The thermodynamic scaling function

L. Schafer, T. A. Witten. Renormalization field theory of polymer solutions. I. Scaling laws. J Chem Phys 66 2121-2130, 1977 A. Knoll, L. Schafer, T. A. Witten. The thermodynamic scaling function of polymer solution. J Physique 42 161-m, 1981. 

Fig. 14.3. The thermodynamic scaling function in the excluded volume limit V (s), divided by the excluded volume overlap s. The broken line gives the asymptotic power law...

Although air shock is occasionally scaled against the linear dimensions of the explosive charge (Ref 20), it is more often scaled to an equivalent weight of TNT. The TNT equivalency is based on energy of explosion obtained in various ways. The preferred method being calculation of either the hydrodynamic or the thermodynamic work function. (Recall section 26.4.) TNT weight equivalence... 

Temperatures required for the thermodynamic potential functions for water, ice, and seawater discussed above need to be expressed in the scale ITS-90, see the next Section 20.2.2. 

Temperature values to be used for the currently valid thermodynamic formulas (EOS-80) of seawater (Fofonoff and Millard, 1983 Mamayev et al., 1991) need to be expressed in the International Practical Temperature Scale of 1968 (IPTS-68). Practically measured temperatures are assumed to be in IPTS-68 before January 1, 1990, and in the International Temperature Scale of 1990 (ITS-90) afterward (Mamayev et al., 1991). Temperatures required for the thermodynamic potential functions for water, ice, and seawater need to be expressed in ITS-90, see Section 20.2.1. 

Absorption methods give evidence on ion pairs but do not necessarily yield the overall association constants required by the thermodynamic excess functions. However, they furnish essential contributions to the elucidation of solvent-solvent and ion-solvent interactions and are the basis for most of the semi-empirical interaction scales usually applied. 

Douslin s experimental data consisted of values of the pressure, measured at fixed values of amount density between 0.75 and T.Okmol m and at rounded values of Celsius temperature (IPTS 48) between the critical temperature (115.22 °C) and 350 C. For application of equations (66) to (68) the pressure at each value of density was expressed in terms of temperature on the thermodynamic scale by a suitable function, which was then differentiated to obtain values for (pp T)p. After the values of the... 

We have already shown that the absolute temperature is an integrating denominator for an ideal gas. Given the universality of T 9) that we have just established, we argue that this temperature scale can serve as the thermodynamic temperature scale for all systems, regardless of their microscopic condition. Therefore, we define T, the ideal gas temperature scale that we express in degrees absolute, to be equal to T 9), the thermodynamic temperature scale that we express in Kelvins. That this temperature scale, defined on the basis of the simplest of systems, should function equally well as an integrating denominator for the most complex of systems is a most remarkable occurrence. 

See W. F. Giauque and D. P. MacDougall, "Experiments Establishing the Thermodynamic Temperature Scale below 1 =K. The Magnetic and Thermodynamic Properties of Gadolinium Phosphomolybdate as a Function of Field and Temperature". J. Am. Chem. Soc., 60, 376-388 (1938). 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

In general, a thermometer is called primary if a theoretical reliable relation exists between a measured quantity (e.g. p in constant volume gas thermometer) and the temperature T. The realization and use of a primary thermometer are extremely difficult tasks reserved to metrological institutes. These difficulties have led to the definition of a practical temperature scale, mainly based on reference fixed points, which mimics, as well as possible, the thermodynamic temperature scale, but is easier to realize and disseminate. The main characteristics of a practical temperature scale are both a good reproducibility and a deviation from the thermodynamic temperature T which can be represented by a smooth function of T. In fact, if the deviation function is not smooth, the use of the practical scale would produce steps in the measured quantities as function of T, using the practical scale. The latter is based on ... 

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