Calculating Earth's Greenhouse Gas Absorption

AI Thread Summary
The discussion centers on calculating the percentage of infrared radiation absorbed by greenhouse gases in Earth's atmosphere. The initial temperature without greenhouse gases is stated as 250K, and with them, it rises to 290K. Using the Stefan-Boltzmann equation, participants initially calculated the absorption percentage, with one suggesting 18% and others arriving at 81%. Confusion arose regarding the calculations and the interpretation of results, particularly in relation to the setup of the problem. Overall, the conversation highlights the complexities involved in accurately determining greenhouse gas absorption using the Stefan-Boltzmann equation.
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-Boltzman 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-Boltzman 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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