# Homework Help: Need Help on Radiation balance question

1. Nov 6, 2008

### aforce20

1. The problem statement, all variables and given/known data

1. If the Sun’s power is reduced by 10%, what would the temperature of the Earth be? Assume an albedo of 0.3 and do not consider greenhouse effects.

2. Relevant equations

There is an equation here in the book but it makes no sense to me

3. The attempt at a solution

Without the understanding of the equation, I have no attempt

2. Nov 6, 2008

### tiny-tim

Hi aforce20!

What equation?

3. Nov 6, 2008

### aforce20

Here is the example from the book that we are supposed to go off of
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The total energy absorbed for a solar constant, or available power per unit area at earths orbit, of 1.35 kW/m2 is, assuming an albedo (reflectivity) of 30%

Pabsorbed = (1 -0.3)( 1.35 kW/m2) ([PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png [Broken] [Broken] [Broken]RE2)

A body at absolute temperature T radiates according to the Stefan-Boltzmann law as

Pradiated = ( 5.67 x 10-8 W/m2 K4) T4 (4[PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png [Broken] [Broken] [Broken]RE2)

where Earths total spherical surgace area is 4[PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png [Broken] [Broken] [Broken]RE2 . Thus, since in the long term the power absorbed must again be radiated for earth to be in equilibrium, Pradiated = Pabsorbed , and [PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png [Broken] [Broken] [Broken]RE2 is a common factor , so

( 1 - 0.3 ) ( 1.35 kW/m2) = 4(5.67 x 10-8 W/m2k4) T4

Therefore,

T4 = ( 0.7) (1350 W/m2)/4(5.67 x 10-8 W/m2 K4) = 4.17 x 109 K4

or

T=254 K

BTW I could not find the pi symbol so I used one from google, that is why it is so huge. Also, this class is for non-science majors so try not go get to technical here.

Thanks

Last edited by a moderator: May 3, 2017
4. Nov 6, 2008

### tiny-tim

Hi aforce20!

(have a pi: π )

The basic equation simply says that the power out must equal the power in.

Which line do you not understand?

5. Nov 6, 2008

### aforce20

I just don't know where to start in solving the problem

6. Nov 10, 2008