Simple thermodynamics

As stated above, free-energy (C) dissipation does not imply that energy (t/) is dissipated it only implies that energy is (partly) transformed from free energy to pure heat, which equals the product of temperature and entropy. Consequently, the rate of free-energy dissipation is equal to the rate of entropy production multiplied by the absolute temperature. 

The so-called dissipation function ( I ) analyzes the rate of free energy dissipation in terms of the different processes in which free energy is dissipated. If, for instance, a chemical reaction occurs with a free-energy difference, AG, and at a rate, whereas at the same time a substance S flows from a space in which it has a high concentration to one where it has a low concentration, the rate at which the free energy is dissipated is  

It may be noted that we define AG such that it equals the chemical potential of the substrate minus the chemical potential of the product. We noted above that the possibility of free-energy dissipation drives a reaction. Free-energy differences like ACr and A/tg in the above equation embody such a possibility they act as forces that drive the reaction. Other examples are the contractile force on a muscle the voltage drop across an electrical resistance the osmotic pressure on a semipermeable membrane. The dissipation function consists of the sum of the products of fluxes (currents) and the (thermodynamic) forces that drive them [4]. 

Generally speaking, a flux (J) in a system can depend on each of the forces ( A ) in that system. Close to equilibrium it can be made feasible [1] that this function is in general proportional, i.e.  

The complete set of equations, relating fluxes and forces can be written in a matrix form and is called the set of phenomenological equations. It was shown by Onsager [1] that the matrix of the phenomenological proportionality constants is symmetrical  

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It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

In summary, T j, gives a truer approximation to a valid equilibrium parameter, although it will be less than T owing to the finite dimensions of the crystal and the finite molecular weight of the polymer. We shall deal with these considerations in the next section. For now we assume that a value for T has been obtained and consider the simple thermodynamics of a phase transition. 

Reaction measurement studies also show that the chemistry is often not a simple one-step reaction process (37). There are usually several key intermediates, and the reaction is better thought of as a network of series and parallel steps. Kinetic parameters for each of the steps can be derived from the data. The appearance of these intermediates can add to the time required to achieve a desired level of total breakdown to the simple, thermodynamically stable products, eg, CO2, H2O, or N2. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonideahties occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and soHd orHquid solutes (rl,i4—r7,r9,i49,r50). 

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

We will be looking at kinetics in Chapter 6. But before we can do this we need to know what we mean by driving forces and how we calculate them. In this chapter we show that driving forces can be expressed in terms of simple thermodynamic quantities, and we illustrate this by calculating driving forces for some typical processes like solidification, changes in crystal structure, and precipitate coarsening. 

From Boyles Law, it is known that the pressure is directly proportional to the temperature, therefore, it was shown that the kinetic energy of the molecules related directly to the temperature of the gas. A simple thermodynamic relation holds for this ... 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

This simple thermodynamic picture is substantially altered if we introduce dissimilar particles into our dispersion. The various interactions now depend on the nature of the two particles, relative to the solvent, and can either favour dispersal or aggregation. Again, this could be the basis for a natural control mechanism as the number and composition of the colloidal building blocks evolve, subtle changes in the interactions could switch a dispersion from stable to unstable. 

The ability to detect discrete rovibronic spectral features attributed to transitions of two distinct conformers of the ground-state Rg XY complexes and to monitor changing populations as the expansion conditions are manipulated offered an opportunity to evaluate the concept of a thermodynamic equilibrium between the conformers within a supersonic expansion. Since continued changes in the relative intensities of the T-shaped and linear features was observed up to at least Z = 41 [41], the populations of the conformers of the He - lCl and He Br2 complexes are not kinetically trapped within a narrow region close to the nozzle orifice. We implemented a simple thermodynamic model that uses the ratios of the peak intensities of the conformer bands with changing temperature in the expansion to obtain experimental estimates of the relative binding energies of these complexes [39, 41]. 

Simple thermodynamic treatment of gas compression stipulates that the maximum temperature (Tmax) attained is dependent on the adiabatic index (y) of the gas ... 

Experiment 2 Saturate distilled water with a rare gas and compare the intensity of the signal with that from air. The luminosity will be enhanced in the rare gas saturated solutions. For any gas atmosphere, add small amounts of volatile water-soluble solutes (e.g. alkyl series alcohols) and quantify the quenching of sonoluminescence as a function of both bulk quencher concentration and surface excess. Good correlation between the extent of quenching and the Gibbs surface excess should be observed. Explain the changes in sonoluminescence intensity when a rare gas atmosphere is used and the quenching of volatile solutes, in terms of simple thermodynamics. 

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

Two simple thermodynamic considerations are suggested upon examination of Fig. 8. The first is that at temperatures below Tml the free energy of the bulk mesophase G m is in general bound to be lower than Gl, the free energy of the amorphous. In the limit of Class II mesophases, since AHml = 0, we will have Gm = Gl at T = 0 K while Gm < Gl at temperatures 0 < T < Tml since it is Sm > Sl at temperatures low enough as compared to Tml (Sect. 3.1). In the case of Class I mesophases AHml > 0. he., mesophases are enthalpically stabilized with respect to the liquid state, while Sm < Sl, so it will be Gm < Gl at temperatures T, with 0 < T < Tml- Note that the above consideration will in... 

Modeling of n (e) can be motivated by a simple thermodynamic model for this electrostatic contribution. The Bom model [34] for the hydration free energy of a spherical ion of radius Ra with a charge qa at its center is... 

The temperature profile of a planetary atmosphere depends both on the composition and some simple thermodynamics. The temperature decreases with altitude at a rate called the lapse rate. As a parcel of air rises, the pressure falls as we have seen, which means that the volume will increase as a result of an adiabatic expansion. The change in enthalpy H coupled with the definition of the specific heat capacity... 

Sato et al.11 realized that for these lyotropic systems, whose phase boundaries have little temperature dependence, an investigation of the handedness in the widest possible temperature interval should be carried out. As the cholesteric handedness in a few cases is opposite at different temperatures, the data at a single temperature are meaningless. Using a simple thermodynamic analysis, they proposed a plot of the cholesteric wavenumber qc (the reciprocal pitch) as a function of the reciprocal temperature 1 IT [Eq. (1)]... 

Q-R factorization is successful in decomposing linear systems of equations. It is also satisfactory when bilinear systems contain component balances and normalization equations. If energy balances are included in the set of process constraints, the procedure has the drawback that only simple thermodynamic relations for the specific enthalpy of the stream can be considered. 

By simple thermodynamic arguments Brown14 has shown that, consistent with the accuracy of this second-order approximation, one may obtain from the form of Eq. (87) the form of the excess Gibbs free energy of mixing (AG ), the enthalpy of mixing of a molten salt (AHm), and the deviation of the surface tension from linearity ... 

The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. 

The reduction and oxidation potentials of a very large number gathered by means of this method are available.54 For reasons similar to those already discussed, the reduction and oxidation potential have no simple thermodynamic meaning. The rate of electron transfer, dimerization of the radicals,... 

Phase behavior 1n concentrated aqueous electrolyte systems is of interest for a variety of applications such as separation processes for complex salts, hydrometal 1urgical extraction of metals, interpretation of geological data and development of high energy density batteries. Our interest in developing simple thermodynamic correlations for concentrated salt systems was motivated by the need to interpret the complex solid-liquid equilibria which occur in the extraction of sodium nitrate from complex salt mixtures which occur in Northern Chile (Chilean saltpeter). However, we believe the thermodynamic approach can also be applied to other areas of technological interest. 

This approach allows a simple thermodynamic treatment of the concentrated region although the approach is not appropriate, either practically or theoretically for the highly dilute region. 

Simple thermodynamic considerations state that the reduction process is favoured (i.e. more positive cu(ii)/cu(p potential values are obtained) if the electron transfer is exothermic (AH° negative) and if the molecular disorder increases (AS° positive). It is therefore evident that the positive potential value for the reduction of azurin (as well as that of the most blue copper proteins) is favoured by the enthalpic factor. This means that the metal-to-ligand interactions inside the first coordination sphere (which favour the stability of the reduced form over the oxidized form) prevail over the metal complex-to-solvent interactions inside the second... 

The action of added ion-pairs may also be visualized as the establishment of an ion-pair atmosphere about a dipolar transition state. Simple thermodynamic treatment predicts linearity of log k3 in cs, but it has been shown that contributions of ion-pair-ion-pair repulsion, higher aggregation, and the effect of salt on the dielectric constant introduce curvature in the log k3-cs plot that is in the direction of a k3-cs dependence. 

No simple thermodynamic model is yet able to explain the large decrease in conductivity when partially substituting one alkali metal for another, i.e. the so-called mixed alkali effect. Systematic analysis of the pre-... 

T2S the simple thermodynamic picture is adequate. The dynamics of equilibration are... 

Spin-spin fluctuations can compete with spin-lattice effects an energy hwic can be supplied by a phonon as well as by a spin fluctuation in the dipolar field. A simple thermodynamic view is shown in Fig. 8. For convenience only two distinct carbon... 

Miscibility or immiscibility can be described in simple thermodynamic terms as follows, at constant temperature. Mixing occurs if the free energy of mixing is negative. 

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