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Radiation heat pump?

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the net radiation between two surfaces per square metre,1mm apart
    one surface flat and the other sigsawed with valleys 100 mm across tops and 100mm deep. Both surfaces perfect black bodies with a perfect vaccuum inbetween.The flat surface been at 273 degrees kelvin and the sigsawed one at 283 degrees kelvin. I'm told radiation at different angles from the surface it radiates from is proportional in intensity to the cosine of the angle to the normal. I think some of the radiation emitted by the sigsawed surface will hit the opposite side of the valley and be reasorbted by it. All the radiation emitted by the flat surface will hit the sigsawed surface and be asorbed by it.

    2. Relevant equations
    total radiation emitted from a square metre of surface area=(56.7*10^-9)*(surface temperture)^4

    3. The attempt at a solution
    radiation from flat surface=(56.7*10^-9)*(273)^4
    =314 watts
    I can't do advanced maths to work out the average intenisty from the angles that would hit the flat surface from the sigsawed one so I divided up each side of the valley into points and found the average of the cosine of the angle to the normals. I get 0.6 of the radiation emitted by a equilvient flat surface of 1 square meter
    radiation from sigsawed surface to flat=0.6*(56.7*10^-9)*(283)^4
    =218 watts

    net radiation =314-218
    =96 Watts from the cold surface to the hot
  2. jcsd
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