title: Vibrational temperature
text: # 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 |
  