Vibrational Temperature

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

θ_{vib} = \frac{h \tilde{ν} c}{k_{B}} = \frac{h ν}{k_{B}}

where $k_{B}$ is the Boltzmann constant, $c$ is the speed of light, $\tilde{ν}$ 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	$\tilde{ν}$	$θ_{v i b}$
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

Vibrational Temperature

References

See also