Thermodynamic state, properties

Heat and work are forms of energy in transfer between the system and the environment. If more heat is introduced into the system than the system performs work on the environment, the difference is stored as an addition to the internal energy U of the system, a property of its state. In a more abstract way, the first law is said to define the fundamental thermodynamic state property, It, the internal energy. 

Entropy, S A thermodynamic state property that measures the degree of disorder or randomness of a system. 

For a given material or substance, the standard state is the reference state for the substance s thermodynamic state properties such as enthalpy, entropy, Gibbs free energy, and so on. 

These are the entropy equations we seek, which relate the entropy to properties such as enthalpy, temperature, and pressure, which we can already measure or solve for. This was derived considering a reversible process but is applicable for any process, since entropy is a thermodynamic state property which does not depend on the path taken to arrive at the final equilibrium state. 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

The molecular and liquid properties of water have been subjects of intensive research in the field of molecular science. Most theoretical approaches, including molecular simulation and integral equation methods, have relied on the effective potential, which was determined empirically or semiempirically with the aid of ab initio MO calculations for isolated molecules. The potential parameters so determined from the ab initio MO in vacuum should have been readjusted so as to reproduce experimental observables in solutions. An obvious problem in such a way of determining molecular parameters is that it requires the reevaluation of the parameters whenever the thermodynamic conditions such as temperature and pressure are changed, because the effective potentials are state properties. 

I mentioned temperature at the end of the last chapter. The concept of temperature has a great deal to do with thermodynamics, and at first sight very little to do with microscopic systems such as atoms or molecules. The Zeroth Law of Thermodynamics states that Tf system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is also in thermal equilibrium with system C . This statement indicates the existence of a property that is common to systems in thermal equilibrium, irrespective of their nature or composition. The property is referred to as the temperature of the system. 

There is thus assumed to be a one-to-one correspondence between the most probable distribution and the thermodynamic state. The equilibrium ensemble corresponding to any given thermodynamic state is then used to compute averages over the ensemble of other (not necessarily thermodynamic) properties of the systems represented in the ensemble. The first step in developing this theory is thus a suitable definition of the probability of a distribution in a collection of systems. In classical statistics we are familiar with the fact that the logarithm of the probability of a distribution w[n is — J(n) w n) In w n, and that the classical expression for entropy in the ensemble is20... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

A surface is that part of an object which is in direct contact with its environment and hence, is most affected by it. The surface properties of solid organic polymers have a strong impact on many, if not most, of their apphcations. The properties and structure of these surfaces are, therefore, of utmost importance. The chemical stmcture and thermodynamic state of polymer surfaces are important factors that determine many of their practical characteristics. Examples of properties affected by polymer surface stmcture include adhesion, wettability, friction, coatability, permeability, dyeabil-ity, gloss, corrosion, surface electrostatic charging, cellular recognition, and biocompatibility. Interfacial characteristics of polymer systems control the domain size and the stability of polymer-polymer dispersions, adhesive strength of laminates and composites, cohesive strength of polymer blends, mechanical properties of adhesive joints, etc. 

Why do some reactions go virtually to completion, whereas others reach equilibrium when hardly any of the starting materials have been consumed At the molecular level, bond energies and molecular organization are the determining factors. These features correlate with the thermodynamic state functions of enthalpy and entropy. As discussed In Chapter 14, free energy (G) is the state function that combines these properties. This section establishes the connection between thermodynamics and equilibrium. 

The first term on the right is the formula for the chemical potential of component a at density pa = na/V in an ideal gas, as would be the case if interactions between molecules were negligible, fee is Boltzmann s constant, and V is the volume of the solution. The other parameters in that ideal contribution are properties of the isolated molecule of type a, and depend on the thermodynamic state only through T. Specifically, V/A is the translational contribution to the partition function of single a molecule at temperature T in a volume V... 

The dynamic behavior of fluid interfaces is usually described in terms of surface rheology. Monolayer-covered interfaces may display dramatically different rheological behavior from that of the clean liquid interface. These time-dependent properties vary with the extent of intermolecular association within the monolayer at a given thermodynamic state, which in turn may be related directly to molecular size, shape, and charge (Manheimer and Schechter, 1970). Two of these time-dependent rheological properties are discussed here surface shear viscosity and dynamic surface tension. 

The sorption of water by excipients derived from cellulose and starch has been considered by numerous workers, with at least three thermodynamic states having been identified [82]. Water may be directly and tightly bound at a 1 1 stoichiometry per anhydroglucose unit, unrestricted water having properties almost equivalent to bulk water, or water having properties intermediate between these two extremes. The water sorption characteristics of potato starch and microcrystalline cellulose have been determined, and comparison of these is found in Fig. 11. While starch freely adsorbs water at essentially all relative humidity values, microcrystalline cellulose only does so at elevated humidity values. These trends have been interpreted in terms of the degree of available cellulosic hydroxy groups on the surfaces, and as a function of the amount of amorphous material present [83]. 

As shown in Fig. 2 [37], and also in the work of Barraclough and Hall [34], moisture uptake onto sodium chloride as a function of relative humidity is reversible as long as RH0 is not attained. This is evidence that actual dissolution of water-soluble crystalline substances does not occur below RH0. This is consistent with thermodynamic rationale that dissolution below RHo would require a supersaturated solution (i.e., an increased number of species in solution would be necessary to induce dissolution at a relative humidity below that of the saturated solution, RH0). In this regard, one should only need to consider the solid state properties of a purely crystalline material below RH0. As will be described, other considerations are warranted for a substance that contains amorphous material. 

In summary, it is clear that water absorbs into amorphous polymers to a significant extent. Interaction of water molecules with available sorption sites likely occurs via hydrogen bonding such that the mobility of the sorbed water is reduced and the thermodynamic state of this water is significantly altered relative to bulk water. Yet accessibility of the water to all potential sorption sites appears to be dependent on the previous history and physical-chemical properties of the solid. In this regard, the water-solid interaction in amorphous polymer systems is a dynamic relationship depending quite strongly on water activity and temperature. 

An emulsion is a dispersed system of two immiscible phases. Emulsions are present in several food systems. In general, the disperse phase in an emulsion is normally in globules 0.1-10 microns in diameter. Emulsions are commonly classed as either oil in water (O/W) or water in oil (W/O). In sugar confectionery, O/W emulsions are most usually encountered, or perhaps more accurately, oil in sugar syrup. One of the most important properties of an emulsion is its stability, normally referred to as its emulsion stability. Emulsions normally break by one of three processes creaming (or sedimentation), flocculation or droplet coalescence. Creaming and sedimentation originate in density differences between the two phases. Emulsions often break by a mixture of the processes. The time it takes for an emulsion to break can vary from seconds to years. Emulsions are not normally inherently stable since they are not a thermodynamic state of matter. A stable emulsion normally needs some material to make the emulsion stable. Food law complicates this issue since various substances are listed as emulsifiers and stabilisers. Unfortunately, some natural substances that are extremely effective as emulsifiers in practice are not emulsifiers in law. An examination of those materials that do stabilise emulsions allows them to be classified as follows ... 

Factors influencing jet breakup may include (a) flow rates, velocities and turbulence of liquid jet and co-flowing gas, (b) nozzle design features, (c) physical properties and thermodynamic states of both liquid and gas, (d) transverse gas flow,[239] (e) dynamic change of surface tension, 1151[2401 (f) swirlj241 242 (g) vaporization and gas compressibility,[243] (h) shock waves,[244] etc. 

At low temperatures, matter will undergo a transition to a color-superconducting state, with a different quasiparticle structure than presumed in our quasiparticle approach. Nonetheless, pairing affects the thermodynamic bulk properties only at the relative order of 0(A2/fi2), where the estimated gap A < 100 MeV is comfortably smaller than the chemical potential. Therefore, our equation of state is a reasonable approximation even at small temperatures (maybe except for the pressure where it becomes very small). 

The first law of thermodynamics, which can be stated in various ways, enuciates the principle of the conservation of energy. In the present context, its most important application is in the calculation of the heat evolved or absorbed when a given chemical reaction takes place. Certain thermodynamic properties known as state functions are used to define equilibrium states and these properties depend only on the present state of the system and not on its history, that is the route by which it reached that state. The definition of a sufficient number of thermodynamic state functions serves to fix the state of a system for example, the state of a given mass of a pure gas is defined if the pressure and temperature are fixed. When a system undergoes some change from state 1 to state 2 in which a quantity of heat, Q, is absorbed and an amount of work, W, is done on the system, the first law may be written... 

The first part of the chapter is devoted to an analysis of these correlations, as well as to the presentation of the most important experimental results. In a second part the following stage of development is reviewed, i.e. the introduction of more quantitative theories mostly based on bond structure calculations. These theories are given a thermodynamic form (equation of states at zero temperature), and explain the typical behaviour of such ground state properties as cohesive energies, atomic volumes, and bulk moduli across the series. They employ in their simplest form the Friedel model extended from the d- to the 5f-itinerant state. The Mott transition (between plutonium and americium metals) finds a good justification within this frame. 

In recent times, the bond indicators , which are the ground state properties of the solid related to its cohesion (metaUic radii, cohesive energy, bulk moduli), have been interpreted in the light of band calculations. The bond in metals and in compounds has been described by an easily understandable and convincing thermodynamic formalism, which we shall illustrate in this chapter. Essentially, narrow bands, as the 5 f electrons form, are considered to be resonant with the wider (spd) conduction band. The 5 f electronic population is seen as a fluid the partial (bonding) pressure of which assists in cohesion along with the partial pressure of another fluid constituted by the conduction electrons of (s and d) character. ... 

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