Calculating Earth's Greenhouse Gas Absorption

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Homework Help Overview

The discussion revolves around calculating the percentage of infrared radiation absorbed by greenhouse gases in Earth's atmosphere, using the Stefan-Boltzmann equation. The original poster presents a scenario where the temperature without greenhouse gases is 250K, and with them, it is 290K.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of flux for both temperatures and the resulting percentage of radiation absorption. Questions arise regarding the correct interpretation of the results and the setup of the problem.

Discussion Status

There is an ongoing exploration of the calculations involved, with some participants providing different results (18% vs. 81%) and questioning the correctness of the initial setup. Guidance is being sought on the approach taken.

Contextual Notes

Participants are examining the implications of their calculations and whether the methodology aligns with the problem requirements. There is uncertainty about the interpretation of the results and the assumptions made in the calculations.

Brad_Ad23
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Ok, here's the question.

Without the greenhouse gases in Earth's atmosphere the temperature would be 250K. With them it is 40K higher (290K). Using the Stefan-Boltzmann equation for flux ( F = σT4) what is the percentage of infrared radiation leaving the Earth's surface taht is absorbed by the greenhouse gases?


I spent awhile on this and the best I could come up with is 18%. But if someone else knows how to do this, help will be appreciated. Thanks!
 
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What is the σ? Post that and show how you used it to get 18%.
 
σ is the Stefan-Boltzmann constant... 5.67 x 10-8 J/m2K4.

I basically calculated the flux F1 for T = 250K and F2 for T = 290.
Then I did xF1= F2-F1 and solved for x.
 
Okay, now what did you get for F1 and F2? I don't get 18%, I get 81%!
 
Hmm, yes I got 81% too. But for some reason it looks like I then did 1-x.

Is the basic setup even right for approaching this problem?
 

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