The effect of pressure on thermodynamic variables

Olsen et al. [279] considered the effect of pressure on the relative concentrations of different Eu + sites in CaF2. Their strategy was to use pressure as a thermodynamic variable to alter the equilibrium between the different Eu + defect complexes. In their experiments, they first fixed the pressure on Eu + CaF2 to a value between 0 kbar and 20 kbar and then varied temperature (up to 420°C) in order to dissociate existing defect complexes, induce fluoride mobility, and form a new, pressure dependent equilibrium distribution of defects. In samples treated at 420°C and 11 kbar, they observed an increase in A site concentration, a comparable decrease in 0 site concentration, and decreases in concentration of... 

High pressure has traditionally been viewed as a macroscopic, thermodynamic experimental variable. Classic applications of pressure have involved equation of state studies of liquids and soHds and measurements of the variation of physical properties as a function of pressure [57,59 - 66]. The basic effect of pressure on a system is a consequence of the thermodynamic stabiHty requirements of the second law [67] and can be expressed most generally as... 

The work on iron-nickel alloys has described shock-compression measurements of the compressibility of fee 28.5-at. % Ni Fe that show a well defined, pressure-induced, second-order ferromagnetic to paramagnetic transition. From these measurements, a complete description is obtained of the thermodynamic variables that change at the transition. The results provide a more complete description of the thermodynamic effects of the change in the magnetic interactions with pressure than has been previously available. The work demonstrates how shock compression can be used as an explicit, quantitative tool for the study of pressure sensitive magnetic interactions. 

At constant temperature, the activity coefficient depends on both pressure and composition. One of the important goals of thermodynamic analysis is to consider separately the effect of each independent variable on the liquid-phase fugacity it is therefore desirable to define and use constant-pressure activity coefficients which at constant temperature are independent of pressure and depend only on composition. The definition of such activity coefficients follows directly from either of the exact thermodynamic relations... 

As chemists, we are most often concerned with reactions proceeding under conditions in which the temperature and pressure are the variables we control. Therefore, it is useful to have a set of properties that describe the effect of a change in concentration on the various thermodynamic quantities under conditions of constant temperature and pressure. We refer to these properties as the partial molar quantities. 

If we change any of the external variables governing the system, such as temperature, pressure, etc., then Eq. (XV.5.1) or (XV.5.2) can be used to estimate the effect of such changes on the rate constant s so long as the changes in external variables do not alter the mechanism of the reaction. But this last proviso defines a very interesting situation. Since Eq. (XV.5.2) involves only thermodynamic factors, the only external variables that need concern us are the thermodynamic variables of state, i.e., those needed to describe an equilibrium state of a system. 

It should be noted that the materials are synthesized under non-equilibrium conditions as the experiments are performed in a dynamic vacuum, and the local vapour pressure of the alkali metal is unknown. The rate and extent of reaction will depend on the nature of the alkali metal, the temperature of the film and the presence of residual ambient gas impurities, which are not controlled in these preliminary experiments. At present, the effect of these variables on the conductivities cannot be assessed. Synthesis in a closed system will be required to determine the relevant thermodynamic parameters. 

For the application of supercritical carbon dioxide as a medium for the production of polyolefins, it is important to have rehable thermodynamic data for the systems involved. Knowledge of the phase behavior of the reaction mixture is crucial to properly choose process variables such as temperature and pressure in order to achieve maximum process efficiency. For this reason, the ethylene-poly (ethylene-co-propylene) (PEP)-C02 system has been taken as a representative model system [3]. The effect of molecular weight as well as the influence of CO2 on the phase behavior has been studied experimentally by cloud-point measurements. In addition, the Statistical Associating Fluid Theory (SAFT) has been applied to predict the experimental results. 

We have studied the problem of pressurized line cooldown both experimentally and analytically. We constructed a small pressurized transfer system to investigate the physical processes involved in line cooldown and to determine the effects of various system variables on line cooldown time. An analysis was developed from thermodynamic principles so that the test data could be correlated and the range of our experimental results extended. The analysis and test data have been found to be in good agreement. 

The principle of Le ChStelier asserts that in general a system will react to lessen the effect of a stress on an intensive variable, if it can do so. This effect was illustrated by considering the shift in equilibrium by changing the temperature or the pressure on a system and by adding a reactant or product to the system. The application of the thermodynamics of chemical equilibrium to biological processes was illustrated through a discussion of the coupling of chemical reactions and active transport. 

In general the net macroscopic pressure tensor is determined by two different molecular effects One pressure tensor component associated with the pressure and a second one associated with the viscous stresses. For a fluid at rest, the system is in an equilibrium static state containing no velocity or pressure gradients so the average pressure equals the static pressure everywhere in the system. The static pressure is thus always acting normal to any control volume surface area in the fluid independent of its orientation. For a compressible fluid at rest, the static pressure may be identified with the pressure of classical thermodynamics as may be derived from the diagonal elements of the pressure tensor expression (2.189) when the equilibrium distribution function is known. On the assumption that there is local thermodynamic equilibrium even when the fluid is in motion this concept of stress is retained at the macroscopic level. For an incompressible fluid the thermodynamic, or more correctly thermostatic, pressure cannot be deflned except as the limit of pressure in a sequence of compressible fluids. In this case the pressure has to be taken as an independent dynamical variable [2] (Sects. 5.13-5.24). 

Epitaxial layers of compound semiconductors are most frequently grown by chemical synthesis reactions. Thermodynamics can predict whether a reaction is feasible at all for the generation of crystalline solid from the vapor phase. It can, furthermore, predict the effect of variations in the experimentally controllable variables, such as input partial pressures and temperature on the yield of the reaction or the composition of solid solutions. 

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