Vibrational temperature

The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as

θvib=hν~ckB=hνkB

where kB is the Boltzmann constant, c is the speed of light, ν~ is the wavenumber, and ν (Greek letter nu) is the characteristic frequency of the oscillator.

The vibrational temperature is used commonly when finding the vibrational partition function.

Molecule | ν~ | θvib

|
|

N2 | 2446 cm−1 | 3521 K
O2 | 1568 cm−1 | 2256 K
F2 | 917 cm−1 | 1320 K
HF | 4138 cm−1 | 5957 K
HCl | 2991 cm−1 | 4303 K

## References

* Statistical thermodynamics University Arizona

## See also

* Rotational temperature
* Rotational spectroscopy
* Vibrational spectroscopy
* Infrared spectroscopy
* Spectroscopy

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