This powerpoint shows a simple calculation for the equilibrium temperature of the Earth assuming there are no greenhouse gases present.

1. Equilibrium Temperature of the Earth

2. Electromagnetic Spectrum

3. Spectrum Graph of intensity versus wavelength or frequency Intensity Energy per unit area per unit time Unit of intensity is

5. Spectrum of sunlight striking the atmosphere and surface of the Earth

6. The fraction of light reflected from the surface of the Earth is called the albedo of the Earth

8. The sunlight strikes the earth on just one side as shown. Thus the total power being absorbed, Pabs, on the earth is Iabs times the area of a circle whose radius is the radius of the earth, Pabs = Iabs(  R 2 ), where R is the radius of the earth.

9. The amount of power being radiated away, P rad , is P rad = I rad (4  R 2 ), where I rad is the intensity being emitted in units of kW/m 2 . Since there is thermal equilibrium, P abs = P rad or I abs (  R 2 ) = I rad (4  R 2 ).

10. Dividing through by  R 2 yields I rad = I abs /4. The Stefan-Boltzmann law for a blackbody says I rad =  T 4 , where T is the temperature of the blackbody and  is the Stefan-Boltzmann constant (  = 5.67x10 -8 W/m 2. K 4 ).

11. Substituting yields  T 4 = I abs /4 = 959 W/m 2 /4 = 240 W/m 2 Or T = 255 K = -18 o C