The characteristic rotational temperature ( or ) is commonly used in

statistical thermodynamics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicatio ...

to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties. It has units of

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

and is defined asP. Atkins and J. de Paula "Physical Chemistry", 9th edition (W.H. Freeman 2010), p.597 :

\theta_ = \frac = \frac,

where

\overline = B/hc

is the

rotational constant In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special r ...

, is a molecular

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between ...

, is the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

, is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

and is the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...

. The physical meaning of is as an estimate of the temperature at which

thermal energy The term "thermal energy" is often used ambiguously in physics and engineering. It can denote several different physical concepts, including: * Internal energy: The energy contained within a body of matter or radiation, excluding the potential en ...

(of the order of ) is comparable to the spacing between rotational energy levels (of the order of ). At about this temperature the population of excited rotational levels becomes important. Some typical values are given in the table. In each case the value refers to the most common isotopic species.

References

See also