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The Sun treated as a perfect Black Body

  1. Dec 14, 2016 #1
    1. The problem statement, all variables and given/known data
    At lunch, the Sun's thermal energy incident on the surface of the Earth is 1.4 kW/m^2. Given the radius of the Sun, R, distance from Earth, r, and treating the Sun like a perfect black body, calculate the total intensity of its radiation and determine its temperature.

    2. Relevant equations

    3. The attempt at a solution
    I have no idea which formula to actually use. I've attempted applying Rayleigh-Jeans and Planck's derivation of it but I simply cannot see how R and r come into play. Perhaps as integer wavelength conditions?
     
  2. jcsd
  3. Dec 14, 2016 #2

    Drakkith

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    Staff: Mentor

    You're given the thermal energy incident on the Earth. How does that play into r, the distance from the Sun to the Earth? What happens to the incident power if r changes?

    Knowing that the Sun outputs a constant amount of power, what has to happen as R varies?
     
  4. Dec 14, 2016 #3
    I know the given power is proportional to T^4 through the Stefan-Boltzmann law but I was not really taught the formula for how the incident power changes with r. I imagine it would be proportional to (1/r)^2? Also, temperature of the Sun would be proportional to either (1/R)^2 or (1/R)^3 for constant output, I think...
     
  5. Dec 14, 2016 #4

    Drakkith

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    The inverse-square law, that's right. So why is this law important? What's happening as the distance changes?

    Ah, but why? What's important about the radius of the Sun? Where exactly is the light emitted from?
     
  6. Dec 14, 2016 #5
    Oooh, ok, so it's only emitted from the surface. Now...if I were to consider the output as constant, it means that the given value in the beginning, let's call it P, would satisfy: P×4πr^2=P'×4πR^2 where P' is what I need to find. And then through Stefan Boltzmann I divide it by the constant and raise it to the power of 1/4 to find out the temperature at the photosphere. I hope that is correct...
     
  7. Dec 14, 2016 #6

    Drakkith

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    What do you get if you do the math?
     
  8. Dec 15, 2016 #7
    Well, for the temperature I got the Sun's temperature at the photosphere (or a very good approximation at least, I got the real value from Wikipedia), so I imagine the total intensity is good as well. Thank you a lot!
     
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