How much energy does the Earth radiate to space?

[Vector1962]

Homework Statement

How much energy is radiated from the Earth to space?
A_E = Area of Earth
ε_E = Emissivity of Earth
T_E = Temperature of Earth
T_sp = Temperature of Space
T_sp = 2.7 K (off of NASA web page)

Homework Equations

P = A_E ε_E σ (T_E⁴ - T_sp⁴)

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?

 

[kuruman]

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.

 

[Vector1962]

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 T_E; If I knew the incoming energy from the sun, would E_{from sun} = A_E ε_E σ (T_E⁴ - T_sp⁴)

 

[kuruman]

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 E_{from sun} = A_E ε_E σ (T_E⁴ - T_sp⁴)

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

 

[Vector1962]

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

 

[kuruman]

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.

 

[Vector1962]

Again, appreciate your reply.
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 T_E calculate wouldn't be both equilibrium and maximum? Of course, orbit is elliptical but just going for concept here.

 

[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.

 

[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.