Relative temperature coefficient

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. 

From [9.31], it follows that the relative temperature coefficient of viscosity = 3t / T 3T = 31nri / 3T for mixtures of chemically non-interacting liquids is described by equation ... 

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 ... 

It is important to mention that all potentials of Figs. 5.5.1 and 5.5.2 are referenced to the standard hydrogen electrode at 25 °C. This is useful for practical applications because the potential of the standard hydrogen electrode has a high relative temperature coefficient. 

The saturation magnetization, J), is the (maximum) magnetic moment per unit of volume. It is easily derived from the spia configuration of the sublattices eight ionic moments and, hence, 40 ]1 per unit cell, which corresponds to = 668 mT at 0 K. This was the first experimental evidence for the Gorter model (66). The temperature dependence of J) (Fig. 7) is remarkable the — T curve is much less rounded than the usual BdUouia function (4). This results ia a relatively low J) value at RT (Table 2) and a relatively high (—0.2%/° C) temperature coefficient of J). By means of Mitssbauer spectroscopy, the temperature dependence of the separate sublattice contributions has been determined (68). It appears that the 12k sublattice is responsible for the unusual temperature dependence of the overall J). 

The most important disadvantages are moderate and ( -ff), relatively high temperature coefficients (xB and CcJT, and poor mechanical properties (low strength, brittleness). The moderate B and perhaps the less serious, as a larger cross-sectional area produces the requited flux. 

Cross-linked polyester composites have a relatively low coefficient of thermal conductivity that can provide beneficial property retention in thick laminates at high temperatures as well as remove the need for secondary insulation. The coefficient of thermal expansion of glass-reinforced composites is similar to aluminum but higher than most common metals. 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

Relative reactivity wiU vary with the temperature chosen for comparison unless the temperature coefficients are identical. For example, the rate ratio of ethoxy-dechlorination of 4-chloro- vs. 2-chloro-pyridine is 2.9 at the experimental temperature (120°) but is 40 at the reference temperature (20°) used for comparing the calculated values. The ratio of the rate of reaction of 2-chloro-pyridine with ethoxide ion to that of its reaction with 2-chloronitro-benzene is 35 at 90° and 90 at 20°. The activation energy determines the temperature coefficient which is the slope of the line relating the reaction rate and teniperature. Comparisons of reactivity will of course vary with temperature if the activation energies are different and the lines are not parallel. The increase in the reaction rate with temperature will be greater the higher the activation energy. 

The acid hydrolysis of diaziridines has been investigated kinetic-ally. The reaction is first order and shows a relatively high temperature coefficient. Thus one finds a relatively high activation enthalpy (23-28 kcal) and a positive activation entropy (2-6 eu). The influence of substitution on nitrogen is small. The velocity of the diaziridine hydrolysis depends only in the weakly acid region on the acid concentration. Between pH 7 and 3 the fc-values rise by nearly 10 . For the... 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

Benson [499] and Livingstone [500] considered the influence of experimental accuracy on measured rate and temperature coefficients. To measure the rate coefficient to 0.1%, the relative errors in each ctj value must be <0.1% and the reaction interval should be at least 50%. Temperature control to achieve this level of precision must be 0.003% or 0.01 K at 300 K. For temperature control to 1 K, the minimum error in the rate coefficient is 5% and in the activation energy, measured over a 20 K interval, is 10%. No allowance is included in these calculations for additional factors such as self-heating or cooling. 

Amide proton temperature coefficients and hydrogen exchange rates can provide information about hydrogen-bonding interactions and solvent sequestration in unfolded or partly folded proteins (Dyson and Wright, 1991). Abnormally low temperature coefficients, relative to random coil values, are a clear indication of local structure and interactions. 

Adverse effects of fenvalerate on survival of terrestrial arthropods were observed at 0.002 to 0.015 pg whole-body topical application, O.llkg/ha aerial application, 5.4 mg/kg in the soil, 50 mg/kg in the diet, and 1.4 g/ant mound (Table 20.4). Synthetic pyrethroids are more effective in biological systems at low temperatures. The relative sensitivity of insects when compared with mammals is attributed in part to this negative temperature coefficient. Thus, warm-blooded animals are less affected than insects and other poikilotherms (Klaassen etal. 1986). Fenvalerate, for example, showed a negative correlation between temperature and toxicity to crickets (Acheta pennsylvanicus), being up to 1.9 times more toxic at 15°C than at 32°C (Harris etal. 1981). A similar case is made for honey bees (Apis mellifera) (Mayer et al. 1987) and for many species of aquatic invertebrates and fish (Mayer 1987). 

Infrared and ultraviolet spectra showed the polymers to contain (presumably terminal) p-methoxyphenyl groups. From the Mayo plots (1/DP - [anisole]/[C4H8]) the relative transfer coefficient kjkp was found to be 5.3 x 10"3, a value which did not vary significantly with temperature. The transfer reaction can be represented as follows ... 

This model was fitted to the data of all three temperature levels, 375, 400, and 425°C, simultaneously using nonlinear least squares. The parameters were required to be exponentially dependent upon temperature. Part of the results of this analysis (K6) are reported in Fig. 6. Note the positive temperature coefficient of this nitric oxide adsorption constant, indicating an endothermic adsorption. Such behavior appears physically unrealistic if NO is not dissociated and if the confidence interval on this slope is relatively small. Ayen and Peters rejected this model also. 

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