The characteristic rotational temperature (θR or θrot) is commonly used in statistical thermodynamics, to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties. It has units of temperature and is defined as
where B is the rotational constant, and is a molecular moment of inertia. Also h is the Planck constant, c is the speed of light, ħ = h/2π is the reduced Planck constant and kB is the Boltzmann constant.
The physical meaning of θR is as an estimate of the temperature at which thermal energy (of the order of kBT) is comparable to the spacing between rotational energy levels (of the order of hcB). At about this temperature the population of excited rotational levels becomes important. Some typical values are 88 K for H2, 15.2 K for HCl and 0.561 K for CO2.
- P. Atkins and J. de Paula "Physical Chemistry", 9th edition (W.H. Freeman 2010), p.597