# Homework Help: Calculate the Average Surface Temperature of Earth

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1. Mar 12, 2016

### lasisdabomb

1. The problem statement, all variables and given/known data
The Earth receives on average about 390 W m−2 of radiant thermal energy from the Sun, averaged over the whole of the Earth. It radiates an equal amount back into space, maintaining a thermal equilibrium that keeps the average temperature on Earth the same. Assuming the Earth is a perfect emitter of radiant energy (e = 1), estimate the average surface temperature of the Earth in °C

2. Relevant equations
P = eσAT^4
P ∝ T^4
λmaxT = 2.898 × 10−3 m K
3. Attempt
I've tried all these formulas, but I'm not getting anywhere. Am I supposed to know the surface area of the Earth because I feel like it's impossible without it

2. Mar 12, 2016

### Qwertywerty

Assume the area of the earth to be $A$, a variable. What, then, is the total power incident on the earth's surface?

3. Mar 12, 2016

### lasisdabomb

Is the 390 m^-2 relevant for the equation. Should that be stated as the P value or should it just be 390W

4. Mar 12, 2016

### Qwertywerty

Do you know what intensity is? It's formula? It's unit?

5. Mar 12, 2016

### lasisdabomb

I've realized how to do it. The Power is average for each m^2 of earth. That means the surface area should be 1m^2 and the Power should be 390.
By subbing everything in, you get an average surface temperature of 288 Kelvin or 15°C

6. Mar 12, 2016

### Qwertywerty

More appropriate wording would be - an average of 390W of power is incident per sq.m on the surface of the earth. This is what you mean, right?

And congratulations, on having solved the problem

7. Mar 12, 2016

### haruspex

Yes, that's the right answer with the given information, but 390 W/m2 is too high. Should be more like 340.
Taking the 30% albedo into account as well would bring the temperature down to 255K, which is the standard result.

8. Mar 12, 2016

### Qwertywerty

Thanks for the info!