How do you find the equilibrium temperature for earth given an input energy?

[SFNQuestions]

Assuming for the moment that sunlight provides all of Earth's energy, how would I figure out the equilibrium temperature given a certain percentage combination of gases? I assume its some kind of exponential solution to a differential equation, but I'm not even sure what to look up.

[swansont]

Your first cut would be from the Stefan-Boltzmann law.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

 

In steady-state, the input and output energy is equal. The size of the sun is small, so you can take the reservoir temperature to be 2.7K (i.e. you can probably ignore it)

[SFNQuestions]

Your first cut would be from the Stefan-Boltzmann law.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

 

In steady-state, the input and output energy is equal. The size of the sun is small, so you can take the reservoir temperature to be 2.7K (i.e. you can probably ignore it)

Alright I just want to make sure because I forgot to clarify: this is for the overall atmosphere of Earth and not the entire interior of the Earth, right?

[Klaynos]

I think what you might be after is the earth's energy budget?

 

http://m.earthobservatory.nasa.gov/Features/EnergyBalance/page6.php

 

I'm not sure I've ever seen a single number for the average temp of the atmosphere (where the atmosphere ends is not a trivial question).

[Essay]

Assuming for the moment that sunlight provides all of Earth's energy, how would I figure out the equilibrium temperature given a certain percentage combination of gases? I assume its some kind of exponential solution to a differential equation, but I'm not even sure what to look up.

 

Here is a good introduction. Just click on "Schedule" for a list of links to each lecture.

 

 

The first five chapters seem to cover the questions you are asking about.

Plus, the "Toy Models" link is fun to play with too.

~

[swansont]

Alright I just want to make sure because I forgot to clarify: this is for the overall atmosphere of Earth and not the entire interior of the Earth, right?

 

 

The surface — that's the area in the formula.

[mistermack]

"How do you find the equilibrium temperature for earth given an input energy?"

 

I think the best way is to look at the temperature record in the ice-cores of Antarctica and compare it to the best calculations of historical solar output. And I believe that has been done in peer-reviewed studies many times over.

Edited February 25, 2017 by mistermack