Thermodynamics equilibrium, thermodynamic description

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

Unsually short NMR T, relaxation values were observed for the metal-bonded H-ligands in HCo(dppe)2, [Co(H2)(dppe)]+ (dppe = l,2-bis(diphenylphosphino)ethane), and CoH(CO) (PPh3)3.176 A theoretical analysis incorporating proton-meta) dipole-dipole interactions was able to reproduce these 7) values if an rCo H distance of 1.5 A was present, a value consistent with X-ray crystallographic experiments. A detailed structural and thermodynamic study of the complexes [H2Co(dppe)2]+, HCo(dppe)2, [HCo(dppe)2(MeCN)]+, and [Co(dppe)2(MeCN)]2+ has been reported.177 Equilibrium and electrochemical measurements enabled a thorough thermodynamic description of the system. Disproportionation of divalent [HCo(dppe)2]+ to [Co(dppe)2]+ and [H2Co(dppe)2]+ was examined as well as the reaction of [Co(dppe)2]+ with H2. 

Statistical thermodynamic descriptions of these transitions in substitutional alloys have been developed for the cases of both binary and ternary alloys , using a simple nearest neighbor bond model of the surface segregation phenomenon (including strain energy effects). Results of the model have been evaluated here using model parameters appropriate for a Pb-5at%Bi-0.04at%Ni alloy for which experimental results will be provided below. However, the model can be applied in principle to the computation of equilibrium surface composition of any ternary solution. 

Let us first summarize the principal features of the thermodynamic equilibrium states that are the principal focus of a thermodynamic description. According to the definitions of Section 2.10, such states are ... 

It is indeed somewhat surprising that the quantity of each phase is in some sense irrelevant to thermodynamic description of the phase-transition phenomenon. Consider, for example, a 1 kg sample of pure water in equilibrium with its own vapor at, say, the normal boiling point (T = 100°C, P = 1 atm), initially with rcvap moles of vapor and nnq moles of liquid, as shown at the left ... 

The starting point for thermodynamic description, whether in the calculus-based or the geometry-based formalism, is the Gibbs fundamental equation for a given equilibrium state S. In the energy representation, this is expressed as... 

The need to abstract from the considerable complexity of real natural water systems and substitute an idealized situation is met perhaps most simply by the concept of chemical equilibrium in a closed model system. Figure 2 outlines the main features of a generalized model for the thermodynamic description of a natural water system. The model is a closed system at constant temperature and pressure, the system consisting of a gas phase, aqueous solution phase, and some specified number of solid phases of defined compositions. For a thermodynamic description, information about activities is required therefore, the model indicates, along with concentrations and pressures, activity coefficients, fiy for the various composition variables of the system. There are a number of approaches to the problem of relating activity and concentrations, but these need not be examined here (see, e.g., Ref. 11). 

Equilibrium and nonequilibrium thermodynamics can be combined to give a complete thermodynamic description of a process or process step. Equilibrium thermodynamics allows us to calculate the changes in thermodynamic properties with the change in process conditions. Nonequilibrium thermodynamics allows us to calculate unambiguously the work that is lost associated with the process taking place. It relates this loss to the process s flows and forces driving these flows and identifies the various friction factors as a function of the relationship between flows and forces. 

The intensive variables T, P, and nt can be considered to be functions of S, V, and dj because U is a function of S, V, and ,. If U for a system can be determined experimentally as a function of S, V, and ,, then T, P, and /q can be calculated by taking the first partial derivatives of U. Equations 2.2-10 to 2.2-12 are referred to as equations of state because they give relations between state properties at equilibrium. In Section 2.4 we will see that these Ns + 2 equations of state are not independent of each other, but any Ns+ 1 of them provide a complete thermodynamic description of the system. In other words, if Ns + 1 equations of state are determined for a system, the remaining equation of state can be calculated from the Ns + 1 known equations of state. In the preceding section we concluded that the intensive state of a one-phase system can be described by specifying Ns + 1 intensive variables. Now we see that the determination of Ns + 1 equations of state can be used to calculate these Ns + 1 intensive properties. 

In equilibrium, the quantity N of a given sorbate, which is absorbed on a given sorbent, depends on its partial pressure (fugacity) P in the gas phase and the temperature T. A basic phenomenological description is specification of the functional dependence between N, P, and T. Both experimental observations and theoretical or thermodynamic descriptions are often the case in univariant functional descriptions the relation between N and P at constant T (an isotherm), between N and T at constant P (an isobar), or between P and T at constant N (an isostere). 

With the establishment of conventions for the Standard State and for the reference zero value of the chemical potential, it is possible to develop fully the thermodynamic description of chemical reactions. This development relies on the concept of thermodynamic activity, introduced in Section 1.2, and on the condition for chemical equilibrium in a reaction 1,15... 

We have seen that, for each equilibrium state, the adsorptive has the same chemical potential in the gas phase and in the adsorbed phase, and that, for a given system, only two variables are required to provide a thermodynamic description of each of these phases. Consequently, there is a relation between the two intensive variables 77 andp. 

Based on the above calculations, both the free energy function (EEE) and the standard enthalpy of formation AH° (298) of NiCp were obtained, the first from its structure and normal mode of vibration by applying the harmonic-oscillator, rigid-rotator approximation, and the second from a Born-Haber thermodynamic cycle.The thermodynamic description of NiCp, together with that of the other participating compounds, permitted a second series of partial equilibrium calculations of the... 

This is the simplest explanation for the observation that when L and M have come to an equilibrium which contains these species in comparable amounts, the concentration of L decreases to near zero even while M remains at its maximal accumulation. Recent measurements of the quasi-equilibrium which develops in asp96asn bacteriorhodopsin before the delayed reprotonation of the Schiff base confirm this kinetic paradox [115]. Two M states have been suggested also on the basis that the rise of N did not correlate with the decay of M [117]. In monomeric bacteriorhodopsin the two proposed M states in series have been distinguished spectroscopically as well [115]. It is well known, however, that kinetic data of the complexity exhibited by this system do not necessarily have a single mathematical solution. Thus, assurance that a numerically correct model represents the true behavior of the reaction must come from testing it for consistencies with physical principles. It is encouraging therefore that the model in Fig. 5 predicts spectra for the intermediates much as expected from other, independent measurements, and the rate constants produce linear Arrhenius plots and a self-consistent thermodynamic description [116]. 

Here we discuss the thermodynamic description of electromagnetic radiation in equilibrium with the walls of an evacuated cavity that contains a tiny porthole for experimental observations. 

---