How much energy does the Earth radiate to space?

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Homework Help Overview

The discussion revolves around calculating the energy radiated from the Earth to space, focusing on the relevant equations and the variables involved, such as the Earth's temperature and emissivity. Participants explore the implications of these variables on the calculations and the assumptions underlying the model.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relevance of the equation for power calculation and the variability of the Earth's average temperature. There are considerations about using an order of magnitude approach and the implications of incoming solar energy on the Earth's temperature.

Discussion Status

The conversation is active with participants providing insights and questioning assumptions about energy re-radiation and equilibrium temperature. There is acknowledgment of the complexity of the topic, and while some clarity is emerging, no consensus has been reached on all points.

Contextual Notes

Participants note the variability in the average temperature of the Earth and the assumptions regarding energy input from the Sun. There is a mention of the political implications surrounding climate discussions, which some participants prefer to avoid in favor of focusing on the scientific understanding.

Vector1962
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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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Vector1962 said:
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.

kuruman said:
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)
 
Vector1962 said:
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?
 
Vector1962 said:
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.
 
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 TE calculate wouldn't be both equilibrium and maximum? Of course, orbit is elliptical but just going for concept here.
 
"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.
 
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.
 

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