- Stefan-Boltzmann's Law (1) for one blackbody gives the radiant energy from a blackbody at a certain temperature T into a receiving background at 0 K.
- Now, if we have two blackbodies, both will radiate into the same background at 0 K as if the other body was not present.
- To get the effect of the two bodies, just sum the contributions and you get (2).
söndag 6 februari 2011
Black Magic of Stefan-Boltzmann's Law for Two BlackBodies
gives the spectral radiance (flux of radiant energy) from an ideal blackbody as function of temperature T and frequency nu. Integrating over frequency gives the total radiance R as Stefan-Boltzmann's Law
with sigma a certain constant referred to as Stefan-Boltzmann's constant.
In the engineering literature the following Stefan-Boltzmann law is presented for the radiant energy exchanged between two blackbodies 1 and 2 of temperature T1 and T2:
(2) R1 = sigma T2^4 - sigma T1^4, R2= - R1 = sigma T1^4 - sigma T2^4,
where R1 is the net radiance received by body 1 and R2 that received by R2.
How is the formula (2) derived? From a Planck Law for two interacting blackbodies? No, it appears to be an ad hoc law derived by the following simple ad hoc argument:
But this is an ad hoc argument without specified physical realization of the summation, thus a black magic argument. This is the argument behind the "backradiation" from a cold atmosphere to a warm Earth surface underlying CO2 climate alarmism. Black magic.
In my new derivation of Planck's Law in Slaying the Sky Dragon, the temperature of the background enters and the radiant energy exchanged between two blackbodies is derived from basic physical principles and not from ad hoc summation without physics.
PS I don't say that (2), as a formula for the net radiative heat exchange, is wrong. What I seek is a derivation of the formula which can help understanding of the physics involved, without resorting to statistics which at least to me is not understandable.