# Stefan-Boltzmann Equation

## Homework Statement

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)

## Homework Equations

P = AE εE σ (TE4 - Tsp4)

## 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?

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kuruman
Homework Helper
Gold Member
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?
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.

First of all, appreciate the reply.

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.
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)

kuruman
Homework Helper
Gold Member
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)
Under the assumption that all the energy coming from the Sun is re-radiated back into space, yes. Is that a good assumption?

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

kuruman
Homework Helper
Gold Member
If all the energy from the Sun is re-radiated back into space, then the calculated TE would be maximum?
No. It will be an equilibrium temperature.

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.

kuruman