hr.

  2. Next, divide this energy by the heat of vaporization of water to find the mass of water that must evaporate. This is 3002.4 kJ/hr / 2260 kJ/kg = 1.33 kg/hr.

So, the jogger must lose about 1.33 kg of water per hour through sweating to remove all the heat they generate.

This problem has been solved

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