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Calculate the Average Surface Temperature of Earth

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  1. Mar 12, 2016 #1
    1. The problem statement, all variables and given/known data
    The Earth receives on average about 390 W m−2 of radiant thermal energy from the Sun, averaged over the whole of the Earth. It radiates an equal amount back into space, maintaining a thermal equilibrium that keeps the average temperature on Earth the same. Assuming the Earth is a perfect emitter of radiant energy (e = 1), estimate the average surface temperature of the Earth in °C

    2. Relevant equations
    P = eσAT^4
    P ∝ T^4
    λmaxT = 2.898 × 10−3 m K
    3. Attempt
    I've tried all these formulas, but I'm not getting anywhere. Am I supposed to know the surface area of the Earth because I feel like it's impossible without it
     
  2. jcsd
  3. Mar 12, 2016 #2
    Assume the area of the earth to be ##A##, a variable. What, then, is the total power incident on the earth's surface?
     
  4. Mar 12, 2016 #3
    Is the 390 m^-2 relevant for the equation. Should that be stated as the P value or should it just be 390W
     
  5. Mar 12, 2016 #4
    Do you know what intensity is? It's formula? It's unit?
     
  6. Mar 12, 2016 #5
    I've realized how to do it. The Power is average for each m^2 of earth. That means the surface area should be 1m^2 and the Power should be 390.
    By subbing everything in, you get an average surface temperature of 288 Kelvin or 15°C
     
  7. Mar 12, 2016 #6
    More appropriate wording would be - an average of 390W of power is incident per sq.m on the surface of the earth. This is what you mean, right?

    And congratulations, on having solved the problem:smile:
     
  8. Mar 12, 2016 #7

    haruspex

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    Yes, that's the right answer with the given information, but 390 W/m2 is too high. Should be more like 340.
    Taking the 30% albedo into account as well would bring the temperature down to 255K, which is the standard result.
     
  9. Mar 12, 2016 #8
    Thanks for the info!
     
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