Monday, December 9, 2013
Let’s start out with some definitions:
Radiant Flux = F, units are in Watts (Joules/sec)
Irradiance = E, units are F per unit area (W/m^2)
Energy of a photon: h*v, where h = Planck’s Constant and v = Frequency
c*/v=lambda lambda = wavelength, c* = 3*10^8 m/s
A Blackbody is a hypothetical substance that absorbs all incident radiation and emits the max possible at all wavelengths. The relationship below is known as Planck’s Law.
When we integrate Planck’s Law, we get the Stefan-Boltzman Law. I just put the whole slide down for this one because I thought it explained a lot.
Alright, now that we have those equations established, we should get onto establishing the equation for the Earth’s radiative equilibrium. We’ve got (or at least we had) the same amount of heat coming in and coming out, and the Earth’s temperature has been staying more or less the same over the past 10,000 years. Of course, the last 50 years have NOT continued this trend, as the Earth is not in steady state and more radiation is being absorbed than emitted and we are heating up as a result.
But if we let F_i = F_o,
The emissivity is the ratio of the actual to the max possible radiation that can be emitted at wavelength lambda.
Kirchoff’s Law says that emissivity exactly equals absorptivity.
Here’s a diagram of the eart and how this stuff works.
Here are the equations to figure out the temperature of the Earth at atmosphere. a_sol was given to be .1 and a_ir was given to be .8. E was calculated using the equation earlier.
Here’s another example.