Thermodynamics phenomenological

The changes in the states of entropy-elastic bodies described in the previous section can be expressed quantitively by phenomenological thermodynamics, starting with one of the fundamental equations in thermodynamics. The relationship of interest here relates the pressure p with the internal energy U, the volume F, and the thermodynamic temperature T (see textbooks of chemical thermodynamics)  

Instead of the change in volume dV, the change in length dl on application of a stretching force F is considered. F and p have opposite signs. Equation (11-8) thus becomes 

If the second law of thermodynamics A = U — TS is differentiated with respect to the length /, this gives 

In thermodynamics, furthermore, the following is quite generally valid  

Since the force F is proportional to the pressure p, and the length / to the volume V, it is possible to write, in analogy to equation (11-12), 

The second term on both sides of Equation (11-16) is identical. What is called the equation of the thermal state for entropy-elastic bodies is therefore 

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It is not particularly difficult to introduce thermodynamic concepts into a discussion of elasticity. We shall not explore all of the implications of this development, but shall proceed only to the point of establishing the connection between elasticity and entropy. Then we shall go from phenomenological thermodynamics to statistical thermodynamics in pursuit of a molecular model to describe the elastic response of cross-linked networks. 

In another sense the title is too restrictive, implying that only pure, phenomenological thermodynamics are discussed herein. Actually, this is far from true. Both thermodynamics and statistical thermodynamics comprise the contents of the chapter, with the second making the larger contribution. But the term statistical is omitted from the title, as it is too intimidating. 

Electrons and ions are the principal particles that play the main role in electrochemistry. This text, hence, emphasizes the energy level concepts of electrons and ions rather than the phenomenological thermodynamic and kinetic concepts on which most of the classical electrochemistry texts are based. This rationalization of the phenomenological concepts in terms of the physics of semiconductors should enable readers to develop more atomistic and quantitative insights into processes that occur at electrodes. 

The point of view adopted toward thermodynamics in this book is the classic or phenomenological one. This approach is the most general but also the least illuminating in molecular insight. The three basic principles of phenomenological thermodynamics are extracted as postulates from general experience, and no attempt is made to deduce them from equations describing the mechanical behavior of material... 

Woll and Hatton [175] have developed a phenomenological thermodynamic model for the partitioning of proteins between aqueous and reverse micellar phases. A simple expression for the protein partition coefficient was derived as a function of pH and surfactant concentration and the partitioning of ribonu-clease A and concanavalin A were shown to correlate well with the model. However, this model was a correlative one but not predictive. 

If we turn from phenomenological thermodynamics to statistical thermodynamics, then we can interpret the second virial coefficient in terms of molecular parameters via a model. We pursue this approach for two different models, namely, the excluded-volume model for solute molecules with rigid structures and the Flory-Huggins model for polymer chains, in Section 3.4. 

How is statistical thermodynamics used for deriving adsorption isotherms What are the similarities and differences between this procedure and the one based on phenomenological thermodynamics How is the kinetic theory of gases used for deriving adsorption isotherms ... 

The results of the discussion on the phenomenological thermodynamics of crystals can be summarized as follows. One can define chemical potentials, /jk, for components k (Eqn. (2.4)), for building units (Eqn. (2.11)), and for structure elements (Eqn, (2.31)). The lattice construction requires the introduction of structural units , which are the vacancies V,. Electroneutrality in a crystal composed of charged SE s requires the introduction of the electrical unit, e. The composition of an n component crystal is fixed by n- 1) independent mole fractions, Nk, of chemical components. (n-1) is also the number of conditions for the definition of the component potentials juk, as seen from Eqn. (2.4). For building units, we have (n — 1) independent composition variables and n-(K- 1) equilibria between sublattices x, so that the number of conditions is n-K-1, as required by the definition of the building element potential uk(Xy For structure elements, the actual number of constraints is larger than the number of constraints required by Eqn. (2.18), which defines nk(x.y This circumstance is responsible for the introduction of the concept of virtual chemical potentials of SE s. 

Since we are considering equilibrium boundaries and interfaces, let us introduce some phenomenological thermodynamics. If 6 symbolizes the orientation (location) of two crystal parts (phases) relative to each other, and s designates a structure parameter that symbolizes the atomic structure of the boundary (composition and structural details), then... 

The beauty and power of phenomenological thermodynamics lies just in the generality and paucity of its basic laws which hold independently of any assumptions concerning the microscopic structure of the systems which they govern. Its quantitative content is limited to conditions of equilibrium. Its conceptual framework is too narrow to permit the description of the temporal behavior of systems, except to the extent that it makes it possible to decide which, of any pair of states of an adiabatically enclosed system, must have been die earlier state. 

Now irreversible processes can be studied on three levels (1) the phenomenological thermodynamic level in which the equations for the macroscopic variables are studied (2) the level of fluctuations, in which we study the nature, growth or decay of small fluctuations either of internal or external origin and (3) the basic level in which we try to identify the microscopic mechanisms of irreversibility. Here I shall be mainly concerned with the first, and to certain extent the second level, through which I believe we can begin to understand how irreversible processes bring about the different aspects of the process of evolution. 

At the phenomenological thermodynamic level, when we go far from equilibrium, the striking new feature is that new dynamical states of matter arise. We may call these states dissipative structures as they present both structure and coherence and their maintenance requires dissipation of energy.6 Dissipative processes that destroy structure at and near equilibrium may create these structures when sufficiently far from equilibrium. 

In the incommensurate phase T < 7] the magnetic structure forms a helix along the c-axis. For the theoretical analysis of the magnetic properties of copper metaborate based on a phenomenological thermodynamic potential, it is essential that the crystal symmetry has no center of inversion. The inversion operation enters only in combination with rotational displacement around the c-axis by 90° A and 433. Therefore, in the thermodynamic... 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

What governs the selectivity To answer this question, let us use the phenomenological thermodynamic expressions for the retention factors (1-4) and (1-5) and apply them to the expression for selectivity (1-6) ... 

It is instructive to compare this result with that obtained by considering the bacteriorhodopsin liposomes as a black box, with gradients of H, K, Cl and their associated forces, plus the light-driven proton pump with its associated force. According to phenomenological thermodynamics, we would described such a system by the following set of equations in matrix form ... 

Ruckenstein, E. (1998). On the phenomenological thermodynamics of hydrophobic bonding. Journal of Dispersion Science Technolology, 19, 329-338. 

Woll, J. M. Hatton, A. T. "A simple phenomenological thermodynamic model for protein partitioning in reversed micellar systems Bioprocess Eng. 1989,4, pp 193-199. 

Caselli, M. Luisi, P. L. Maestro, M. Roselli, R. J. Phys. Chem. 1988, 92, 3899-3905. Woll, J. M. Hatton, T. A. "A Simple Phenomenological Thermodynamic Model for Protein Partitioning in Reversed Micellar Systems Bioproc. Eng., in press. 

With Eq. (1.88), we conclude our discussion of phenomenological thermodynamics of confined fluids. In Chapter 2, we shall turn to an interpretation of the various thermodynamic quantities introduced above in terms of interactions between the microscopic constituents forming the system at a molecular level of description (i.e., atoms and molecules). 

The vertical , submolecular reality of molecular fragments, e.g., AIM, functional groups, reactants, etc., so important for the language of chemistry, cannot be directly validated experimentally, since it is not an observable . It can only be verified indirectly, by the demonstrated close analogy to phenomenological thermodynamics. Indeed, consistent chemical interpretations... 

Besides immense applications, the foundations of phenomenological thermodynamics are attempted to be reformulated in nearly every textbook or monography on the subject, cf., e.g., [1-16], see also thorough discussions in [17-23]. The main reason for this situation consists in the fact that thermodynamics gives in principle only an incomplete description because the macroscopic objects it deals with are too intricate and composed of an immense number of particles the detailed behavior of which is mostly not necessary to know (disregarding the practical impossibility of such description). Moreover in nonequilibrium situations time rates and gradients of properties play an important role and thus the memory and neighborhood influences on a state in a considered time and place become more important. 

Basic ideas of (phenomenological) thermodynamics need to use some nonmechanical concepts, like temperature, internal energy, or entropy. ... 

In (phenomenological) thermodynamics we study the (macroscopic) thermodynamic system (also called the body) and we assume that we know how its state can be described. " By process we understand realizable time sequence of states from the initial to the final state. 

WUmanski, K. Foundations of Phenomenological Thermodynamics (in Pohsh). PWN, Warsaw (1974)... 

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