Thermodynamic properties concepts

The concept of equilibrium is central in thermodynamics, for associated with the condition of internal eqmlibrium is the concept of. state. A system has an identifiable, reproducible state when 1 its propei ties, such as temperature T, pressure P, and molar volume are fixed. The concepts oi state a.ndpropeity are again coupled. One can equally well say that the properties of a system are fixed by its state. Although the properties T, P, and V may be detected with measuring instruments, the existence of the primitive thermodynamic properties (see Postulates I and 3 following) is recognized much more indirectly. The number of properties for wdiich values must be specified in order to fix the state of a system depends on the nature of the system and is ultimately determined from experience. 

The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

What Are the Key Ideas Equilibrium between two phases is reached when the rates of conversion between the two phases are the same in each direction. The rates are equal when the molar Gibbs free energy of the substance is the same in each phase and therefore there is no tendency to change in either direction. The same concepts apply to the dissolving of a solute. The presence of a solute alters the entropy of a solvent and consequently affects its thermodynamic properties. 

The Boltzmann constant is represented by kB. It is more difficult to use Monte Carlo methods to investigate dynamic events as there is no intrinsic concept of time but an ensemble average over the generated states of the system should give the same equilibrium thermodynamic properties as the MD methods. A good review of both MD and the Monte Carlo methods can be found in the book by Frenkel and Smit [40]. 

Since the interplay of theory and experiment is central to nearly all the material covered in this chapter, it is appropriate to start by defining the various concepts and laws needed for a quantitative theoretical description of the thermodynamic properties of a dilute solid solution and of the various rate processes that occur when such a solution departs from equilibrium. This is the subject matter of Section II to follow. There Section 1 deals with equilibrium thermodynamics and develops expressions for the equilibrium concentrations of various hydrogen species and hydrogen-containing complexes in terms of the chemical potential of hy-... 

Finally, the whole concept of using macroscopic (i.e. thermodynamic) properties to derive a microscopic picture of the adsorbed water is open to question (1, 8.). 

It has already been noticed (see 3.9.4) that according to the mentioned concepts several ternary compounds may be considered as the result of a sort of structural interaction between binary compounds. As a consequence some regular trend could also be predicted for their occurrence in their phase diagrams and in the description (and perhaps modelling) of their thermodynamic properties. A few details about this type of structural relationships will be considered in the following and, in this introduction, examples of blocks of simple structural types and of their combination in more complex types will be described. 

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

The book begins with a chapter describing the history and growth of CALPHAD. This provides a useful point of departure for a more detailed account of the various strands which make up the CALPHAD approach. Chapters 3 and 4 then deal with the basic thermodynamics of phase diagrams and the principles of various experimental techniques. This is because one of basic pillars of the CALPHAD approach is the concept of coupling phase diagram information with all other available thermodynamic properties. It is a key factor in the assessment and characterisation of the lower-order systems on which the properties of the higher-... 

It must always be remembered that optimisation is not an exact science and, therefore, it is sometimes difficult to define confidence limits in the final optimised values for the coefficients used in the thermodynamic models. The final outcome is at least dependent on the number of experimental measurements, their accuracy and the ability to differentiate between random and systematic errors. Concepts of quality can, therefore, be difficult to define. It is the author s experience that it is quite possible to have at least two versions of an optimised diagram with quite different underlying thermodynamic properties. This may be because only experimental enthalpy data were available and different entropy fiinctions were chosen for the different phases. Also one of the versions may have rejected certain experimental measurements which the other version accepted. This emphasises the fact that judgement plays a vital role in the optimisation process and the use of optimising codes as black boxes is dangerous. 

It was also observed, in 1973, that the fast reduction of Cu ions by solvated electrons in liquid ammonia did not yield the metal and that, instead, molecular hydrogen was evolved [11]. These results were explained by assigning to the quasi-atomic state of the nascent metal, specific thermodynamical properties distinct from those of the bulk metal, which is stable under the same conditions. This concept implied that, as soon as formed, atoms and small clusters of a metal, even a noble metal, may exhibit much stronger reducing properties than the bulk metal, and may be spontaneously corroded by the solvent with simultaneous hydrogen evolution. It also implied that for a given metal the thermodynamics depended on the particle nuclearity (number of atoms reduced per particle), and it therefore provided a rationalized interpretation of other previous data [7,9,10]. Furthermore, experiments on the photoionization of silver atoms in solution demonstrated that their ionization potential was much lower than that of the bulk metal [12]. Moreover, it was shown that the redox potential of isolated silver atoms in water must... 

The goal here is to provide a systematic, if streamlined, derivation of the quantities of interest using statistical thermodynamics. These concepts are outside the range of topics usually considered in mechanical engineering or chemical engineering treatments of fluid flow. However, the results are essential for understanding and estimating the thermodynamic properties that are needed. 

The property concept may appear so generic as not to require special attention. However, for thermodynamic purposes, the considered set of properties differs significantly from that in other areas of science. Allowed thermodynamic properties are closely tied to specific experimental circumstances of the chosen system, including its quiescence and stability, and a number of the variables that are commonly assumed in a Newtonian mechanical description (such as position and momentum) play no thermodynamic role. The following definition may be adopted ... 

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

For the diligent reader, thermochemical conventions are well-discussed in D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney and R. L. Nuttall, The NBS Tables of Chemical Thermodynamic Properties Selected Valuesfor Inorganic and C, and C2 Organic Substances in SI Units , J. Phys. Chem. Ref. Data, 11 (1982), Supplement 2. However, the various subtleties expressed in this source, such as the above-cited ambiguities in temperature and pressure, have but negligible effect on any of the conclusions about cyclopropane and its derivatives in this chapter the data are too inexact and the concepts we employ are simply too sloppy to be affected. 

EQUATION OF STATE. Alsu called characterisin ci/tniinni. a relation, empirical or derived, between thermodynamic properties of a substance or system. The equation of stale must be single-valued in terms of its variables This is a direct consequence >r the concept of state. 

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