Thermal energy basics

We discuss now the terms in Eq. (3.14) in detail. In order to have a maximum for the entropy we must have the right-hand side of Eq. (3.14) negative. Since the temperature occurs as a square term, the heat capacity must be positive. We can split the term T C still in a different way, namely T x C T. We can identify the term C T as a thermal energy. Basically, any energy cannot drop below zero, thus CvT > 0 and the temperature in the first factor of T x C T must be positive in a system... 

The simplest and most basic model for the diffusion of atoms across the bulk of a solid is to assume that they move by a series of random jumps, due to the fact that all the atoms are being continually jostled by thermal energy. The path followed is called a random (or drunkard s) walk. It is, at first sight, surprising that any diffusion will take place under these circumstances because, intuitively, the distance that an atom will move via random jumps in one direction would be balanced by jumps in the opposite direction, so that the overall displacement would be expected to average out to zero. Nevertheless, this is not so, and a diffusion coefficient for this model can be defined (see Supplementary Material Section S5). 

Phase change materials are used basically for the storage of thermal energy. They have a wide range of applications, including ... 

The basic principles of the thermal energy storage with phase change materials have been reviewed (101). 

Welsh suggested correctly that similar transitions take place even if the molecular pair is not bound. The energy of relative motion of the pair is a continuum. Its width is of the order of the thermal energy, Efree 3kT/2. Radiative transitions between free states occur (marked free-free in the figure) which are quite diffuse, reflecting the short lifetime of the supermolecule. In dense gases, such diffuse collision-induced transitions are often found at the various rotovibrational transition frequencies, or at sums or differences of these, even if these are dipole forbidden in the individual molecules. The dipole that interacts with the radiation field arises primarily by polarization of the collisional partner in the quadrupole field of one molecule the free-free and bound-bound transitions originate from the same basic induction mechanism. 

This monograph deals with kinetics, not with dynamics. Dynamics, the local (coupled) motion of lattice constituents (or structure elements) due to their thermal energy is the prerequisite of solid state kinetics. Dynamics can explain the nature and magnitude of rate constants and transport coefficients from a fundamental point of view. Kinetics, on the other hand, deal with the course of processes, expressed in terms of concentration and structure, in space and time. The formal treatment of kinetics is basically phenomenological, but it often needs detailed atomistic modeling in order to construct an appropriate formal frame (e.g., the partial differential equations in space and time). 

An excited molecule X can pass into the basic level again. This can be performed by radiation—i.e., by emission of the energy difference as a photon hvx—or by nonradiation by internal quenching where the energy difference is dissipated as thermal energy. Furthermore there is the possibility that the excitation energy is not dissipated by radiation but by interaction with a guest molecule Y. This interaction can be described by diffusion of excitons and/or dipole-dipole resonance. 

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