Equilibrium state specification

A statistical ensemble can be viewed as a description of how an experiment is repeated. In order to describe a macroscopic system in equilibrium, its thennodynamic state needs to be specified first. From this, one can infer the macroscopic constraints on the system, i.e. which macroscopic (thennodynamic) quantities are held fixed. One can also deduce, from this, what are the corresponding microscopic variables which will be constants of motion. A macroscopic system held in a specific thennodynamic equilibrium state is typically consistent with a very large number (classically infinite) of microstates. Each of the repeated experimental measurements on such a system, under ideal... 

The jump conditions must be satisfied by a steady compression wave, but cannot be used by themselves to predict the behavior of a specific material under shock loading. For that, another equation is needed to independently relate pressure (more generally, the normal stress) to the density (or strain). This equation is a property of the material itself, and every material has its own unique description. When the material behind the shock wave is a uniform, equilibrium state, the equation that is used is the material s thermodynamic equation of state. A more general expression, which can include time-dependent and nonequilibrium behavior, is called the constitutive equation. 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

To the best of our knowledge, the supercoil conformation of the monoden-dron jacketed polystyrene is one of the first observations of a defined tertiary structure in synthetic polymers. The plectoneme conformation could be caused by underwinding or overwinding of a backbone from its equilibrium state [168]. Quick evaporation of the solvent certainly can cause a residual torsion in the molecule as it contracted in itself. Unlike macroconformations of biomolecules, where the tertiary structures are often stabilized by specific interactions between side groups, the supercoil of the monodendron jacketed polymers is metastable. Eventually, annealing offered a path for the stress relaxation and allowed the structural defects to heal [86]. 

The preparation period consists of the creation of a non-equilibrium state and, possibly, of the frequency labeling in 2D experiments. Usually, the preparation period should be designed in such a way that in the created non-equilibrium state, the population differences or coherences under consideration deviate as much as possible from the equilibrium values. During the relaxation period, the coherences or populations evolve towards an equilibrium (or a steady-state) condition. The behavior of the spin system during this period can be manipulated in order to isolate one specific type of process. The detection period can contain also the mixing period of the 2D experiments. The purpose of the detection period is to create a signal which truthfully reflects the state of the spin system at the end of the relaxation period. As always in NMR, sensitivity is a matter of prime concern. 

In Part II we discussed how to measure the electrical parameters n and pn (and/or p and pp), namely, by means of the conductivity and Hall coefficient. Now we must ask how these parameters relate to the more fundamental quantities of interest, such as impurity concentrations and impurity activation energies. Much can be learned from a consideration of thermal excitation processes only, i.e., processes in which the only variable parameter is temperature. Thus, we are specifically excluding cases involving electron or hole injection by high electric fields or by light. We are also excluding systems that have been perturbed from their thermal equilibrium state and have not yet had sufficient time to return. Some of these nonequilibrium situations will be considered in Part IV. 

Specific volume, usually designated by v, is the volume of a unit weight of material. Thus in cgs units v is in cm3/g, and in mks units it is m3/kg. Of course, v = 1/p where p is the density of the material. This article is concerned with the specific volume of products of steady detonation of condensed expls. One further restriction is that these products are at the CJ state, ie, at the equilibrium state attained upon completion of the detonation reaction. Because of product expansion and rarefaction waves, this state of immense pressures and high temps is very shortlived. Consequently it is intuitively obvious that direct measurements of Vj, the specific volume of materials at the CJ state, is virtually impossible. To date no such direct measurements are available, and vt must be obtained from indirect measurements or else computed theoretically We will now proceed to describe theoretical computations of vt, followed by semi-empirical calcns based on exptl data... 

Kinetics describe the course in space and time of a macroscopic chemical process. Processes of a chemical nature are driven by a system s deviation from its equilibrium state. By formulating the increase of entropy in a closed system, one can derive the specific thermodynamic forces which drive the system back towards equilibrium (or let the system attain a steady non-equilibrium state). 

As an example of the difference between stochastic and deterministic properties consider Figure 3.15. A deterministic property is illustrated by any common thermodynamic property, such as temperature, as illustrated by the vertical line in Figure 3.15. For a specific equilibrium state, the probability of observing a specific temperature is 1, that is, a certainty that is called deterministic. 

We know from experience that any isolated system left to itself will change toward some final state that we call a state of equilibrium. We further know that this direction cannot be reversed without the use of some other system external to the original system. From all experience this characteristic of systems progressing toward an equilibrium state seems to be universal, and we call the process of such a change an irreversible process. In order to characterize an irreversible process further, we use one specific example and then discuss the general case. In doing so we always use a cyclic process. 

Polymers above their Tg are in a state of equilibrium much like simple liquids. However, upon cooling below Tg, polymers are not able to achieve an equilibrium state since the polymer chain segments lack sufficient mobility to reach this state in realizable time scales. Thus, glassy polymers exist in a nonequilibrium state that is a function of the prior history of the sample. It is useful to think of simple volumetric thermal expansion where at equilibrium the specific volume at a given temperature and pressure is Veq(T,p) the specific volume of a rubbery polymer is given by Veq. The... 

This result means in general for single-reaction equilibrium between two species A and B that two degrees of freedom exist, and that pressure as well as temperature must be specified to fix the equilibrium state of the system. However, here, the specification that the gases are ideal removes the pressure dependence, which in the general case appears through the, s. 

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