Thermal expansion defined

When a value of thermal expansion is reported, it must include the pressure and temperature range for which it is valid. Thermal expansion as defined here must not be used interchangeably with the coefficient of isobaric thermal expansion defined above. 

B coefficient of isobaric thermal expansion, defined by Equation 8-25... 

Since different instruments are designed to accept a variety of sample lengths, the change in length per unit starting length is conventionally recorded as a function of temperature, as shown in Figure 7.1. The slope of the trace is the coefficient of linear thermal expansion, defined by ... 

In addition to the coefficient of thermal expansion there is a quantity called the coefficient of linear thermal expansion, defined by... 

ASTM D883 defines a filler as "...a relatively inert material added to a plastic to modify its strength, permanence, working properties, or other quaHties or to lower costs." EiHers (qv) that modify the properties and characteristics of epoxies are employed in epoxy resins for a variety of reasons. Then principal functions are to control viscosity, reduce shrinkage and the coefficient of thermal expansion, effect a cost reduction, and color the epoxy resins. 

The term PDC is defined as polycrystalline diamond compact. The term TSP is defined as thermally stable polycrystalline diamond. TSP materials are composed of manufactured polycrystalline diamond which has the thermal stability of natural diamond. This is accomplished through the removal of trace impurities and in some cases the filling of lattice structure pore spaces with a material of compatible thermal expansion coefficient. 

This is defined as the increase in volume of unit volume of a substance when its temperature is raised by one degree. It is important in that the coefficient of expansion of LPG in its liquid form is relatively high, so that when filling a storage vessel adequate space must always be provided to allow for possible thermal expansion of the liquid. 

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

Optical devices are placed in the light path in order to shape the primary beam. Beam-position monitors, shutters, slits, monochromators, stabilizers, absorbers, and mirrors are utilized for this purpose. The effective beam shape and its flux are defined by these components. In particular, if mirrors are cooled, vibration must be avoided and thermal expansion should be compensated. 

Modern temperature scale proposed by G. Fahrenheit, defined by a thermometer, a law and three fixed points. Fahrenheit s thermometer was a mercury-in-glass one. Thermal expansion versus temperature was assumed linear. Three fixed points were defined 0°F temperature of a mixture of water, ice and ammonium chloride 32°F temperature of melting ice 96°F temperature of human body... 

When the computed stress range varies, whether from thermal expansion or other conditions, SE is defined as the greatest computed displacement stress range. The value of N in such cases can be calculated by eq. (Id)... 

Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

The term S] is defined by the authors as an ionicity factor and assumes a value of 0.5 for oxides and silicates, 0.75 for halides, 0.40 for calcogenides, 0.25 for phosphides and arsenides, and 0.2 for nitrides and carbides (Z is the anion charge). Equation 1.94 is based on the thermal expansion data listed in table 1.15. 

The analogy with thermal expansion coefficients is evident when one compares equations 1.98 and 1.99 with equations 1.90 and 1.91, respectively. For compressibility, as for thermal expansion, a mean coefficient that defines the volumetric variation (V2 — ft) for a finite pressure range (T2— I)) may be introduced. This coefficient, the mean volumetric isothermal compressibility, is given by... 

We now distinguish solid state transformations as first-order transitions or lambda transitions. The latter class groups all high-order solid state transformations (second-, third-, and fourth-order transformations see Denbigh, 1971 for exhaustive treatment). We define first-order transitions as all solid state transformations that involve discontinuities in enthalpy, entropy, volume, heat capacity, compressibility, and thermal expansion at the transition point. These transitions require substantial modifications in atomic bonding. An example of first-order transition is the solid state transformation (see also figure 2.6)... 

If the heat capacity functions of the various terms in the reaction are known and their molar enthalpy, molar entropy, and molar volume at the 2) and i). of reference (and their isobaric thermal expansion and isothermal compressibility) are also all known, it is possible to calculate AG%x at the various T and P conditions of interest, applying to each term in the reaction the procedures outlined in section 2.10, and thus defining the equilibrium constant (and hence the activity product of terms in reactions cf eq. 5.272 and 5.273) or the locus of the P-T points of univariant equilibrium (eq. 5.274). If the thermodynamic data are fragmentary or incomplete—as, for instance, when thermal expansion and compressibility data are missing (which is often the case)—we may assume, as a first approximation, that the molar volume of the reaction is independent of the P and T intensive variables. Adopting as standard state for all terms the state of pure component at the P and T of interest and applying... 

Sideridis, E. (1994). Thermal expansion coefficients of fiber composites defined by the concept of the interphase. Composites Sci. Technol. 51, 301-317. 

Liquid crystal polymers (LCP) are polymers that exhibit liquid crystal characteristics either in solution (lyotropic liquid crystal) or in the melt (thermotropic liquid crystal) [Ballauf, 1989 Finkelmann, 1987 Morgan et al., 1987]. We need to define the liquid crystal state before proceeding. Crystalline solids have three-dimensional, long-range ordering of molecules. The molecules are said to be ordered or oriented with respect to their centers of mass and their molecular axes. The physical properties (e.g., refractive index, electrical conductivity, coefficient of thermal expansion) of a wide variety of crystalline substances vary in different directions. Such substances are referred to as anisotropic substances. Substances that have the same properties in all directions are referred to as isotropic substances. For example, liquids that possess no long-range molecular order in any dimension are described as isotropic. 

Thermal Expansion. Thermal expansion is a measnre of the expansion or contraction of a solid when it is heated or cooled. In the most general case, the coefficient of thermal expansion, a, sometimes called the volnme thermal expansion coefficient, is defined as fhe change in volnme per nnit volnme, V, with temperature, T, at constant pressure, P ... 

Expansion. An increase of dimension. It can be cubical or volume expansion — increase in three dimensions linear — increase in length thermal — increase in volume due to increase in temperature. The rate varies with temp and depends on the coefficient of thermal expansion, which.is defined in Ref 2 and described more fully below under "Expansion, Thermal Coefficient of ... 

Expansion, Thermal Coefficient of. CoeF ficient of Thermal Expansion (Warmeaus-dehnungs-koeffizient, in Ger) is defined in Vol 3 of Encycl, p C391-L... 

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