Saturday, December 27, 2008

Stephan-Boltzmann Equation

Here is a beautiful photograph of our planet. The climate of earth is what makes it our home and able to support all of us. Water dominates the climate as it covers most of the surface. As a liquid it readily absorbs sunlight, but at both low and high temperatures it changes into a state that reflects more sunlight.

After energy from sunlight is absorbed, it must be removed from the earth. If it didn't then the earth would become too hot. If too much sunlight were reflected or the atmosphere did not abosrb sunlight, then the earth would become cold and the oceans would freeze.

The overall temperature of the earth is governed by physical science. The applicable physical laws existed before humans gave them names. The basic equation for the climate of Earth is the Stephan-Boltzamm law which states that temperature is proportional to the forth power of the amount of radiation energy:

Surface Temperature (Kelvin) = Constant * Radiation Energy^0.25 Stephan-Boltzmann Constant = 5.6704 x 10^-8 Watt/m^2 K^2 Radiation Energy (watts/meter^2)

The amount of Radiation Energy is a function of Total Solar Irradiance (TSI), how much is not reflected (1-albedo) and how easily energy is emitted (emissivity).

Radiation Energy = TSI * Fraction not reflected * Emissivity

Total Solar Irradiance (typically 1365.5 Watts/second-meter^2) Albedo (unitless, typically 0.3 for earth) Emissivity (unitless, tpically 0.81)

Combining both equations together with typical values yields:

Surface Temperature = 287K = 14.3 C = 57.5 F

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