Standard representations temperature dependence

Figure 6 shows the dependency ijl T) for eight different liquids with greatly different temperature coefficients of the viscosity, whose viscosities cover six decades within the range of T= 20-80°C. Figure 7 depicts the standard representation of this behavior. Surprisingly this proves that all these liquids behave similarly in the /r(I) respect. In addition, it proves that this standard representation is invariant to reference temperature. Water is a special juice it behaves like the other liquids only in the vicinity of the standardization range yo(2 —To) 0. 

Example 11 Standard representation of the temperature dependence of viscosity... 

Fig. 8 a Standard representation of the temperature dependence of viscosity in the form of the relationship x/[t0 =/[y0 (T- T0)]. The solid curve a represents the reference-invariant approximation by the y-fu notion (see section 8.2), whereas the dotted line corresponds to the engineering representation, eq. (8.9) from [27],... 

Fig. 11 Standard representation of the temperature dependence of viscosity of aqueous sugar solutions of different concentrations as well as their reference-invariant approximation using ip = -0.500 (solid curve). For key parameters a(x)...

While many earlier compilations of data have used the Electron Convention, the most recent tabulation of standard enthalpies described in the NIST Webbook (http //www.nist.gov) employs the Ion Convention. It does not introduce any temperature dependence, however small, to ion enthalpies of formation and is, therefore, considered a simpler and less confusing representation of data. This convention is also consistent with the literature of the ion physics and chemistry community over the past 50 years. In any application of tabulated thermochemical data, investigators are cautioned to be exceedingly clear about the conventions of the data they employ. 

In discussing Fig. 4.1 we noted that the apparent location of Tg is dependent on the time allowed for the specific volume measurements. Volume contractions occur for a long time below Tg The lower the temperature, the longer it takes to reach an equilibrium volume. It is the equilibrium volume which should be used in the representation summarized by Fig. 4.15. In actual practice, what is often done is to allow a convenient and standardized time between changing the temperature and reading the volume. Instead of directly tackling the rate of collapse of free volume, we shall approach this subject empirically, using a property which we have previously described in terms of free volume, namely, viscosity. 

The next step is to perform a simultaneous regression of NaCl(aq) apparent molal volumes from 25-350 C. Over this wide range of temperature, however, and particularly above 300 C, standard-state properties based on the infinitely dilute reference state exhibit a very complex behavior (7,8), which is related to various peculiarities of the solvent. Thus in their representation of NaCl(aq) volumetric properties, Rogers and Pitzer (7) adopted a reference composition of a hydrated fused salt, NaCl IOH2O, to minimize the P and T dependence of the reference state volume and to adequately fit volumetric ta to 300°C and 1 kb. In this study the (supercooled) fused salt is used as the reference state. The equation for the apparent molal volume on this basis can be easily derived from that for the excess Gibbs energy of Pitzer and Simonson (, and is given by ... 

Fig. 70. Schematic representation of results of numerical calculations made by Huth (1974) on (A) the dependence of the domain-wall radius of the various terms contained in eq. (30). (B) The relative magnitudes of the quantities MHna and Hc when plotted as a function of the wall radius. The shaded regions correspond to unstable domains when temperature and bias field do not correspond to standard conditions. In part (C) of the figure the same relationships as in (B) are shown for standard conditions...

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