# Stefan-Boltzmann Equation

1. Apr 13, 2017

### Vector1962

1. The problem statement, all variables and given/known data
How much energy is radiated from the earth to space?
AE = Area of Earth
εE = Emissivity of Earth
TE = Temperature of Earth
Tsp = Temperature of Space
Tsp = 2.7 K (off of NASA web page)

2. Relevant equations

P = AE εE σ (TE4 - Tsp4)

3. The attempt at a solution
Isn't the relevant equation the answer to the question? The average temperature of the earth is "all over the place" depending on which web site, college, governmental agency or science club you look at. If I picked an temperature of the earth, then I could calc. the power correct?

2. Apr 13, 2017

### kuruman

Correct. This looks like an "order of magnitude" calculation. Pick a temperature and see what power of 10 you get. Then you will have a feeling of big it is.

3. Apr 13, 2017

### Vector1962

First of all, appreciate the reply.

Suppose I don't know the average temp of the Earth, and suppose "incoming energy" is holding the average temperature of Earth at TE; If I knew the incoming energy from the sun, would Efrom sun = AE εE σ (TE4 - Tsp4)

4. Apr 13, 2017

### kuruman

Under the assumption that all the energy coming from the Sun is re-radiated back into space, yes. Is that a good assumption?

5. Apr 13, 2017

### Vector1962

If all the energy from the Sun is re-radiated back into space, then the calculated TE would be maximum?

6. Apr 13, 2017

### kuruman

No. It will be an equilibrium temperature.

7. Apr 13, 2017

### Vector1962

I think I see that it would be an equilibrium temperature. If Earths orbit around Sun is assumed circular then the energy delivered to the earth is constant; I don't see why the TE calculate wouldn't be both equilibrium and maximum? Of course, orbit is elliptical but just going for concept here.

8. Apr 14, 2017

### kuruman

"Maximum" means "it can increase no more." In this oversimplified model, the temperature of the Earth will increase if the temperature of the Sun increases for whatever reason. It's not like boiling water that has a maximum temperature of 100 oC regardless of how much heat you are putting in. Why the average temperature of the Earth is what it is and where it is headed is, as you know, a complicated issue that has been highly politicized in the recent past.

9. Apr 14, 2017

### Vector1962

Ahhh... I see. Only "maximum" if energy input is constant (at its maximum) and unchanging. No politics please. Just going for understanding. I think I have what I'm looking for. Appreciate your time.