Fundamental thermodynamics

From fundamental thermodynamic relations, the temperature and pressure dependence of Henry s constant can be shown (18,50,51) to be ... 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodyuamics are internal energy and entropy These properties, together with the two laws for which they are essential, apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly... 

Nitric acid is one of the three major acids of the modem chemical industiy and has been known as a corrosive solvent for metals since alchemical times in the thirteenth centuiy. " " It is now invariably made by the catalytic oxidation of ammonia under conditions which promote the formation of NO rather than the thermodynamically more favoured products N2 or N2O (p. 423). The NO is then further oxidized to NO2 and the gases absorbed in water to yield a concentrated aqueous solution of the acid. The vast scale of production requires the optimization of all the reaction conditions and present-day operations are based on the intricate interaction of fundamental thermodynamics, modem catalyst technology, advanced reactor design, and chemical engineering aspects of process control (see Panel). Production in the USA alone now exceeds 7 million tonnes annually, of which the greater part is used to produce nitrates for fertilizers, explosives and other purposes (see Panel). 

Ingraham, T. R., in Applications of Fundamental Thermodynamics to Metallurgical Processes, ed. Fitterer, G. R. Gordon Breach, New York London, 179 (1967)... 

Any computation, whether performed by a slide rule, computer workstation or brain, is inherently a physical process, and as such is subject to whatever laws and limitations apply to physical systems in general. It is a natural question to ask, then, whether there exists a fundamental thermodynamic limit to computation i.e. 

The recognition that there is no fundamental thermodynamic limitation to constructing fully reversible, energy dissipationless, computers both classical and quantum. 

At present, it is known that the structures of the ECC type (Figs 3 and 21) can be obtained in principle for all linear crystallizable polymers. However, in practice, ECC does not occur although, as follows from the preceding considerations, the formation of linear single crystals of macroscopic size (100% ECC) is not forbidden for any fundamental thermodynamic or thermokinetic reasons60,65). It should be noted that the attained tenacities of rigid- and flexible-chain polymer fibers are almost identical. The reasons for a relatively low tenacity of fibers from rigid-chain polymers and for the adequacy of the model in Fig. 21 a have been analyzed in detail in Ref. 65. 

Thermodynamics gives limited information on each of the three coefficients which appear on the right-hand side of Eq. (1). The first term can be related to the partial molar enthalpy and the second to the partial molar volume the third term cannot be expressed in terms of any fundamental thermodynamic property, but it can be conveniently related to the excess Gibbs energy which, in turn, can be described by a solution model. For a complete description of phase behavior we must say something about each of these three coefficients for each component, in every phase. In high-pressure work, it is important to give particular attention to the second coefficient, which tells us how phase behavior is affected by pressure. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

In Chapter 1 we described the fundamental thermodynamic properties internal energy U and entropy S. They are the subjects of the First and Second Laws of Thermodynamics. These laws not only provide the mathematical relationships we need to calculate changes in U, S, H,A, and G, but also allow us to predict spontaneity and the point of equilibrium in a chemical process. The mathematical relationships provided by the laws are numerous, and we want to move ahead now to develop these equations.1... 

The ability to measure temperature and temperature differences accurately and reproducibly is essential to the experimental study of thermodynamics. A thermometer constructed with an ideal gas as its working fluid yields temperatures that correspond to the fundamental thermodynamic temperature scale. However, such thermometers are extremely difficult to use, are not amenable to miniaturization, and are very expensive. Therefore, other means to measure temperatures that reproduce the ideal gas or thermodynamic temperature scale (Kelvin) have had to be developed. The international temperature scale represents a method to determine temperatures over a wide range with measuring devices that are easier to use than the ideal gas thermometer. The goal is to make temperature measurements that correspond to the thermodynamic temperature as accurately as possible. 

The first volume entitled Chemical Thermodynamics Principles and Applications is appropriate for use as a textbook for an advanced undergraduate level or a beginning graduate level course in chemical thermodynamics. In the ten chapters of this volume, we develop the fundamental thermodynamic relationships for pure-component and variable-composition systems and apply them to a variety of chemical problems. 

In Chapter 1, we describe the fundamental thermodynamic variables pressure (p), volume (V), temperature (T), internal energy ((/), entropy (5), and moles (n). From these fundamental variables we then define the derived variables enthalpy (//), Helmholtz free energy (A) and Gibbs free energy (G). Also included in this chapter is a review of the verbal and mathematical language that we will rely upon for discussions and descriptions in subsequent chapters. 

In this section we will see how all these rules can be described mathematically by a single and simple kinetic model based on fundamental thermodynamic and catalytic principles."... 

During this period of intensive development of unit operations, other classical tools of chemical engineering analysis were introduced or were extensively developed. These included studies of the material and energy balance of processes and fundamental thermodynamic studies of multicomponent systems. 

The most fundamental thermodynamic approach of Rudakov (6) applies to all condensed systems. The actual linear relationship is argued to exist between enthalpy (AH) and entropy (AS) of intermolecular interaction, as reflected in an approximately linear relationship between the total enthalpy and entropy. Special attention has been given to hydrophobic interaction (89, 90) in water solutions, which makes the isokinetic behavior more pronounced and markedly changes its slope. 

This Journey started where most of our studies are initiated from our interest in fundamental thermodynamic properties quantified by solution ealorimetry. From these data it became clear that nucleophilic carbenes (most of them anyway) are... 

This assay system developed by Chaires [136] is a new, powerful and effective tool based on the fundamental thermodynamic principle of equilibrium dialysis for the discovery of ligands that bind to nucleic acids with structural and sequence selectivity. Here, identical concentrations of various nucleic acid samples are dialysed in dispodialysers against a common ligand solution. At equilibrium, the contents of the ligand bound to each nucleic acid are determined and this is correlated directly to the ligand s specificity to a particular sequence. 

As in energy representation the fundamental thermodynamic equation in entropy representation (3) may also be subjected to Legendre transformation to generate a series of characteristic functions designated as Massieu-Planck (MP) functions, m. The index m denotes the number of intensive parameters introduced as independent variables, i.e. 

When comparing similar or parallel reactions, consideration of the changes in Gibbs free energy A G, enthalpy AH and entropy AS can be valuable. The equilibrium constant is related to these quantities by two fundamental thermodynamic expressions... 

Techniques for accurate and reproducible measurement of temperature and temperature differences are essential to all experimental studies of thermodynamic properties. Ideal gas thermometers give temperatures that correspond to the fundamental thermodynamic temperature scale. These, however, are not convenient in most applications and practical measurement of temperature is based on the definition of a temperature scale that describes the thermodynamic temperature as accurately as possible. The analytical equations describing the latest of the international temperature scales, the temperature scale of 1990 (ITS-90) [1, 2]... 

The enthalpy change can be found from the following two fundamental thermodynamic relationships which, in the case of ideal gases, are valid for irreversible processes as well as reversible ones ... 

Most problems associated with approximate kinetics are avoided when Michaelis Menten-type rate equations are utilized. Though this choice sacrifices the possibility of analytical treatment, reversible Michaelis Menten-type equations are straightforwardly consistent with fundamental thermodynamic constraints, have intuitively interpretable parameters, are computationally no more demanding than logarithmic functions, and are well known to give an excellent account of biochemical kinetics. Consequently, Michaelis Menten-type kinetics are an obvious choice to translate large-scale metabolic networks into (approximate) dynamic models. It should also be emphasized that simplified Michaelis Menten kinetics are common in biochemical practice almost all rate equations discussed in Section III.C are simplified instances of more complicated rate functions. 

LS measurements on binary liquid mixtures have been directed primarily as a means of obtaining fundamental thermodynamic information such as chemical potentials and the excess mixing functions. Although molecular weights could in fact be derived from some published data, this has largely not been done by the authors, since such an exercise on substances of known molecular weight would have been subsidiary to the main purpose of their studies. 

The fundamental thermodynamic equation relating activity coefficients and composition is the Gibbs-Duhem relation which may be expressed as ... 

In-situ electrochemical techniques may be conveniently used to analyse the fundamental thermodynamic and kinetic parameters which are responsible for the performance of electrodes. The methods are nondestructive and may be applied to the actual galvanic cell. The data may be easily determined as a function of the discharge state. 

Perturbation of the fundamental thermodynamic variables pressure and temperature can thus be used to obtain the temporal resolution of every kinetically significant step in an enzymatic reaction. Such perturbations, combined with pH-dependence studies and several different spectroscopic tools, will detect conformational changes if they occur dur-... 

Cvm and R constants) be regarded as the fundamental thermodynamic equation of an ideal gas. With the aid of the two laws of thermodynamics, show that Equations (5.1) and (5.2) are contained implicitly in Equation (6.134). 

A fundamental thermodynamic state function (symbolized by S), and as such, not dependent on the path by which a particular state is reached. For a reversible process, the differential change in entropy, dS, is equal to the amount of energy absorbed by the system, dq, divided by the absolute temperature, T. Thus,... 

In this set of four fundamental thermodynamic expressions, one should note that only entropy cannot be directly determined experimentally, whereas P, V, and T are all measurable properties. 

These are the fundamental thermodynamic equations from which we can develop our energy balances in batch, stirred, and tubular reactors. 

Nath S (1994) A fundamental thermodynamic principle for conpling in oxidative phosphorylation. 16th Int Congr Biochemistry and Molecular Biology, New Delhi, India, vol II,... 

As the Gibbs standard free energy for the peptide-nonpolar ligand interaction decreases, and AGassoci becomes increasingly negative, enhanced retention will occur. The relationship between the relative retention of a specific peptide in a RPC separation process carried out at constant pressure, P, and constant molar volume, V, can thus be expressed in terms of the following well-known, fundamental thermodynamic relationship ... 

Hence, the logarithm of the capacity factor, In /d , can be related in terms of fundamental thermodynamic considerations to the temperature, T, through the expression... 

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