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?
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.
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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.
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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.
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