The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as θ v i b = h ν k B {displaystyle heta _{vib}={frac {h u }{k_{B}}}} where k B {displaystyle k_{B}} is Boltzmann's constant, and ν {displaystyle u } (Greek letter nu) is the characteristic frequency of the oscillator. The vibrational temperature is used commonly when finding the vibrational partition function. Statistical thermodynamics University Arizona