The document discusses the equilibrium temperature of the Earth using concepts from the electromagnetic spectrum and solar energy absorption. It calculates the absorbed solar intensity and the equilibrium temperature, concluding that the Earth's temperature is approximately 255 K (-18 °C). The albedo effect, the solar constant, and the Stefan-Boltzmann law are key components of this analysis.

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

7. Simple Calculation to Determine the Equilibrium Temperature of the Earth The intensity from the sun that reaches the outer atmosphere of the earth is called the solar constant. The solar constant is equal to 1.37 kW/m 2 . The albedo, a, of the earth is usually taken to be 0.3 which means that 30% of the sunlight is reflected. Thus the intensity, Iabs, absorbed by the earth is Iabs = (1-a)1.37 = 0.7x1.37 = 0.959 kW/m 2.

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