Definitions in thermodynamics

In this chapter we will review some of the principles of thermochemistry, with particular attention to the air-water vapor system. Basic definitions in thermodynamics are reviewed along with important physical properties and definitions for gaseous mixtures. It is important that these definitions be learned early on. Note, however, that this chapter is only meant as a review. The references listed at the end of this chapter should be consulted for a detailed treatment of these subjects. Further, example problems are included at the end of the chapter to stress principles discussed. 

There is no change in (internal) energy of the gas as its volume is increased (i.e. gas is expanded) whilst the temperature is kept constant. This provides a convenient mathematical definition (in thermodynamic terms) of an ideal gas. 

The notion of work is not regarded as being in need of definition in thermodynamics, since it is a concept which is already defined by the primary science of mechanics. 

It is in principle impossible to measure the potential drop at only one electrode/ electrolyte interface. Two electrodes always have to be combined in an electrochemical cell. To normalize all potential measurements, the standard hydrogen electrode is used as a reference with [H" ] = 1.0 M (pH = 0) and p(H2) = 1.013 bar at an inert metal electrode such as platinum. Its potential is °=0 V by definition. This definition is directly linked to the definition in thermodynamics of AGf (H" ) = 0 for the formation of hydrogen ions under standard conditions. The cell voltage between an electrode and the standard hydrogen electrode is called the electrode potential E. Work function measurements have related this hydro-gen-based potential scale to the vacuum scale used in physics. The standard hydro-... 

The new international temperature scale, known as ITS-90, was adopted in September 1989. However, neither the definition of thermodynamic temperature nor the definition of the kelvin or the Celsius temperature scales has changed it is the way in which we are to realize these definitions that has changed. The changes concern the recommended thermometers to be used in different regions of the temperature scale and the list of secondary standard fixed points. The changes in temperature determined using ITS-90 from the previous IPTS-68 are always less than 0.4 K, and almost always less than 0.2 K, over the range 0-1300 K. 

The ultimate definition of thermodynamic temperature is in terms of pV (pressure X volume) in a gas thermometer extrapolated to low pressure. The kelvin (K), the unit of thermodynamic temperature, is defined by specifying the temperature of one fixed point on the scale—the triple point... 

Fig. 3. Definition of thermodynamic work of adhesion, Wa (a) disjoining surfaces in vacuum (b) disjoining surfaces in fluid medium m and (c) disjoining surfaces in presence of vapors from adhesive.

Piezoelectric solids are characterized by constitutive relations among the stress t, strain rj, entropy s, electric field E, and electric displacement D. When uncoupled solutions are sought, it is convenient to express t and D as functions of t], E, and s. The formulation of nonlinear piezoelectric constitutive relations has been considered by numerous authors (see the list cited in [77G06]), but there is no generally accepted form or notation. With some modification in notation, we adopt the definitions of thermodynamic potentials developed by Thurston [74T01]. This leads to the following constitutive relations ... 

This expression shows that the maximum possible useful work (i.e., reversible work) that can be obtained from any process occurring at constant temperature and pressure is a function of the initial and final states only and is independent of the path. The combination of properties U + PV - TS or H - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, F, the free energy (sometimes called the Gibbs Free Energy). Using this definition, Equation 2-143 is written... 

This is called Avogadro s theorem (1811) it appears here simply as a definition of molecular weighty and this is really the manner in which the relation is applied in chemistry. The kinetic theory of gases gives a new, and much deeper, significance to the statement by introducing the conception of the molecule this, however, does not concern us in thermodynamics, and since the molecular weights are purely relative numbers, the deductions made in this hook are equally strict whichever standpoint is adopted. 

Temperature Scales A quantitative description of temperature requires the definition of a temperature scale. The two most commonly encountered in thermodynamics are the absolute or ideal gas (°A) scale and the thermodynamic or Kelvin (K) scale."... 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

The present text on thermodynamics is quite concise, and it is hoped that it will prepare readers well both for using thermodynamic methods and for delving more deeply into the subject with the supporting aid of a good deal of standard reference texts (some of which) are listed at the end of the chapter). The text presented here introduces some of the common concepts and definitions in vogue in thermodynamics, and a familiarity with them is considered the first useful step in the study of thermodynamics. 

This relationship is expressed in extensive properties that depend on the extent of the system, as opposed to intensive properties that describe conditions at a point in the system. For example, extensive properties are made intensive by expressing them on a per unit mass basis, e.g. s = S/m density, p 1 /v, v V/m. For a pure system (one species), Equation (1.2) in intensive form allows a definition of thermodynamic temperature and pressure in terms of the intensive properties as... 

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. 

A term used in thermodynamics to designate a region separated from the rest of the universe by definite boundaries. The system is considered to be isolated if any change in the surroundings the portion of the universe outside of the boundaries of the system) does not cause any changes within the system. See Closed System Isolated System Open System... 

The term on the left-hand side U -I- pv) is very important in thermodynamics and is called the enthalpy. It is given the symbol H. Thus by definition... 

The definition of crystal is itself a developing concept, as demonstrated by the ongoing discussions [5, 6]. Most ot the theoretical background proposed in this chapter is valid for a perfect crystal, i.e., an infinite mathematical object with an idealized crystal structure ideal crystal) in thermodynamic equilibrium at a given presstrre P and temperature T. In textbooks, only the gas phase thermodynamics is usually discussed in detail, whereas little attention is paid to the solid state. A full thermodynamic treatment of solids is beyond the scope of this chapter and the reader is referred to specific books on the subject, for example [7]. 

The thermodynamic dead volume includes those static fractions of the mobile phase that have the same composition as the moving phase, and thus do not contribute to solute retention by differential interaction in a similar manner to those with the stationary phase. It is seen that, in contrast to the kinetic dead volume, which by definition can contain no static mobile phase, and as a consequence is independent of the solute chromatographed, the thermodynamic dead volume will vary from solute to solute depending on the size of the solute molecule (i.e. is dependent on both ( i )and (n). Moreover, the amount of the stationary phase accessible to the solute will also vary with the size of the molecule (i.e. is dependent on (%)). It follows, that for a given stationary phase, it is not possible to compare the retentive properties of one solute with those of another in thermodynamic terms, unless ( ), (n) and (fc) are known accurately for each solute. This is particularly important if the two solutes differ significantly in molecular volume. The experimental determination of ( ), (n) and( ) would be extremely difficult, if not impossible In practice, as it would be necessary to carry out a separate series of exclusion measurements for each solute which, at best, would be lengthy and tedious. 

Equation (4.87) was obtained under the assumption of strict thermodynamic equilibrium between the particle and the surrounding radiation field that is, the particle at temperature T is embedded in a radiation field characterized by the same temperature. However, we are almost invariably interested in applying (4.87) to particles that are not in thermodynamic equilibrium with the surrounding radiation. For example, if the only mechanisms for energy transfer are radiative, then a particle illuminated by the sun or another star will come to constant temperature when emission balances absorption but the particle s steady temperature will not, in general, be the same as that of the star. The validity of Kirchhoff s law for a body in a nonequilibrium environment has been the subject of some controversy. However, from the review by Baltes (1976) and the papers cited therein, it appears that questions about the validity of Kirchhoff s law are merely the result of different definitions of emission and absorption, and we are justified in using (4.87) for particles under arbitrary illumination. 

It is easy to see some of the factors affecting the equilibrium composition. From the definition in Eq. 9.42, large values of Kp dictate that the products of the reaction are favored over the reactants that is, thermodynamics pushes the forward reaction toward completion. From Eq. 9.44, a reaction that is very exothermic, AH° << 0, favors product formation that is, Kp will be very large. 

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. 

The distinction between reversible and irreversible work is one of the most important in thermodynamics. We shall first illustrate this distinction by means of a specific numerical example, in which a specified system undergoes a certain change of state by three distinct paths approaching the idealized reversible limit. Later, we introduce a formal definition for reversible work that summarizes and generalizes what has been learned from the path dependence in the three cases. In each case, we shall evaluate the integrated work w 2 from the basic path integral,... 

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. 

The thermodynamic temperature. Hie definition of thermodynamic temperature in kelvins (Eq. 6-8) also follows from Eq. 6-6. See textbooks of thermodynamics for further treatment. 

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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