Vibrational temperature

The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as [math]\displaystyle{ \theta _{vib}= \frac {h \tilde{\nu} c}{k_{B}} = \frac{h\nu}{k_B} }[/math]

where [math]\displaystyle{ k_B }[/math] is Boltzmann's constant, [math]\displaystyle{ c }[/math] is the speed of light, and [math]\displaystyle{ \nu }[/math] (Greek letter nu) is the characteristic frequency of the oscillator.

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

Molecule | [math]\displaystyle{ \tilde{v} }[/math](cm−1) | [math]\displaystyle{ \theta_{vib} }[/math] (K)

|
|

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

## References

Statistical thermodynamics University Arizona

## See also

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

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