Orientation polarization and hindered rotation in the view of thermodynamics

The orientation polarization of dipoles in an electric field is evaluated in textbooks directly by averaging over a Boltzmann distribution yielding the Langevin function. Here, the interaction of a dipole with a field is considered as a special case of the hindered rotation in an external single fold potential. The partition function of the system is explicitly calculated first. From this function, the internal energy, and from that the polarization and the specific heat are deduced, making the lengthy Langevin treatment in standard textbooks obsolete. Additionally, the decrease of entropy by the external potential is derived from the partition function in dependence of the potential strength. The entropy loss by rotational hindering also is relevant for the phase transition from vapor to liquid. The specific heat of the hindered rotation in the liquid is higher than for the free molecule in the gas phase, and possibly also for a normal harmonic vibration. This may contribute significantly to the high specific heat of water.