Temperature determination by IR spectroscopy

1 Determining the rotational temperature from the rotational structure of vibrational-rotational bands 

As an example let us consider a linear heteronuclear molecule of the point group such as CO. For this molecule, the degeneracy of states at the higher rotational levels (i 0) is Z/ + 1. The Boltzmann distribution function therefore leads to 

If the levels are close to each other and the temperature is not too low, the rotational partition function Q,- can be expressed by 

Hence the number of molecules in a particular level Ej depends on the absolute temperature, the value of the moment of inertia, and the actual value of J. The value of rij increases with increasing temperature and decreases with increasing/. Fig. 6.8-4 

These results are in accordance with the maxima of the thermal population of the rotational states shown in Fig. 6.8-4. This method, of course, can only be applied if the rotational lines can be obtained from the spectra. Due to the fact that the values are integers, temperature determination by equation (6.8-4) yields uncertain values, especially at higher temperatures. In principle it is possible to obtain the temperature of a sample from the intensities of distinct rotational lines or from the intensity ratio of two consecutive lines. This will be exemplified later by rotational Raman lines. 

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