Intensive thermodynamic properties chemical potential

Two phases at the same temperature and pressure are in mutual equilibrium when the chemical potentials of each of the components are the same in the both phases. Under these conditions material from one phase can be reversibly converted to the other by the addition or removal of energy in the form of heat. The intensive thermodynamic properties of a system consisting of a single component and a single phase are functions of two independent variables. The choice of irulependent variables is arbitrary but temperature and pressure are a common choice. A system of C components and P independent phases has P(C + IJ variables. Equilibrium among the phases introduces ( C + 2J(P - ) constraints. The net number of independent variables is then A = C - P + 1, which is the well-known Gibbs phase rale. 

The chemical potentials sought are intensive properties of the system, in the usual thermodynamic language [26]. Furthermore, AUa is a quantity of molecular order of magnitude. Specifically, the AUa defined by (9.13) should be system-size independent for typical configurations of thermodynamically large systems. Because of... 

The phase rule states that, when equilibrium conditions are sustained, a minimum number of intensive properties of the (subsurface) system can be used to calculate its remaining properties. An intensive property is a property that is independent of the amount of substance in the domain. Examples of intensive properties include temperature (7), pressure (P), density (p), and chemical potential (p), which is a relative measure of the potential energy of a chemical compound. The phase rule specifies the minimum number of intensive properties that must be determined to obtain a comprehensive thermodynamic depiction of a system. 

Equation (6.35b) shows that the new intensive variable, chemical potential pi, as introduced in this chapter, is actually superfluous for the case c = 1, because its variations can always be expressed in terms of the old variations dT dP. Thus, as stated in Inductive Law 1 (Table 2.1), only two degrees of freedom (independently variable intensive properties) suffice to describe the thermodynamic variability of a simple c = 1 system. This confirms (as expected) that chemical potential pu only becomes an informative thermodynamic variable when chemical change is possible, that is, for c > 2 chemical components. 

Thermodynamic Model. In the equilibrium state, the intensive properties -temperature, pressure and chemical potentials of each component- are constant in the overall system. Since the fugacities are functions of temperature, pressure and compositions, the equilibrium condition... 

The most important chemical thermodynamic property is the chemical potential of a substance, denoted /x.18 The chemical potential is the intensive property that is the criterion for equilibrium with respect to the transfer or transformation of matter. Each component in a soil has a chemical potential that determines the relative propensity of the component to be transferred from one phase to another, or to be transformed into an entirely different chemical compound in the soil. Just as thermal energy is transferred from regions of high temperature to regions of low temperature, so matter is transferred from phases or substances of high chemical potential to phases or substances of low chemical potential. Chemical potential is measured in units of joules per mole (J mol 1) or joules per kilogram (J kg 1). 

In nonequilibrium systems, the intensive properties of temperature, pressure, and chemical potential are not uniform. However, they all are defined locally in an elemental volume with a sufficient number of molecules for the principles of thermodynamics to be applicable. For example, in a region A , we can define the densities of thermodynamic properties such as energy and entropy at local temperature. The energy density, the entropy density, and the amount of matter are expressed by uk(T, Nk), s T, Nk), and Nk, respectively. The total energy U, the total entropy S, and the total number of moles N of the system are determined by the following volume integrals ... 

Wyman (5,6,7) introduced the binding potential, which he represented by the Russian L for linkage. This is a molar thermodynamic property that is defined by a Legendre transform that introduces the chemical potential of the ligand as an independent intensive property. The binding potential is given by... 

The chemical potential provides the fundamental criteria for determining phase equilibria. Like many thermodynamic functions, there is no absolute value for chemical potential. The Gibbs free energy function is related to both the enthalpy and entropy for which there is no absolute value. Moreover, there are some other undesirable properties of the chemical potential that make it less than suitable for practical calculations of phase equilibria. Thus, G.N. Lewis introduced the concept of fugacity, which can be related to the chemical potential and has a relationship closer to real world intensive properties. With Lewis s definition, there still remains the problem of absolute value for the function. Thus,... 

This is sometimes called the fundamental equation of chemical thermodynamics. juf may be thought of as the increase in the free energy of the system when one mole of component i is added to an infinitely large quantity of the mixture so that it does not significantly change the overall composition. Chemical potential is an intensive property and can be regarded as providing the force which drives chemical systems to equilibrium. Consider a chemical i distributed between two phases a and / as illustrated in Fig. 4.5. Let its chemical potential be /q(a) and juf(/l) in these phases. At constant T and P if we transfer dnf moles of i from to / ,... 

The basic thermodynamic functions are internal energy U, enthalpy H, entropy S, and Gibbs free energy G. These are extensive properties of a thermodynamic system and they are first order homogenous functions of the components of the system. Pressure and temperature are intensive properties of the system and they are zero-order homogenous functions of the components of the system. Electrochemical potentials are the driving force in an electrochemical system. The electrochemical potential comprises chemical potential and electrostatic potential in the following relation. 

In the thermodynamic limit (N,V cx), p = N/V = constant), Pn(p,T) becomes an intensive property that is immediately related to the excess chemical potential, that is, to the chemical potential of a chain relative to an ideal gas of chains at the same temperature and ttoisity... 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

Thermodynamic criteria of equilibrium expressed in terms of the intensive properties pressure, temperature and chemical potential lead directly to Gibbs phase... 

Contrary to the bulk liquid phase which is homogeneous in three directions in space, has a characteristic composition, and is also autonomous (i.e., its extensive properties depend only on the intensive variables characterising this phase such as the temperature T, the pressure P, and the chemical potentials of the solvent /ri and the solute /u-2), the formal thermodynamic description of a Solid-Liquid interface presents a serious difficulty. In the interfacial region, the density a> of any extensive quantity changes continuously throughout the thickness (Fig. 6.1a). 

As intensive studies on the ECPs have been carried out for almost 30 years, a vast knowledge of the methods of preparation and the physico-chemical properties of these materials has accumulated [5-17]. The electrochemistry ofthe ECPs has been systematically and repeatedly reviewed, covering many different and important topics such as electrosynthesis, the elucidation of mechanisms and kinetics of the doping processes in ECPs, the establishment and utilization of structure-property relationships, as well as a great variety of their applications as novel electrochemical systems, and so forth [18-23]. In this chapter, a classification is proposed for electroactive polymers and ion-insertion inorganic hosts, emphasizing the unique feature of ECPs as mixed electronic-ionic conductors. The analysis of thermodynamic and kinetic properties of ECP electrodes presented here is based on a combined consideration of the potential-dependent differential capacitance of the electrode, chemical diffusion coefficients, and the partial conductivities of related electronic and ionic charge carriers. 

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