# Kirchhoff’s Law 2

Kirchhoff’s Law states that for a blackbody emissivity = absorptivity. In our wave equation with small damping as a model of blackbody in radiative equilibrium with an exterior forcing, this is built into the model for frequencies below high-frequency cut-off.

This is because for these frequencies the outgoing radiation simply reproduces the part of the incoming radiation which is not reflected. Or put differently: In radiative equilibrium there is below cut-off no distinction between incoming radiation and outgoing radiation as explained in the previous post.

However, if the incoming waves (the forcing) contain frequencies above the present cut-off  of the absorbing body, then the game changes, as these frequencies contribute to the internal energy of the body increasing its temperature and are not (re-)emitted. This is a case with positive absorptivity and zero emissivity of the frequencies above cut-off.

This leads to coefficients of absorptivity depending on temperature, which complicates the picture.

The effect is that different bodies with different cut-off at the same distance to the Sun, can take on different equilibrium temperatures, as evidenced in e.g. Satellite Thermal Control Engineering and What Is the Temperature of Space?

## 2 thoughts on “Kirchhoff’s Law 2”

1. I think you have Kirchhoff’s law slightly wrong but that does not change the out come of your thoughts.
In Perry’s Chemical Engineering Handbook P5-25 it states “According to Kirchhoff’s law the emissivity and absorptivity of a surface, in surroundings at its own temperature, are the same for both monochromatic and total radiation.” Black body is not mentioned, the surface can be a gray body. The key words are “in surroundings at its own temperature”. Absorptivity and emissivity can be different. Absorptivity is associated with a source which is at a higher temperature and has different wavelength of emitted radiation than the absorbing surface which emits at its temperature to a surface or absorbing media at lower temperature.
There are no black bodies so you should forget about that. The sun is not a black body as shown by its emitting spectrum. In fact no one knows the diameter or area of the sun’s surface at its core. No one knows the temperature of the core. The visual projection of the sun is a representation of the outer part of its atmosphere which absorbs energy from its core and emits radiation at some other temperature.. Outside that, it appears that there is an even hotter corona of sub-atomic particles associated with very high energy.
Getting back to heat transfer,I suggest that you read the Chapter 5 of Perry’s Chemical Engineering Handbook and particularly the section “Heat Transfer by radiation” starting at 5-23. I have no objection to the use of the words “cut-off frequency or wavelength” For engineers who have experience with combustion and radiation in plant it is unnecessary. Net heat, like electricity only flows in one direction -from high potential to low potential and, if there is no potential difference, there is no flux. Maybe I am wrong but if you you describe your theory in engineering terms (which have been used by practical engineers for over 100 years) than maybe more will see the “light” although I have some doubt about brain washed so-called climate scientist who appear not to understand technology.