Walther equation

Viscosity—Temperature. Oil viscosity decreases with increa sing temperature in the general pattern shown in Eigure 8, an example of ASTM charts which are available in pad form (ASTM D341). A straight line drawn through viscosities of an oil at any two temperatures permits estimation of viscosity at any other temperature, down to just above the cloud point. Such a straight line relates kinematic viscosity V in mm /s(= cSt) to absolute temperature T (K) by the Walther equation. 

The viscosity of hydrocarbons and temperature are related by the Walther equation (76) ... 

Temperature Suseeptibility. This is the term used to designate the change in consistency of an asphalt with changes in temperature. The Walther equation slope constant m can be used as a fundamental measure. 

The Walther Equation and ASTM Viscosity-Temperature Charts... 

We must perforce devote some time and attention to the concept known as the vlscoilty Index, which has become embedded in the terminology of technological lubrication with some unfortunate connotations. Whereas the Walther equation and the ASTM viscosity-temperature charts are frankly empirical devices used to linearize the viscosity-temperature relations for convenience and utility, the viscosity index is an attempt to impart the mystique of quality by assigning an evaluative aspect to the... 

Viscosity Calculation The Walther Equation—ASTM D341... 

The viscosity of a sample at some temperature can be calculated using the Walther equation if viscosities in centistokes at two other temperatures are available (note this equation holds true only for centistokes measurements). This linear equation is... 

This sequence was repeated until solution convergence was obtained. However, to do so required the embodiment of the appropriate film thickness statement and an expression for the dependence of lubricant viscosity on temperature. For the present investigation where thermal aspects were included, the Walther equation was used, i.e. 

This relationship is known as the Nernst equation, after Walther Nernst (1864-1941), a brilliant and egocentric colleague of Arrhenius, who first proposed it in 1888. Recalling that, at 25°C, the quantity RT/F is 0.0257 V,... 

Nemst equation An equation relating cell voltage E to the standard voltage ° and the concentrations of reactants and products E = E° — (0.0257/ )(lnQ), 493,508-509q application, 494-495 ion concentrations, 494-495 Nernst, Walther, 493... 

When both solutions are binary and identical in nature and differ only by their concentration and the component E of the held strength is given by Eq. (4.18), the diffusion potential 9 can be expressed by Eq. (4.19). An equation of this type was derived by Walther Nemst in 1888. Like other equations resting on Eick s law (4.1), this equation, is approximate and becomes less exact with increasing concentration. For the more general case of multicomponent solutions, the Henderson equation (1907),... 

Harry B. Gray and Walther Ellis,13 writing in Chapter 6 of reference 13, describe three types of oxidation-reduction centers found in biological systems. The first of these, protein side chains, may undergo oxidation-reduction reactions such as the transformation of two cysteine residues to form the cystine dimer as shown in equation 1.28 ... 

Analysis of pump-probe absorption data of Walther et al. (2005 not shown here) indicated two stretched exponentials characterizing the geminate recombination. In agreement with pump-probe results, their transient grating data (reproduced in Figure 1.12) have been fitted by an equation,... 

One of the widely used methods of analysis of kinetic data is based on extraction of the distribution of relaxation times or, equivalently, enthalpic barrier heights. In this section, we show that this may be done easily by using the distribution function introduced by Raicu (1999 see Equation [1.16] above). To this end, we use the data reported by Walther and coworkers (Walther et al. 2005) from pump-probe as well as the transient phase grating measurements on trehalose-embedded MbCO. Their pump-probe data have been used without modification herein, while the phase grating data (also reproduced in Figure 1.12) have been corrected for thermal diffusion of the grating using the relaxation time reported above, r,, and Equation (1.25). 

FIGURE 1.13 Experimental results (points) obtained from pump-probe (left) and transient phase grating (right) measurements of MbCO recombination as a function of time, t, following photodissociation. Solid lines were computed from equations (26) and (27), and the best-fit parameter values are listed in Table 1.2. (From Walther, M., Raicu, V., Ogilvie, J. R, Phillips, R., Kluger, R., and Miller, R. J. D. 2005. J. Phys. Chem. B 109 20605-11. With permission.)... 

The reduction potential of a half-cell depends not only on the chemical species present but also on their activities, approximated by their concentrations. About a century ago, Walther Nemst derived an equation that relates standard reduction potential ( ") to the reduction potential (E) at any concentration of oxidized and reduced species in the cell ... 

Torssell et al. (1949) attempted to develop a mathematical relationship among the viscosity, temperature, and total solids content of skim milk and whole milk. After showing that Walther s equation... 

Also shown in Figure 15.2 is a graph of an equation relating log A to /T derived by Walther Nernst. We will describe his contribution more fully in the next section. 

About the same time that Haber was making his measurements, Walther Nernst also studied the ammonia synthesis reaction at high temperatures and obtained results that differed significantly from those obtained by Haber.2 Nernst s measurements were made at high pressures (approximately 60 atm). His results are also shown in Figure 15.3, and they do not appear to differ in a major way from those of Haber, until the effect of pressure is taken into account, as we will now see. From equation (15.12), we find that Kx is related to K by... 

The most comprehensive dataset for a silicate has been compiled for quartz dissolution over a range of temperature and pressure (e.g., Rimstidt and Barnes, 1980 Knauss and Wolery, 1988 Wollast and Chou, 1988 Brady and Walther, 1990 Dove and Crerar, 1990 Hiemstra and van Riemsdijk, 1990 Dove and Elston, 1992 Dove and Rimstidt, 1994 Tester et al., 1994 Dove, 1995). Dove (1994, 1995) has modelled the rate of dissolution of quartz as a function of temperature by the rate equation,... 

As discussed earlier. Equation (32) generally predicts that log dissolution rate versus pH has a V shape (Figure 3), where the trough of low dissolution rate occurs approximately at pH = pHppzc (however, see discussion in Brantley and Stillings, 1996 Walther, 1996 Mukhopadhyay and Walther, 2001 Oelkers, 2001b). Parameters for Equation (32) for feldspar minerals are summarized in Table 2 however, the value of the rate constants appropriate at neutral and basic pH ( HjO. oh) have generally not been well-constrained. Under neutral pH, dissolution is so slow that rates may be unmeasurable in laboratory timeframes, and many workers have set the second term equal to zero in Equation (32). 

Nernst equation An equation that correlates chemical energy and the electric potential of a galvanic cell or battery. Links the actual reversible potential of an electrode (measured in volts), E, at nonstandard conditions of concentration or pressure, to the standard reversible potential of the electrode couple, EO, which is a thermodynamic value. The Nernst equation is named after the German physical chemist Walther Nernst. 

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