The Sun treated as a perfect Black Body

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Homework Help Overview

The discussion revolves around calculating the total intensity of radiation from the Sun, treated as a perfect black body, based on the thermal energy incident on Earth. The problem involves concepts from thermodynamics and radiation, specifically the Stefan-Boltzmann law and the inverse-square law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the thermal energy incident on Earth and the distance from the Sun, questioning how changes in distance affect incident power. They discuss the implications of the Sun's radius and its role in radiation emission.

Discussion Status

Some participants have offered insights into the proportional relationships involved in the problem, particularly regarding the inverse-square law and the implications of the Stefan-Boltzmann law. There is an ongoing exploration of how to relate the given values to the temperature and intensity, with some participants expressing uncertainty about the formulas and their application.

Contextual Notes

Participants note a lack of familiarity with specific formulas related to how incident power changes with distance and the implications of the Sun's radius on temperature calculations. There is an acknowledgment of the need to clarify these relationships further.

Keiner Nichts
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Homework Statement


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.

Homework Equations



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?
 
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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?
 
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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...
 
Keiner Nichts said:
I imagine it would be proportional to (1/r)^2?

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

Keiner Nichts said:
Also, temperature of the Sun would be proportional to either (1/R)^2 or (1/R)^3 for constant output, I think...

Ah, but why? What's important about the radius of the Sun? Where exactly is the light emitted from?
 
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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...
 
What do you get if you do the math?
 
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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