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What are some qualitative guidelines one should know regarding the temperature dependencies (of the gas and maybe the radiation, if that makes sense) for an absorption spectroscopy measurement?

How does, for example, a rise in temperature influence the absorption lines?

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I am aware of one effect: doppler broadening. When the temperature increases, the speed distribution spreads out. That spreads out the distribution of the velocity component in the direction of your light source. The light the particles see from the light source then get red- or blue-shifted relative to what actually comes out of the source. So the particle population ends up absorbing a broader range of wavelengths than it did at a lower temperature. The effect is $\Delta\lambda/\lambda_0 \propto \sqrt{T/m}$

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Temperature will change the population of the different states of the molecule, particularly the rotational states (i.e. in temperatures in ranges that are easily reached in the lab/ some factor around 300 K).

This will affect the intensity of the respective absorption lines in rotational (or rot.-vib.) spectra and therefore the hull shape of the P and Q branches will change

I just found example applets: http://rkt.chem.ox.ac.uk/tutorials/rotation/rot_spectra.html

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