Operational thermodynamic definition

However, because the determination of o(H+), a single ion activity, is thermodynamically impossible, an operational pH definition is given as outlined in (1) and (2) below ... 

Abstract The primary method for pH is based on the measurement of the potential difference of an electrochemical cell containing a platinum hydrogen electrode and a silver/silver chloride reference electrode, often called a Harned cell. Assumptions must be made to relate the operation of this cell to the thermodynamic definition of pH. National metrology institutes use the primary method to assign pH values to a limited number of primary standards (PS). The required comparability of pH can be ensured only if the buffers used for the calibration of pH meter-electrode assemblies are traceable to... 

The primary definition is the thermod5mamlc one (sec. 1.2.3), according to which the tension is the force per unit length needed to expand the area by an infinitesimal amount, isothermally and reversibly. It is typical for thermodynamic definitions that they are based on processes that in principle can be Ccirried out, i.e. they involve operational quantities. When the expansion cannot be carried out isothermally and reversibly it is impossible to define the interfacial tension operationally. This is for instance the case with solids (sec. 1.2.24) but also with monolayers in which expansion involves energy dissipation as a result of the irreversible breaking of bonds. 

Initial concepts of temperature came from the physical sensation of the relative hotness or coldness of bodies. This sensation of warmth or cold is so subjective relative to our immediate prior exposure that it is difficult to use for anything but simple qualitative comparison. The need to assign a quantitative value to temperature leads to the definition of a temperature scale. The concept of fixed points of temperature arises from the observation that there exist some systems in nature that always exhibit the same temperatures. The scientific or thermodynamic definition of temperature comes from Kelvin, who defined the ratio of the thermodynamic or absolute temperatures of two systems as being equal to the ratio of the heat added to the heat rejected for a reversible heat engine operated between the systems. This unique temperature scale requires only one fixed point, the triple point of water, for its definition. 

Every solution has a maximum amount that it can be supersaturated before it becomes unstable. The zone between the saturation curve and this unstable boundary is called the metastable zone and is where all crystallization operations occur. The boundary between the unstable and metastable zones has a thermodynamic definition and is called the spinodal curve. The spinodal is the absolute limit of the metastable region where phase separation must occur immediately. In practice, however, the practical limits of the metastable zone are much smaller and vary as a function of conditions for a given substance. This is because the presence of dust and dirt, the cooling rate employed and/or solution history, and the use of agitation can all aid in the formation of nuclei and decrease the metastable zone. Figure 1.17 gives an estimated metastable zone width for KCl in water. 

There remains the question of the physical-i.e., operational [9] -definition of the terms. It appears to the writers that the derivation as a force balance is merely intuitional, and, as a consequence, it leaves the quantities and yg o undefined operationally. Thus, if these be viewed as forces parallel to the solid surface, one must ask with what property of the solid they are to be identified. Unlike the case with liquids, there is for solids a surface or stretching tension (the work per unit stretching of the surface [20, 25, 28]), in general nonisotropic. If this is what is involved, liquid drops on a crystalline surface of low symmetry should not be circular in cross section this is apparently contrary to observation. From the thermodynamic derivation, however, we see that one is dealing with the work of exchanging one type of solid interface for another, and that surface free energies, not stretching tensions, are the proper quantities. 

Empirical Prediction. To this point, surface tension has been described in terms of an operational definition, a thermodynamic definition, and through its molecular origin. In practice, however, these three approaches do not constitute any pragmatic means for estimating usable values for the surface tension of... 

Definition of Absolute Temperature.— The temperatures of two bodies are proportional to the quantities of heat respectively taken in and given out in localities at one temperature and at the other, respectively, by a material system subjected to a complete cycle of perfectly reversible thermodynamic operations, and not allowed to part with or take in heat at any other temperature or, the absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator at the higher and lower of the temperatures respectively. ... 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

Thus, physical scientists have become increasingly aware of the need to define concepts in terms of operations instead of relying on inmitive feelings of a priori recognition. To avoid possible pitfalls in thermodynamic applications, it is desirable that all thermal and energy concepts likewise be approached with an operational attitude. The use of operational definitions is particularly important in a phenomenological science such as thermodynamics. 

It is also evident from the definition [Equation (4.3)] that absolute values of H are unknown because absolute values of U cannot be obtained from classic thermodynamics alone. Therefore, from an operational point of view, it is possible only to consider changes in enthalpy AH. Such changes can be defined readily by the expression... 

Thus, Prigogine and Petrosky (PP) introduced the model of a Large Poincare system (EPS). As stated above, the latter is, in fact, a large system, to which the operation of Thermodynamic limit is applied. Clearly, there exists no real system satisfying strictly the definition of a EPS This infinite system is an idealization, on which, by the way, all of statistical mechanics is based. One should thus be more specific about the statement The irreversible processes... cannot be interpreted as approximations of the fundamental laws (statement 1). Quite explicitly, the approximations that are avoided in the PP theory are (a) the arbitrary coarse-graining and (b) the restriction to small parameters. 

This observed behavior of soy proteins complicates the definition of soy protein solubility, the comparison of solubility data, and the interpretation of solubility experiments. Because the thermodynamic criteria are not met, protein solubility becomes an operationally defined quantity that depends upon the experimental methods of measurement. A number of different operational definitions have been used to measure protein solubility. Each has its own advantages and disadvantages, and limited utility. This plurality, though often desirable, makes it difficult to compare experimental results. 

The rigor and power of equilibrium thermodynamics is purchased at the price of precise operational definitions. In this section, we wish to carefully define four of the most important thermodynamic terms system, property, macroscopic, and state. Although each term has an everyday meaning, it is important to understand the more rigorous and precise aspects of their usage in the thermodynamic context. 

It is simplistic to suppose that only an infinite system warrants macroscopic designation. We suspect that certain quite small systems (e.g., 1 mm3 of He gas) might be satisfactorily macroscopic for thermodynamic purposes. Let us frame the definition of macroscopic in more precise and operational terms that allow a realistic finite limit to be established. 

Elementary mechanical work forms were considered in Section 2.8. In the present section, we present a broader overview of the varieties of work that are commonly encountered in thermodynamic investigations. The goal is to introduce experimental techniques and operational terminology that underlie the definition and measurement of each work type. We also draw attention to formal patterns among the different forms of work that anticipate their unification with heat in a generalized energy-conservation principle. 

Chemists and physicists must always formulate correctly the constraints which crystal structure and symmetry impose on their thermodynamic derivations. Gibbs encountered this problem when he constructed the component chemical potentials of non-hydrostatically stressed crystals. He distinguished between mobile and immobile components of a solid. The conceptual difficulties became critical when, following the classical paper of Wagner and Schottky on ordered mixed phases as discussed in chapter 1, chemical potentials of statistically relevant SE s of the crystal lattice were introduced. As with the definition of chemical potentials of ions in electrolytes, it turned out that not all the mathematical operations (9G/9n.) could be performed for SE s of kind i without violating the structural conditions of the crystal lattice. The origin of this difficulty lies in the fact that lattice sites are not the analogue of chemical species (components). 

This section reviews some basic definitions and formulas in thermodynamics. These definitions will be used to develop energy balances to describe cooling tower operations. In our discussions we will use the following terms system, property, extensive and intensive properties, and... 

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