Stefan-Boltzmann Law

            Blackbodies are purely hypothetical bodies—they do not exist in nature—that emit the maximum possible radiation at every wavelength. The single factor that determines how much energy a blackbody radiates is its temperature. Although, the amount of radiation emitted by an object is not linearly proportional to its temperature which is where the Stefan-Boltzmann law comes into play. The blackbody version of the Stefan-Boltzmann law expresses that the intensity of energy radiated by a blackbody increases according to the fourth power of its absolute temperature.

I = σT⁴

where I denotes the intensity of radiation in watts per square meter, σ (Greek lowercase sigma) is the Stefan-Boltzmann constant (5.67 × 10−8 watts per square meter per K4), and T is the temperature of the body in kelvins.

            At any rate due to the fact that blackbodies do not exist in nature most liquids and solids can be treated as graybodies, meaning they emit some percent of the maximum amount of radiation possible at a given temperature. Which brings us to the graybody version of the Stefan-Boltzmann law that includes the emissivity factor, meaning that the electromagnetic energy emitted by any graybody will be some fraction of what would be emitted by a blackbody.

I = ƐσT⁴

That percent of energy radiated by a substance relative to that of a blackbody is considered emissivity (ε), ranging from just above zero to just below 100 percent. However, the atmosphere is an exception to this because emission depends on a number of factors (i.e. the amount of water vapor and other gases in the air). Still, we can say that the atmosphere is not a perfect emitter of radiation because it emits less radiation at any particular temperature than would a blackbody.