Solid entropy

To predict the sign of A S, look to see if the process involves a phase change, a change in the number of gaseous molecules, or the dissolution (or precipitation) of a solid. Entropy generally increases for phase transitions that convert a solid to a liquid or a liquid to a gas, reactions that increase the number of gaseous molecules, and dissolution of molecular solids or salts with +1 cations and —1 anions. 

Saberian-Broudjenni, M. Wild, G. Charpentier, J.C. Fortin, Y. Euzen, J.P. Patoux, R. Contribution a L etude Hydrodynamique Des Reacteurs a Lit Fludise Gaz-Liquide-Solide. Entropie 1984, 120, 30. 

The thermodynamic analysis for Pa in Ref. 19 represents an educated guess with no measured values, except for spectroscopic data for the gas. The choice of 12.4 for the solid entropy is an average between Th and U however, a recent though still somewhat preliminary measurement in the UK (25) on the same metal we are using indicates the value may be of the order of 13.2. This could well be the result of electronic perturbations from the first (or at least partial) 5f electron below the Fermi level. This entropy value is also shown in Fig. 4, and has moved toward the unique position of the other f-bonded actinides. 

Product solid entropy, kcal/mol K selectivity surface area, m. Selectivity of species i. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

We assume for simplicity that the adsorbed phase has the same entropy as the solid so that only an energy change is associated with the transfer of material from the bnlk to the adsorbed phase, then ... 

Hoover W G and Ree F H 1967 Use of computer experiments to locate the melting transition and calculate the entropy in the solid phase J. Chem. Phys. 47 4873-8... 

We shall assume that Cp = 0 at 7 = 0 K. We wish to obtain the absolute entropy of solid lead at 298 K. Each entry in Table 1-2 leads to a value of CpjT. The... 

Draw the curve of Cp vs. T and Cp/T vs. T from the following heat capacity data for solid chlorine and determine the absolute entropy of solid chlorine at 70.0 K... 

The tables in this section contain values of the enthalpy and Gibbs energy of formation, entropy, and heat capacity at 298.15 K (25°C). No values are given in these tables for metal alloys or other solid solutions, for fused salts, or for substances of undefined chemical composition. 

It should be noted that the methodology for a and b results in a ASf s associated with the phase change from a sohd at 0 K to the liquid at Tmit No entropy changes resulting from solid transitions are taken into account, and ASfus for a substance that undergoes such a transition will be overestimated by this technique. 

The critical size of the stable nucleus at any degree of under cooling can be calculated widr an equation derived similarly to that obtained earlier for the concentration of defects in a solid. The configurational entropy of a mixture of nuclei containing n atoms widr o atoms of the liquid per unit volume, is given by the Boltzmann equation... 

The thermodynamic properties of the solid silicates show the expected entropy change of formation from the constituent oxides of nearly zero, which is typical of the reaction type... 

To melt ice we have to put heat into the system. This increases the system entropy via eqn. (5.20). Physically, entropy represents disorder and eqn. (5.20) tells us that water is more disordered than ice. We would expect this anyway because the atoms in a liquid are arranged much more chaotically than they are in a crystalline solid. When water freezes, of course, heat leaves the system and the entropy decreases. 

Driving forces for solid-state phase transformations are about one-third of those for solidification. This is just what we would expect the difference in order between two crystalline phases will be less than the difference in order between a liquid and a crystal the entropy change in the solid-state transformation will be less than in solidification and AH/T will be less than AH/T . 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

Piezoelectric solids are characterized by constitutive relations among the stress t, strain rj, entropy s, electric field E, and electric displacement D. When uncoupled solutions are sought, it is convenient to express t and D as functions of t], E, and s. The formulation of nonlinear piezoelectric constitutive relations has been considered by numerous authors (see the list cited in [77G06]), but there is no generally accepted form or notation. With some modification in notation, we adopt the definitions of thermodynamic potentials developed by Thurston [74T01]. This leads to the following constitutive relations ... 

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