Vibrational temperature

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, $\tilde{\nu }$ is the wavenumber, 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	$\tilde{\nu }$	${\theta }_{vib}$
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

See also

• Rotational temperature
• Rotational spectroscopy
• Vibrational spectroscopy
• Infrared spectroscopy
• Spectroscopy