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Black Body Net Heat Absorption Problem

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data
    A naked person, whose skin area is 1.7 m2, sits in a sauna that has a wall
    temperature of 61oC. If the person’s skin temperature is 37oC, find the net rate at
    which the person absorbs heat by radiative transfer (assume an emissivity e of 1).
    How much liquid must the person consume after 30 minutes to replace the sweat
    evaporated as a result of this heat absorption. (assume the latent heat of vaporisation
    of sweat is 2427 kJ/kg at 37oC.

    2. Relevant equations

    Stefan-Boltzmann Law: P = e[tex]\sigma[/tex]AT4

    3. The attempt at a solution

    Plugging in the numbers and using the the temperature of the sauna walls and human body termperature to give the NET rate of absorption:

    P = 1 x 5.67x10-8 x 1.7 x (614 - 374)
    = 1.15 W

    Multiplying this power by the 30 minute time period will give the heat energy, Q, absorbed by the person:

    P x t = 1.15 x 30 x 60 = 2077J

    We are given the latent heat of vaporisation of sweat so dividing Q by this value will give the mass of water lost:

    M = 2077 / 2427x103 = 0.9 g

    This mass of water seems too small to be reasonable. Although this calculation will only give an approximate value I would nevertheless expect it to be above 10g at the very least. Having checked my calculation I cannot find any obvious mistakes, my only real doubt is my calculation of the net rate of absorption but I cannot see how else I would calculate this value.

    Thanks for the help.
     
  2. jcsd
  3. May 10, 2010 #2

    Redbelly98

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    Welcome to PF.
    You need to use absolute temperatures here, not the °C values. The rest of your method looks pretty good, though note that water's heat of vaporization is around 2300 J/g, not 2300x103J/g.
     
  4. May 11, 2010 #3
    Thanks for the reply. I made the absolute temperature correction and got 229g/229mL which seems much more reasonable.

    Thanks again!
     
  5. May 11, 2010 #4

    Redbelly98

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    You're welcome! Yup, 8 ounces, or a small glass of water, definitely reasonable.
     
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