Vibrational temperature
# Vibrational temperature

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

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

where $k_{B}$ is Boltzmann's 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}}$$(cm^{−1})$ | $\theta _{vib}$ (K) |
| - | - | - |
| $N_2$ | 2446 | 3521 |
| $O_2$ | 1568 | 2256 |
| $F_2$ | 917 | 1320 |
| HF | 4138 | 5957 |
| HCl | 2991 | 4303 |
