Characteristic temperature Compressibility

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). 

Essentially the characteristic temperature is a measure of the temperature at which the atomic heat capacity is changing from zero to 6 cal deg for silver (0 = 215 K) this occurs around 100 K, but for diamond (0 = 1860 K) with a much more rigid structure, the atomic heat capacity does not reach 5 cal deg i until 900 K. Those elements that resist compression and that have high melting points have high characteristic temperatures. Equations have been derived relating y/ u ) to the characteristic temperature 0. At room temperature diamond, with a characteristic temperature of 1860 K, has a root-mean-square amplitude of vibration, / u ) of 0.02 A, while copper and lead, with characteristic temperatures of 320 and 88 K, respectively, have values of 0.14 and 0.28 A for (u ). - Similar types of values are obtained for crystals with mixed atom (or ion) types. For example, average values of / u ) for Na+ and Cl in sodium chloride (0 = 281 K) are 0.14 A at 86 K and 0.23 A at 290 K. ° ... 

Characteristic temperature A quantity 0 obtained from a study of the variation of the specific heat of a material with absolute temperature T. At low temperatures the specific heat varies as (T/0) . Materials with high melting points and that resist compression have high values of 0. 

It may be mentioned that the Debye characteristic temperature can be derived from other properties of the element, particularly from the compressibility and Poisson s (elasticity) ratio. Where such data are available it is thus possible to obtain reasonably accurate heat capacities, at moderate and high temperatures, from elasticity measurements. 

VFa/HFP/TPE Reactivity. It is well known to those f2miliar wi the characteristics of fluoroelastomers that polymers of unusu dly high fluorine content, e.g., VF2/HFP/TFE terpol rs tAiich contain about 45 wt% VF2 and about equal amounts of HFP and TFE, exhibit some compromise in cure rate and high-temperature compression set resistance in order to achieve their increased fluid resistance. In order to determine idiether there are discernible chemical reasons for these differences, the behavior of VF2/HEP/IFE polymers toward bases in solution was investigated. 

There is a very different story to tell when normal flame propagation gives place to detonation. In this phenomenon the expansion caused by the rise in temperature compresses the adjacent layers and thereby heats them suflSciently to bring them to the point of reaction. Something like a wave of adiabatic compression traverses the tem with a velocity of the order of magnitude of that of sound. The detonation wave differs from a soxmd wave in that a fresh evolution of heat occurs in each volume element, whereby the temperature is maintained and the compression intensified. The speed of travel is about three powers of ten greater than that of normal fiame, and for a given explosive mixture has a characteristic and constant value. 

The prediction of miscibility requires knowledge of the parameters T" (the characteristic temperature), p (the characteristic pressure) and V (the characteristic specific volume) of the corresponding equation of state which can be calculated from the density, thermal expansivity and isothermal compressibility. The isobaric thermal expansivity and the isothermal compressibility can be determined experimentally from p-V-Tmeasurements where these values can be calculated from V T) and V(p)j. The characteristic temperature T is a measure of the interaction energy per mer, V is the densely packed mer volume so that p is defined as the interaction energy per... 

EOV EOS theory was developed by formulation of canonical function of the Boltzmann distribution of energies and derivation of thermodynamic pressure. The theorem of corresponding states says that the same compressibility factor can be expected for all fluids when compared at reduced temperature and pressure. A two-parameter correlation for compressibility factor, Z, can be derived using the theorem of corresponding states. EOV EOS obeys the corresponding state principle. Characteristic temperature, pressure, and specific volume used in EOV EOS are tabulated for 16 commonly used polymers. 

It may be remarked that the equilibration between the different forms of energy of a system of molecules which are not undergoing reaction is usually attained quite rapidly due to the coUisional process. It is only under rather exceptional conditions that the equilibration is not attained, for example, in flames or in the rapid adiabatic compressions due to sound waves. In the latter instance the vibrational energy does not attain equilibrium with the translational (and rotational) energy within the period of the wave. Under such conditions it may occur that the various translational states are at approximate equilibriiun with each other and have a statistical parameter 7, and also that the vibrational states are at equilibrium amongst themselves with a characteristic temperature However, if... 

The second system constitutes a low Mach number internal gas flow with non-adiabatic walls, i.e., a compressible gas flow [119]. In the foregoing discussion we have seen how the case Ma 0 with an adiabatic wall is an example of incompressible flow. In other instances there is significant heat transfer through the wall. In this case we can isolate the flow situation by imagining that the wall is held at some fixed temperature Tw that is different from To. The non-dimensional scale for the temperature is redefined, so we need to redo the analysis of the resulting dimensionless equations. The problem now has a characteristic temperature scale. To — Tw, which is a driving force for the conduction of heat from the wall into the fluid. Since we expect that all temperatures wfll he between these two values, the... 

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