THE AVERAGE TEMPERATURE OF THE EARTH. The Earth is definitely not a blackbody; c
ID: 1469250 • Letter: T
Question
THE AVERAGE TEMPERATURE OF THE EARTH.
The Earth is definitely not a blackbody; clouds, greenhouse gases, ground features, oceans, snow and ice all affect both the absorption of solar radiation and the emission of (thermal) EM radiation into space in all directions. Currently, all the complex effects combine to give a global average surface temperature of about 14.6degree C However, you can get a simple estimate for the equilibrium surface temperature by finding out for what temperature the emitted power (given by the Stefan-Boltzmium equation) is equal to the absorbed power from sunlight hitting the Earth. Use the intensity of sunlight above the atmosphere, and assume that the absorption efficiency is equal to the emissivity epsilon, so that factor is the some on both sides of the equation. You should end up with a temperature which is not too far from the actual global average temperatureExplanation / Answer
The amount of solar power that would fall on a spherical body, e.g., earth, would be equal to the cross-sectional area of the planet times the solar constant S0
Thus
S0R2 -------------(1)
For a blackbody, according to the Stefan-Boltzman Law, the amount of energy emitted is
4R2T4 ------------------------(2)
If the planet is in a state of equilibrium, neither heating nor cooling, the energy absorbed must be in equilibrium with the energy radiated or emitted. In mathematical terms, expression (1) must equal expression (2)
S0R2= 4R2T4
T = (S0/4)^1/4 = [(1350)/(4*5.67*10^-8)]^1/4 =277.8 = 278 K
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