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Albedo equations giving different results

  1. Sep 21, 2010 #1
    1. This question isn't so much a homework question per se, however I am having difficulty using certain equations to find the albedo of the Earth. In attempting to find the albedo, I am using two equations, shown below, however each equation gives a different answer. I am given the following variables:

    - Power absorbed at the surface of the Earth is 240 W/m^2
    - Solar Constant(S) is 1.37 kW/m^2
    - Earth is assumed to be a perfect blackbody, thus emissivity is 1
    - Temperature(T) on the Earth is assumed to be 255 kelvin
    σ is Stefan Boltzmann constant, 5.67 x 10^-8
    ε is emissivity of the Earth
    α is albedo

    2. Relevant equations

    T = [tex]\sqrt[4]{\frac{S(1-\alpha)}{4\epsilon\sigma}}[/tex] <-- this is a given equation found by combining the Stefan Boltzmann law with an equation for incoming power.

    albedo = total scattered power/total incident power <--this is from a provided data booklet

    3. The attempt at a solution

    The actual work isn't too hard, when the 1st equation is moved around to find the albedo, it reads:

    [tex]\alpha[/tex] = -[tex]\frac{T^{4}4\sigma}{S}[/tex] + 1

    This equation, when solved, gives the answer [tex]\alpha[/tex]=0.3, this is the correct response according to the book

    When I use the second equation, I take the solar constant S as the total incident power. In order to find the total scattered power, I'm subtracting the amount absorbed (given as 240W/[tex]m^{2}[/tex]) from the solar constant because the difference isn't absorbed by the earth, meaning it is reflected into space or scattered. However I get this:

    [[tex]\frac{1.37*10^{3} - 240}{1.37*10^{3}}[/tex] = 0.82

    This value is incorrect and I'm not sure why, given a presumed correct equation, I'm getting a wrong answer. Am I misusing the equation somehow?
  2. jcsd
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