# Vibrational temperature

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

${\displaystyle \theta _{vib}={\frac {h\nu }{k_{B}}}}$

where ${\displaystyle k_{B}}$ is Boltzmann's constant

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

Molecule ${\displaystyle {\tilde {v}}}$(cm−1) ${\displaystyle \theta _{vib}}$ (K)
N2 2446 3521
O2 1568 2256
F2 917 1320
HF 4138 5957
HCl 2991 4303

## References

Statistical thermodynamics University Arizona