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

\theta _{\text{vib}}={\frac {h{\tilde {\nu }}c}{k_{\text{B}}}}={\frac {h\nu }{k_{\text{B}}}}

where $k_{\text{B}}$ is the Boltzmann constant, $c$ is the speed of light, and $\nu$ (Greek letter nu) is the characteristic frequency of the oscillator.

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

Molecule	${\tilde {v}}$	$\theta _{vib}$
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

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References

See also