Thermodynamic functions/quantitie

In Chapter 2 we discuss briefly the thermodynamic functions whereby the abstract fugacities are related to the measurable, real quantities temperature, pressure, and composition. This formulation is then given more completely in Chapters 3 and 4, which present detailed material on vapor-phase and liquid-phase fugacities, respectively. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

Other thermodynamic functions can be computed from these quantities. This is still not an ideal way to compute properties due to the necessity of accounting for all energy states of the system in order to obtain Q. 

The first law of thermodynamics states that energy is conserved that, although it can be altered in form and transferred from one place to another, the total quantity remains constant. Thus, the first law of thermodynamics depends on the concept of energy but, conversely, energy is an essential thermodynamic function because it allows the first law to be formulated. This couphng is characteristic of the primitive concepts of thermodynamics. 

Figure 4.16 demonstrates that thermodynamic functions are not very exciting. That is, no unusual changes or effects occur. But these functions are very useful in calculating the thermodynamic quantities ArV, Ar//, ArG,... for a chemical reaction. When the reaction is written as,f... 

Another distinction that we make among the thermodynamic functions is to describe p, V, T, U, and 5 as the fundamental properties of thermodynamics. The other quantities, H, A, and G are derived properties, in that they are defined in terms of the fundamental properties, with... 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

The contribution of the transition to the thermodynamic functions can be evaluated once the coefficients B and d have been determined. Experimental determination of the transition temperature and one additional thermodynamic quantity at one specific temperature is sufficient to describe the transition thermodynamically using this model. 

Entropy, which has the symbol S, is a thermodynamic function that is a measure of the disorder of a system. Entropy, like enthalpy, is a state function. State functions are those quantities whose changed values are determined by their initial and final values. The quantity of entropy of a system depends on the temperature and pressure of the system. The units of entropy are commonly J K1 mole-1. If S has a ° (5°),... 

The defect interaction energies appearing in Eq. (33) are, for the purposes of the present article, assumed to be known either from theory or experiment. Certain other quantities appear in the final expressions for the thermodynamic functions and must therefore be known. The quantity defined by the relation... 

It is this last characteristic that is used most frequently in testing thermodynamic functions for exactness. If the differential li/ of a thermodynamic quantity J is exact, then J is called a thermodynamic property or a state function. 

Local association of the reduced cation and the oxygen vacancy is clearly suggested by the thermodynamics of the hypo-stoichiometric mixed oxides (Ui yPUy)02 x, where the thermodynamic functions do not depend on x and y separately, but rather on a quantity, called plutonium valence , which contains the ratio x/ y73,87) Q sters consisting of this association have been proposed in order to explain the thermodynamics of actinide hypostoichiometric dioxides. 

The quantities G, //, and S are called extensive thermodynamic functions because the magnitude of the quantity in each case depends on the amount of substance in the system. The change in Gibbs free energy under addition of unit concentration of component / at constant concentrations of the other components is called the partial Gibbs free energy of the /-component, i.e., the chemical potential of the /-component in the system. The chemical potential is an intensive thermodynamic quantity, like temperature and concentrations. The formal definition is... 

A variety of other thermodynamic functions may be evaluated from this. For example, the chemical potential — the quantity equalized in equilibrium calculations — of species / in a multi-component system is given by... 

The determination of the thermodynamic functions of individual components in a multicomponent system is based either on the total molar thermodynamic quantity (1) as in Equation 1... 

So far, in this discussion we have considered mechanical properties of the gas (in the sense of classical mechanics) that involve m and v. Nonmechanical properties are quantities like the temperature and thermodynamic functions. We can begin to make a connection between the two by comparing Eq. 8.6 with the ideal gas law pV = nRT. Equating the two, we obtain the kinetic theory result... 

The final set of thermodynamic quantities to illustrate is the entropy, also listed in Table 8.1. The largest contribution by far is from translation, calculated from Eq. 8.106. The portion of the entropy attributable to rotational and vibrational degrees of freedom are calculated by Eqs. 8.108 and 8.109, respectively. The electronic contribution to S from Eq. 8.101 is large (certainly relative to the role it played for the other thermodynamic functions just considered), 5.763 (= R In 2, from the ground-state degeneracy contribution) J/mole-K. Thus the net value of S at 298.15 K is calculated to be 198.542 J/mole-K, com-... 

Detailed analysis of the results published by Casper and Schulz 2) and measurements with the new chromatograph mentioned above 3) have shown that irrevesible thermodynamics, including two different kinetic effects, has to be applied to explain the resolution of the PDC-column 4 5 9) and to obtain the MWD of narrowly distributed polystyrene samples 6 8). In this way, not only the MWD is obtained, but also kinetic constants and thermodynamic functions of the polymer transfer between sol and gel, as well as hydrodynamic and kinetic spreading parameters of the system investigated, can be calculated from PDC-measurements performed at different constant column temperatures, with the same sample injected. The usual static quantities (such as the exponent of the partition function, ratio of the gel/sol volumes, etc.) proposed by Casper and Schulz can then be obtained by extrapolating the results to the theta temperature of the system. In addition, spreading phenomena alone can directly be... 

There are two interpretations of the statistical quantity A, both being closely related to the geometrical interpretation of the term phase boundary . From a purely macroscopic point of view, the gel of course represents a phase to which thermodynamical functions of state are related. Nevertheless, such a macroscopic image with a sharp boundary can hardly be correct in a PDC-column considering the range of end-to-end distances of the transported coils in the concentration profile, because the transported P-mer and the stationary gel are chemically equal in PDC. The two possible definitions of the quantity A(P) are ... 

The thermodynamic functions of transfer of individual ions cannot, of course, be studied experimentally, since only complete electrolytes are thermodynamic components, so that an extrathermodynamic assumption is needed in order to split the measurable quantity into the contributions from the individual ions. A commonly employed assumption is that for a reference electrolyte with large, univalent, nearly spherical cation and anion of nearly equal sizes the measured... 

The thermodynamic functions for the gas phase are more easily developed than for the liquid or solid phases, because the temperature-pressure-volume relations can be expressed, at least for low pressures, by an algebraic equation of state. For this reason the thermodynamic functions for the gas phase are developed in this chapter before discussing those for the liquid and solid phases in Chapter 8. First the equation of state for pure ideal gases and for mixtures of ideal gases is discussed. Then various equations of state for real gases, both pure and mixed, are outlined. Finally, the more general thermodynamic functions for the gas phase are developed in terms of the experimentally observable quantities the pressure, the volume, the temperature, and the mole numbers. Emphasis is placed on the virial equation of state accurate to the second virial coefficient. However, the methods used are applicable to any equation of state, and the development of the thermodynamic functions for any given equation of state should present no difficulty. 

The thermodynamic functions have been defined in terms of the energy and the entropy. These, in turn, have been defined in terms of differential quantities. The absolute values of these functions for systems in given states are not known.1 However, differences in the values of the thermodynamic functions between two states of a system can be determined. We therefore may choose a certain state of a system as a standard state and consider the differences of the thermodynamic functions between any state of a system and the chosen standard state of the system. The choice of the standard state is arbitrary, and any state, physically realizable or not, may be chosen. The nature of the thermodynamic problem, experience, and convention dictate the choice. For gases the choice of standard state, defined in Chapter 7, is simple because equations of state are available and because, for mixtures, gases are generally miscible with each other. The question is more difficult for liquids and solids because, in addition to the lack of a common equation of state, limited ranges of solubility exist in many systems. The independent variables to which values must be assigned to fix the values of all of the... 

In the previous sections concerning reference and standard states we have developed expressions for the thermodynamic functions in terms of the components of the solution. The equations derived and the definitions of the reference and standard states for components are the same in terms of species when reactions take place in the system so that other species, in addition to the components, are present. Experimental studies of such systems and the thermodynamic treatment of the data in terms of the components yield the values of the excess thermodynamic quantities as functions of the temperature, pressure, and composition variables. However, no information is obtained concerning the equilibrium constants for the chemical reactions, and no correlations of the observed quantities with theoretical concepts are possible. Such information can be obtained and correlations made when the thermodynamic functions are expressed in terms of the species actually present or assumed to be present. The methods that are used are discussed in Chapter 11. Here, general relations concerning the expressions for the thermodynamic functions in terms of species and certain problems concerning the reference states are discussed. 

The energy and entropy functions have been defined in terms of differential quantities, with the result that the absolute values could not be known. We have used the difference in the values of the thermodynamic functions between two states and, in determining these differences, the process of integration between limits has been used. In so doing we have avoided the use or requirement of integration constants. The many studies concerning the possible determination of these constants have culminated in the third law of thermodynamics. 

The affinity of irreversible processes is a thermodynamic function of state related to the creation of entropy and uncompensated heat during the processes. The second law of thermodynamics indicates that all irreversible processes advance in the direction of creating entropy and decreasing affinity. This chapter examines the property affinity in chemical reactions and the relation between the affinity and various other thermodynamic quantities. 

In conclusion, the partial molar quantity in thermodynamics functions consists of its unitary term and its mixing term as shown above. 

Furthermore, in analogy to the partial molar quantities of thermodynamic functions, the partial molar chemical exergy, echem l, can be defined for a substance i in a gaseous mixture, in a liquid solution, and in a solid solution as shown in Eq. 10.35 ... 

The enthalpy change AH, being an important thermodynamic function of state, is identical with the negative value of the heat of reaction (Qp), when the reaction proceeds under constant pressure in a purely chemical way (e. g. in a calorimeter), the A// = — Qp. The quantity AH expresses, therefore, the value of the total energy set free or absorbed during a reaction proceeding under constant pressure. 

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