LECTURE TEXT Orientation polarization and hindered rotation in the view of thermodynamics Walter Langel 1 Received: 4 September 2017 / Accepted: 13 October 2017 Ó Springer International Publishing AG 2017 Abstract 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. Keywords Orientation polarization  Hindered rotation  Partition function  Entropy of vaporization  Specific heat  Heat capacity of water Introduction The orientation polarization of an electric dipole in an external field is derived in several textbooks [1–4] by the so- called Langevin treatment. The average component of the dipole moment l z  parallel to the electric field E in z-di- rection is calculated, and the corresponding orientation polarization P orient is obtained by dividing this dipole moment by the volume V 1 of the partially oriented molecule. Findenegg and Hellwege [4] showed that the partition function of the polar gas molecule in the electric field was the product of the classical rotational partition function for the kinetic energy q kin and of q pot for the potential energy. Here, it is shown that the dedicated calculation of the average dipole moment parallel to an external field and the polarization is a special case of evaluating the partition function q pot of this system under appropriate assumptions. This q pot gives access to thermodynamic functions inac- cessible in the common approach. The paper is organized as follows: First, the Langevin treatment is reviewed, then the partition function q pot is introduced. The internal potential energy is derived from that and it is shown that this results in the same expression for the polarization as the textbook approach. Then, the entropy loss and the specific heat gain are deduced and the implications for the properties of liquids are discussed. The conclusion compiles the advantages of the present approach with respect to the standard evaluation of the dipole orientation. Langevin treatment The Langevin function is usually derived [1–4] for mole- cules with a permanent dipole seeing an external field. For a given orientation of the dipole l ~ with an angle H relative to the field E ~ , a potential energy DU pot ¼l ~  E ~ ¼l  E  cos H ¼ l z   E ð1Þ & Walter Langel langel@uni-greifswald.de 1 Institut fu ¨r Biochemie, Universita ¨t Greifswald, Felix- Hausdorff-Straße 4, 17489 Greifswald, Germany 123 ChemTexts (2017)3:15 DOI 10.1007/s40828-017-0053-9