Water triple point constants

We wish to mention the recent proposal for a redefinition of Kelvin in terms of mechanical units through the Boltzmann constant [6-7] the Kelvin should be defined as the unit of thermodynamic temperature such that the value of the Boltzmann constant is 1.3806505 x 10 23 JK 1 exactly. Of course, this value of the Boltzmann constant should be consistent with a thermodynamic temperature of the triple point of water of 273.16 K. 

The values of the constants in the Uiermometric function are determined with reference to fixed thermometnc points whose temperatures are arbitrarily assumed. The fixed thermometric points most frequently employed are the ice point, steam point and triple point of water. 

The ideal gas temperature scale is of especial interest, since it can be directly related to the thermodynamic temperature scale (see Sect. 3.7). The typical constant-volume gas thermometer conforms to the thermodynamic temperature scale within about 0.01 K or less at agreed fixed points such as the triple point of oxygen and the freezing points of metals such as silver and gold. The thermodynamic temperature scale requires only one fixed point and is independent of the nature of the substance used in the defining Carnot cycle. This is the triple point of water, which has an assigned value of 273.16 K with the use of a gas thermometer as the instrument of measurement. 

Parameters B, C, etc., are functions of temperature and the identity of the chemical species parameter a, however, is the same function of temperature for all species. Data taken for various gases at a specific constant temperature (fixed by use of a reproducible state such as the triple point of water or the normal boiling point of water) show that plots of PV vs. P have the same limiting value of PV as P - 0 for all gases. For P - 0, Eq. (3.6) becomes... 

The idea of a thermodynamic temperature scale was first proposed in 1854 by the Scottish physicist William Thomson, Lord Kelvin [iv]. He realized that temperature could be defined independently of the physical properties of any specific substance. Thus, for a substance at thermal equilibrium (which can always be modeled as a system of harmonic oscillators) the thermodynamic temperature could be defined as the average energy per harmonic oscillator divided by the Boltzmann constant. Today, the unit of thermodynamic temperature is called kelvin (K), and is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 

The value of 1/a for nitrogen at 1 atm is 272. Experiments with other gases indicate that the ice point, 0°C, is equivalent to a value of near 273 K. The Kelvin scale is now defined with high accuracy such that the triple point of water (where ice, water and water vapour are all in equilibrium, at 0.01°C) has the temperature 273.1600° on the Kelvin scale. The triple point is more accurately defined than the ice point. On this basis 0°C is 273.15 K. Measurement on this ideal gas scale is best conducted with a constant pressure helium thermometer, although there are small deviations from the absolute scale. A comparison of the four temperature scales discussed above is given in Table 1.1. 

The Kelvin or thermodynamic temperature scale uses a single fixed point to define the size of a degree—the triple point of water at 273.16 Kelvin (K). Special low-pressure, constant-volume gas thermometers are used in a handful of laboratories to approximate the thermodynamic temperatures of other fixed points. 

In the definition of ITS-90, interpolation formulas are provided for the calibration of SPRTs. These formulas are rather involved, including reference functions and deviation functions. For temperature above 0°C, the reference function is a 9th-order polynomial with fixed coefficients and the deviation function is a cubic polynomial with four constants, determined by calibration at the triple point of water (0.01°C) and the freezing points of tin (231.928°C), zinc (419.527°C), aluminum (660.323°C), and silver (961.78°C). These equations are complex and usually of interest only to... 

The Kelvin scale of temperature is a consequence of the perfect gas laws leading to the construction of the constant-volume gas thermometer. The fixed point of Kelvin temperature (absolute temperature) is defined with reference to the triple point of water (where ice water and water vapour coexist). 

Vo is the initial volume of a certain amount of gas at, for example, a temperature of 0 °C (ice point), and is its temperature on the Celsius scale. A graphic or analytic extrapolation of the isobars F(5) (Fig. 10.2) leads to an important conclusion AU the linear functions F(5) belonging to different constant pressures, will intersect with the temperature axis at about 3= —267 °C (actually at 273.15 °C, as later measurements have shown), independent of the type of gas and amount of substance. The experiments carried out by Charles and Gay-Lussac were therefore a further indication of the existence of an absolute zero point of temperature. This had already been postulated in 1706 by Guillaume Amonton. It seemed, therefore, reasonable to introduce a new temperamre scale and to measure temperature from this point because volume is never negative. This is how we arrive at the so-called absolute temperature scale. We were already introduced to this scale in Sect. 3.8 (but there we did not use the ice point but the more convenient triple point of water to fix the scale). Further, it also becomes clear that Eq. (10.2) is an example of a... 

Table 5.27 Compressibility of Water Table 5.28 Mass of Water Vapor In Saturated Air Table 5.29 Van der Waals Constants for Gases Table 5.30 Triple Points of Various M aterlals 5.9.1 Some Physical Chemistry Equations for Gases...

The regression constants A, B, and D are determined from the nonlinear regression of available data, while C is usually taken as the critical temperature. The hquid density decreases approximately linearly from the triple point to the normal boiling point and then nonhnearly to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range of temperature. Liquid density data to be regressed should be at atmospheric pressure up to the normal boihng point, above which saturated liquid data should be used. Constants for 1500 compounds are given in the DIPPR compilation. 

The second law of thermodynamics says that in a Carnot cycle Q/T = constant. This law allows for the definition of a temperature scale if we arbitrarily assign the value of a reference temperature. If we give the value T3 = 273.16K to the triple point (see Gibbs law, Section 8.2) of water, the temperature in kelvin units [K] can be expressed as ... 

The variation of the defined dissociation constant, obtained on the basis of this dielectric model, is plotted in Fig. 1.6. The reaction Eq. (1.3) in liquid water becomes unfavorable from the perspective of the free energy upon exceeding 500 K on the saturation curve, where the liquid density falls below about 85% of the triple-point density. Nevertheless, this sulfonic acid head group would still be considered a strong acid in bulk aqueous solution at these elevated temperature and reduced-density conditions. These results give perspective for the view that insufficient hydration can result in incomplete dissociation of sulfonic acid species in membranes. 

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