Two selective emitter with different absorption dependence on

frequency do not violate laws of thermodynamics. Temperature

linked strictly only with the ideal BBR emitter. Nonideal emitter means

no discussion on temperature.

My guess is:

When the temperature is low, there is a higher amount of CO2 at the low energy level, and the spectrum of the blackbody radiating outward from point A includes the absorption spectrum of CO2. Emissivity1

Seems like your experimental setup does not satisfy the requeriment for a blackbody.

1. A small cavity to allow incident radiation to enter, but a very low probability to get out. OK

2. In the Kirchoff theory it is assumed all the energy is redistribuited among all internal degrees of freedom, then the system should have an almost continuum absorption spectra, under these conditions the blackbody radiation does not depend on the material it is made. In your case, the system has a discrete absorption spectra and then it has memory, thats why the spectra emited depends on the gas contained.

3. If the energy is high enough, I should espect an envelope over the CO2 outward spectra, and the envelope follows the Planck formula.

The blackbody cavity filled with CO₂ gas. This situation introduces additional complexities to the standard blackbody radiation model, which is typically based on an idealized cavity with no interactions with gases or other materials inside it. Here are some points to consider:

Blackbody Radiation and Planck's Law

• Ideal Blackbody: An ideal blackbody absorbs all incident radiation and re-emits it according to Planck's law, which depends only on the temperature of the blackbody and is independent of the material.
• Planck's Formula: For an ideal blackbody at temperature TTT, the spectral radiance B(ν,T)B(\nu, T)B(ν,T) is given by: B(ν,T)=8πν2c3hνehν/kT−1B(\nu, T) = \frac{8 \pi \nu^2}{c^3} \frac{h \nu}{e^{h \nu / k T} - 1}B(ν,T)=c38πν2​ehν/kT−1hν​where ν\nuν is the frequency, ccc is the speed of light, hhh is Planck's constant, and kkk is Boltzmann's constant.

Influence of CO₂ Gas in the Cavity

• Absorption and Emission Lines: CO₂ molecules have specific absorption and emission lines in the infrared region due to their vibrational and rotational transitions.
• Non-Ideal Spectrum: The presence of CO₂ gas means that the radiation spectrum will show characteristic absorption and emission lines superimposed on the blackbody spectrum. These spectral lines correspond to the specific energy level transitions of the CO₂ molecules and deviate from the continuous spectrum predicted by Planck's law.

Modified Spectrum

• Characteristic Spectrum of CO₂: The spectrum will contain peaks (emission lines) and dips (absorption lines) at wavelengths corresponding to the vibrational and rotational transitions of CO₂ molecules. This modified spectrum does not match the continuous blackbody spectrum given by Planck's law.
• Thermal Equilibrium: If the CO₂ gas and the cavity walls are in thermal equilibrium, the gas molecules will emit and absorb radiation in a way that can still be described by Planck's law at a macroscopic level, but with the detailed structure of the CO₂ spectrum visible.

Understanding the Deviation

• Spectral Lines Impact: The deviations from the Planck spectrum are due to the discrete energy levels of CO₂ molecules. These deviations manifest as specific spectral lines, which are not accounted for in the ideal blackbody radiation model.
• Line Broadening: In real situations, these lines may also be broadened due to various effects such as Doppler broadening and pressure broadening, which can further modify the observed spectrum.