Vibrational temperature

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

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

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

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