fredag 28 maj 2010
Size of Backradiation?
In Computational Blackbody Radiation I present and analyze a wave-equation model for blackbody radiation with statistical mechanics replaced by finite precision computation.
The radiative interaction of two blackbodies Body 1 and 2, can in a simplified version of this model be described as a system of the form
dT1/dt = R T2 - R T1 = R (T2 - T1), dT2/dt = R T1 - R T2 = - R (T2 - T1)
with T1 and T2 the temperatures of the two bodies (or with R T1 replaced by R T1^4 and R T2 by R T2^4 to connect to Stefan-Boltzmann's Radiation Law), and R is a radiation constant. Here the term R T2 in the equation for T1 represents heat absorbed from Body 2 while emitting R T1, and vice versa.
Adding the equations, we find the balance d(T1 + T2)/dt = 0 and conclude that T1 + T2 stays constant, irrespective of the strength R of the interaction.
This connects to the discussion in the comments to the previous post Thermodynamics of Global Climate 2 about the size of the "backradiation" from the atmosphere, which connects to the size of R in the model. Clearly, in the model you can assign any value to R, strong or weak interaction, without affecting the mean value T1 + T2.
As indicated in the above formulas, one can also view the net exchange R (T1 - T2 ) to work on the difference T1 - T2 rather the absolute values T1 and T2, which may be closer to a reality
The above argument is intended to support to the idea that "circulating radiation" and "backradiation" is fictional rather than real.