Volume Expansion of Solids

If V2 and Vi are the volumes at fa and fi, respectively, then Ua = Vi(l + CAt), C being the coefficient of cubical expansion and Af the temperature interval. Where only a single temperature is stated, C represents the true coefficient of volume expansion at that temperature. 

Joule-Thomson coefficients for substances listed in Table 2-184 are given in tables in the Thermodynamic Properties section. 

For this subsection, the following units conversions are applicable To convert the Joule-Thomson coefficient, x, in degrees Celsius per atmosphere to degrees Fahrenheit per atmosphere, multiply by 1.8. 

To convert bars to pounds-force per square inch, multiply by 14.504 to convert bars to kilopascals, multiply by 1 x 10.  

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J. Dewar gives 0-0000787 for the coefficient of expansion of solid dodecahydrated disodium hydrophosphate, and H. Kopp, between 5° and 35°, gives for the volume v at 0° when iq is the volume at 0°, v=u1(l+0-0000830890—O Oe47O9902 +O O91797403), and for the molten salt between —37° and 68°, v=v (l +0-0004350). C. Porch gives for a soln. of dipotassium hydrophosphate the coeff. of expansion XlO6 between ... 

The effect of temperature on retention has been described experimentally,(4-8) but the functional dependence of k with temperature has only recently been described.W A thermodynamic model was outlined relating retention as a function of temperature at constant pressure to the volume expansivity of the fluid, the enthalpy of solute transfer between the mobile phase and the stationary phase and the change in the heat capacity of the fluid as a function of temperature.(9) The solubility of a solid solute in a supercritical fluid has been discussed by Gitterman and Procaccia (10) over a large range of pressures. The combination of solute solubility in a fluid with the equation for retention as a function of pressure derived by Van Wasen and Schneider allows one to examine the effect of solubility on solute retention. 

TEM observations of the oxidized scale have revealed mullite grains with transgranular cracks, a phenomenon that is not surprising when one considers that the oxidation of SiC produces a volume expansion of 100%. When the reaction product contains a solid as well as a liquid product, as in the present situation, the volume expansion can be accommodated by squeezing out the liquid phase, resulting in a liquid cap on top of the solid reaction products. This has been observed by Luthra and Park,13 and is apparent in the micrograph shown in Fig. 8.5. 

The thermal expansion of solids depends on their structure symmetry, and may be either isotropic or anisotropic. For example, graphite has a layered structure, and its expansion in the direction perpendicular to the layers is quite different from that in the layers. For isotropic materials, ay w 3 a . However, in anisotropic solid materials the total volume expansion is distributed unequally among the three crystallographic axes and, as a rule, cannot be correctly measured by most dilatometric techniques. The true thermal expansion in such case should be studied using in situ X-ray diffraction (XRD) to determine any temperature dependence of the lattice parameters. 

The theoretical volume expansion upon melting can be obtained by calculating the volumes of the solid and liquid at coexistence from Eq. (3.6), using the measured For the time-averaged WCA system, we obtain a theoretical fractional volume expansion of... 

Since the significant structures theory as used by Eyring and collaborators is able to predict quite accurately all the thermodynamic and many physical properties of a liquid using a model that assumes the volume expansion of a liquid to be due to the introduction of holes in the solid lattice, it seems quite likely that the theory might also be applied to the plastic crystal state. In order to test this idea, the theory was applied to the plastic crystal state of CBr4, for which good experimental data are available. ... 

The infiltration of water into clay-like materials causes changes in the pore structure of the material. Water molecules place in the solid matrix and become immobile. In consequence the effective porosity and the intrinsic permeability decrease. If the volume expansion of the material is restrained, swelling pressure is observed which increases linearly with the degree of water saturation, Studer et al. (1984), and BSrgesson (1984). The correlation between swelling pressure p, and void ratio e can be expressed best with the following empirical relationship, Bdrgesson et al. (1995) ... 

It is well known that the volume of ice is greater than that of water by about 8%. F or most liquids the density increases on transforming the liquid to ice, as the solid is usually denser than the liquid. This clearly shows that ice is more stmctured and has more open space in its molecular arrangement. The volume expansion of water upon freezing is an anomalous behavior because volume decreases upon freezing for other simple liquids. It is this very anomaly by which fish can survive in low-temperature regions because ice floats on the upper layer of the lake and the lower layer of the lake still contains liquid water which is of higher density. 

Water Uptake, Volume Expansion, and Solids Loss of KDML 105 after Drying at Different Drying Conditions... 

For periodic structures, the continuity equations may also be solved explicitly by multipole expansion to yield tractable series solutions [59,60], T o a first approximation, these treatments are equivalent at low volume fractions of solids. Experimental studies of diffusion of small nonadsorbing solutes within ordered assemblies of colloids is has been well predicted by these treatments [31,59,60]. However, these theories do not consider solutes of nonzero size, and another method is necessary to examine this. 

SO that the open spaee ereated within individual partieles can accommodate the volume expansion of the solid skeleton. 

Fig. 36.1 Density p(7) profiles of water droplets measured using (a) Raman and FTIR (1.4 nm) (Reprinted with permission from [6]) and (b) small-angle scattering of X-rays (SAXS) (Reprinted with permission from [17]) showing cooling densification in the liquid (I T > 273 K), freezing expansion (II 273 > T> 205(244) K), cooling densification in the solid (III 205(244) K > T > 80 K, which varies with droplet size) and (c) slight volume expansion of H2O and D2O at very low temperatures. (IV T < 80 K) (Reprinted with permission from [18])...

Foamed plastics with high cell density and narrow cell size distributions offer superior mechanical properties such as higher toughness and specific tensile stress, as well as better thermal and acoustic insulation properties when compared to their solid counterparts [1-3]. Due to the substantial increase in price of plastic resins in recent years, reducing raw material cost is one research area that is of major economical interest to plastics manufacturers. To this end, research has been undertaken to investigate the fundamental mechanism governing volume expansions of plastic foams [4-6]. 

Fig. 2.22. At very high pressures the observed pressure-volume relations of porous samples show expansions due to the very high temperatures produced in collapsing the voids. The figure shows representative behavior at porous sample densities of 25% to 100% of solid density.

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

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