Does emission depend linearly on concentration?

[nordmoon]

Is it possible to find out the relative concentration of c02 by looking at the emission or absorption from a hot gas, T = 1000K, containing among other C02? What I want to find out is if the emission depends linearly on the concentration. (in the IR region)

What theoretically equations may I used to find this out? I have been looking at literature of Radiative transfer but I do see how this can be possible. I have data from the hitran database (giving wavelength, intensity (or equivalent width), Einstein coeff, statistical weights, FWHM, lower level energy and such)

Does anyone know?

 

[sylas]

Is it possible to find out the relative concentration of c02 by looking at the emission or absorption from a hot gas, T = 1000K, containing among other C02? What I want to find out is if the emission depends linearly on the concentration. (in the IR region)

What theoretically equations may I used to find this out? I have been looking at literature of Radiative transfer but I do see how this can be possible. I have data from the hitran database (giving wavelength, intensity (or equivalent width), Einstein coeff, statistical weights, FWHM, lower level energy and such)

Does anyone know?

I am not totally sure, but I don't think it will have a strong dependence on concentration beyond a certain point. Once the gas is optically thick, you'll have a kind of radiative equilibrium within the volume, and thermal emissions will only escape from outer edges of your volume. The total power of emission will then be a function of temperature and surface area of the volume. As concentration drops, the optical depth changes to give, I guess, a smaller effective radiating surface. As you become optically thin, I guess it thermal emissions will become linear with concentration of the gases.

I'm thinking out loud here. If I get better info I'll correct myself. Don't take this as gospel, but as an aspect of the problem that might be worth thinking about.

Different gases have different emissivity spectra, of course, and that's going to alter the relationship between optical depth and concentration. Some gases will shed energy more efficiently at 1000K than others, but I don't know where CO2 stands on that.

Cheers -- Sylas

 

[charng]

I can provide an answer to your question. The relationship between emission and concentration does not necessarily depend linearly on each other. In fact, it is more common for the relationship to be logarithmic, meaning that as concentration increases, the emission increases at a decreasing rate. This is known as the Beer-Lambert Law, which states that the absorption or emission of a substance is directly proportional to its concentration.

To determine the relative concentration of CO2 by looking at emission or absorption from a hot gas, you can use the Beer-Lambert Law in combination with the known properties of CO2, such as its absorption spectrum in the infrared region. This can be done through radiative transfer calculations, which take into account the absorption and emission properties of the gas and the temperature of the system.

Other equations that can be used to determine the emission-concentration relationship include the Boltzmann distribution and the Planck's Law of blackbody radiation. However, these equations may not be as applicable to your specific situation and may require additional information and calculations.

In order to determine the emission-concentration relationship for CO2, you can use the data from the hitran database that you mentioned. This database contains information on the spectral properties of various gases, including CO2. By using this data and applying the appropriate equations, you can determine the relationship between emission and concentration for CO2 in the infrared region.

I hope this information helps you in your research. Keep in mind that the relationship between emission and concentration may vary depending on the specific conditions and properties of the gas being studied. It is always important to carefully consider the equations and data being used in order to accurately determine this relationship.