Absolute temperature coefficient

Permittivity of mixtures at different temperatures can be calculated with high accuracy from absolute temperature coefficients of permittivity and their values using equations identical in form to [9.24]- [9.26]. For example, the calculation of temperature coefficients... 

The index of refraction is affected by temperature variations. This can be ascertained through the temperature coefficient of refractive index, denoted dn /dT. Hence, the Abbe number also changes with temperature. There are two ways of showing the temperature coefficient of the refractive index. One is the absolute temperature coefficient of refractive index dn ldT), measured in a vacuum, and the other is the relative temperature coefficient of refractive index dn-JdT),, measured in ambient air (101.3 kPa in dry air). They are related by the following formula ... 

The coefficient of dE is the inverse absolute temperature as identified above. We now define the pressure and chemical potential of the system as... 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

For particles of any shape at an absolute temperature T, Einstein showed that f is related to the experimental diffusion coefficient D by the expression... 

Vitreous siUca aimealed at 1100°C has been designated NIST Standard Reference Material 739 (LI and L2). Its expansion coefficient, a, may be calculated for 300—700 K from the following expression (144), where Tis the absolute temperature in Kelvin. 

No tables of the coefficients of thermal expansion of gases are given in this edition. The coefficient at constant pressure, l/t)(3 0/3T)p for an ideal gas is merely the reciprocal of the absolute temperature. For a real gas or liquid, both it and the coefficient at constant volume, 1/p (3p/3T),, should be calculated either from the equation of state or from tabulated PVT data. 

T = absolute temperature. Subscript 1 (or G), radiating surface (or gas) temperature subscript E, exit-gas subscript o, base temperature subscript E, pseudoadiabatic flame temperature based on C averaged from to Te-U = overall coefficient of heat transfer, gas convec tion to refractory wall to ambient air. 

Electrical Properties at Low Temperatures The eleciiical resistivity of most pure metalhc elements at ambient and moderately low temperatures is approximately proportional to the absolute temperature. At very low temperatures, however, the resistivity (with the exception of superconductors) approaches a residual value almost independent of temperature. Alloys, on the other hand, have resistivities much higher than those of their constituent elements and resistance-temperature coefficients that are quite low. The electrical resistivity of alloys as a consequence is largely independent of temperature and may often be of the same magnitude as the room temperature value. 

The factor B = D/RT is the mobility and contains the diffusion coefficient D, the gas constant R, and the absolute temperature T. The equation includes a diffusion and a migration term. Correspondingly Eq. (2-23) gives the first diffusion law for Zj = 0 and Ohm s Law for grad /i, = 0. For transfer across a phase boundary ... 

Temperature programming was introduced in the early days of GC and is now a commonly practiced elution technique. It follows that the temperature programmer is an essential accessory to all contemporary gas chromatographs and also to many liquid chromatographs. The technique is used for the same reasons as flow programming, that is, to accelerate the elution rate of the late peaks that would otherwise take an inordinately long time to elute. The distribution coefficient of a solute is exponentially related to the reciprocal of the absolute temperature, and as the retention volume is directly related to the distribution coefficient, temperature will govern the elution rate of the solute. 

Tn normal work, "C is used in preference to the absolute temperature K. However, it is essential that K be used when working with the gas laws, radiation, and the coefficient of cubical expansion. The symbol for normal temperature is 0 followed by a suffix, while T always denotes absolute temperature. 

Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

It is possible, in some situations, that two different phenomena which proceed at different rates with different temperature coefficients or activation energies will affect the physical properties. In such complex cases, it is not expect to obtain a linear relation between the logarithm of life and reciprocal absolute temperature. If one obtains a nonlinear curve, however, it may he possible to identify the reaction causing the nonlinearity and correct for it. When one can make such a correction, one obtains a linear relationship. 

The heat evolved per unit isothermal increase of pressure is equal to the continued product of the absolute temperature, the specific volume, and the coefficient of expansion o. 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

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