Thermal temperature dependence

Seeley J V, Morris R A, Viggiano A A, Wang FI and Flase W L 1997 Temperature dependencies of the rate constants and branching ratios for the reactions of Cr(Fl20)g 3 with CFIjBr and thermal dissociation rates for CI (CFl3Br) J. Am. Chem. Soc. 119 577-84... 

In order to Introduce thermal effects into the theory, the material balance equations developed in this chapter must be supplemented by a further equation representing the condition of enthalpy balance. This matches the extra dependent variable, namely temperature. Care must also be taken to account properly for the temperature dependence of certain parameters In... 

The glass-transition temperature, T, of dry polyester is approximately 70°C and is slightly reduced ia water. The glass-transitioa temperatures of copolyesters are affected by both the amouat and chemical nature of the comonomer (32,47). Other thermal properties, including heat capacity and thermal conductivity, depend on the state of the polymer and are summarized ia Table 2. 

Values of thermal conductivity are temperature-dependent and vary widely for different materials. Table 1 summarizes the thermal conductivity values of a few materials relevant to heat-exchanger analysis (1,2). 

Commercial condensed phosphoric acids are mixtures of linear polyphosphoric acids made by the thermal process either direcdy or as a by-product of heat recovery. Wet-process acid may also be concentrated to - 70% P2O5 by evaporation. Liaear phosphoric acids are strongly hygroscopic and undergo viscosity changes and hydrolysis to less complex forms when exposed to moist air. Upon dissolution ia excess water, hydrolytic degradation to phosphoric acid occurs the hydrolysis rate is highly temperature-dependent. At 25°C, the half-life for the formation of phosphoric acid from the condensed forms is several days, whereas at 100°C the half-life is a matter of minutes. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

The responsivity and g-r noise may be analyzed to obtain background photon flux and temperature dependence of responsivity, noise, and detectivity. Typically, n > p, and both ate determined by shallow impurity levels. The minority carrier density is the sum of thermal and optical contributions. 

Density. The density of transparent vitreous sihca is approximately 2.20 g/cm. Translucent and opaque glasses have lower densities owing to the entrapped bubbles. The density of translucent Vitreosil, for example, is 2.07—2.15 g/cm (87,119). The density of transparent vitreous sihca decreases with increasing hydroxyl content and with lower fictive (glass stmcture equihbrium) temperatures. The fictive temperature depends on the thermal history and on glass viscosity (120). 

Many special-purpose electrical thermometers have been developed, either for use in practical temperature measurement, or as research devices for the study of temperature and temperature scales. Among the latter are thermometers which respond to thermal noise (Johnson noise) and thermometers based on the temperature dependence of the speed of sound. 

Effect of Temperature and pH. The temperature dependence of enzymes often follows the rule that a 10°C increase in temperature doubles the activity. However, this is only tme as long as the enzyme is not deactivated by the thermal denaturation characteristic for enzymes and other proteins. The three-dimensional stmcture of an enzyme molecule, which is vital for the activity of the molecule, is governed by many forces and interactions such as hydrogen bonding, hydrophobic interactions, and van der Waals forces. At low temperatures the molecule is constrained by these forces as the temperature increases, the thermal motion of the various regions of the enzyme increases until finally the molecule is no longer able to maintain its stmcture or its activity. Most enzymes have temperature optima between 40 and 60°C. However, thermostable enzymes exist with optima near 100°C. 

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). 

The majority of the NOx produced in the combustion chamber is called thermal NOx. It is produced by a series of chemical reactions between the nitrogen (N2) and the oxygen (O2) in the air that occur at the elevated temperatures and pressures in gas turbine combustors. The reaction rates are highly temperature dependent, and the NOx production rate becomes significant above flame temperatures of about 3300 °F (1815 °C). Figure 10-19 shows schematically, flame temperatures and therefore NOx production... 

The temperature dependence of the thermal conductivity of CBCF has been examined by several workers [10,13,14]. Typically, models for the thermal conductivity behavior include a density term and two temperaUrre (7) terms, i.e., a T term representing conduction within the fibers, and a term to account for the radiation contribution due to conduction. The thermal conductivity of CBCF (measured perpendicular to the fibers) over the temperature range 600 to 2200 K for four samples is shown in Fig. 6 [14]. The specimen to specimen variability in the insulation, and typical experimental scatter observed in the thermal conductivity data is evident in Fig. 6. The thermal conductivity of CBCF increases with temperature due to the contribution from radiation and thermally induced improvements in fiber structure and conductivity above 1873 K. 

Recently, Dinwiddie et al. [14] reported the effects of short-time, high-temperatme exposures on the temperature dependence of the thermal conductivity of CBCF. Samples were exposed to temperatures ranging from 2673 to 3273 K, for periods of 10, 15, and 20 seconds, to examine the time dependent effects of graphitization on thermal conductivity measured over the temperature range from 673 to 2373 K. Typical experimental data are shown in Figs. 7 and 8 for exposure times of 10 and 20 seconds, respectively. The thermal conductivity was observed to increase with both heat treatment temperature and exposure time. 

Fig. 6. The temperature dependence of thermal conductivity for CBCF in the as fabricated condition. Reprinted from [14], copyright 1996 Technomic Publishing Company, Inc., with permission.

Dinwiddle et al. [14] proposed a model for the behavior of the CBCF in which the temperature dependence of thermal conductivity (Aj-) may be expressed as... 

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