Compressibility and Expansion Coefficients

The basic properties of water such as viscosity, dissociation constant, dielectric constant, compressibility, and the coefficient of thermal expansion play a major role in determining optimal reaction conditions for obtaining maximum benefits in both SCWO and WAO processes. The properties of water change dramatically with temperature, particularly near the critical point [24-26]. A well-known example, the variation of pAw with temperature at the saturation pressure, is shown in Fig. 3. The dissociation constant of water goes through a maximum around 250°C (pAw minimum), and then undergoes a sharp decline as the temperature approaches the critical point. The density and the dielectric constant of water also show sharp changes close to the critical point, as shown in Fig. 4. 

The effectiveness of a refrigeration cycle is measured by its coefficient of performance. For given values of Tc and TH, the highest possible value is attained by the Carnot refrigerator. The vapor-compression cycle with reversible compression and expansion approaches this upper limit. A vapor-compression cycle with expansion in a throttle valve has a somewhat lower value, and this is reduced further when compression is not isentropic. The following example provides an indication of the magnitudes of coefficients of performance. 

Shah et al. carried out a Monte-Carlo simulation in the isothermal-isobaric (NPT) ensemble of [C4mim][PF6] [12]. The authors calculated the molar volume, cohesive energy density, isothermal compressibility, cubic expansion coefficient, and liquid structure as a function of temperature and pressure. A united atom force field was developed using a combination of ab initio calculations and literature parameter values were also developed. Calculated molar volumes were within 5% of experimental values, and a reasonable agreement was obtained between calculated and experimental values of the isothermal compressibility and cubic expansion coefficient. [PF6] anions were found to cluster preferentially in two favorable regions near the cation, namely around the C2 carbon atom, both below and above the plane of the imidazole ring [12],... 

It is obvious that properties such as isothermal compressibility, isobaric expansion coefficient and heat capacity, which display an extremum near the critical density, cannot be intermediate between those of vapor and liquid. As an example, we show in Figs. 4a and 4b the isobaric heat capacity of supercritical water along an Isobar. The sharp spike in Fig. 4a, with temperature as the abscissa, is the equivalent of the broad maximum in Fig. 4b, with density as abscissa. 

Nuclear motion drags along the electronic cloud, so that as temperature rises, molecular envelopes oscillate more and more. If the intermolecular potential were perfectly harmonic, the overall volume effect would be nil, because the compressions and expansions would average out but the potential is much steeper on the compression side (Fig. 4.4), so expansion is hindered less than contraction and molecules effectively occupy more and more space as mobility increases. So thermal expansion is very strictly dependent on the shape of the potential curve, that is on the strength and anisotropy of the intermolecular potential, in a typical structure-property relationship. The simple equation that defines the isobaric thermal expansion coefficient a is... 

The volumetric (P-V-T) behavior of gases under ordinary pressures is described approximately by the ideal gas law. For higher pressures, several more accurate equations of state were introduced. A calculation practice was introduced for ordinary calculations Gases are treated as though they were ideal. The volumes of solids and liquids are computed with the compressibility and the coefficient of thermal expansion. For ordinary calculations they are treated as though they had constant volume. 

Two other important quantities are the isobaric expansivity ( coefficient of themial expansion ) and the isothermal compressibility k, defined as... 

Figure 4.14 Behavior of thermodynamic variables at Tg for a second-order phase transition (a) volume and fb) coefficient of thermal expansion a and isothermal compressibility p.

By an assortment of thermodynamic manipulations, the quantities dn/dp and [N (d G/dp )o] can be eliminated from Eq. (10.48) and replaced by the measurable quantities a, /3, and dn/dT the coefficients of thermal expansion, isothermal compressibility, and the temperature coefficient of refractive index, respectively. With these substitutions, Eq. (10.48) becomes... 

The typical mechanical properties that qualify PCTFE as a unique engineering thermoplastic are provided ia Table 1 the cryogenic mechanical properties are recorded ia Table 2. Other unique aspects of PCTFE are resistance to cold flow due to high compressive strength, and low coefficient of thermal expansion over a wide temperature range. 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

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