Triple point constants

Trigonometric series, A-65 to 67 Trillion, definition, 1-38 Triple point constants... 

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...

Revised material in Section 5 includes an extensive tabulation of binary and ternary azeotropes comprising approximately 850 entries. Over 975 compounds have values listed for viscosity, dielectric constant, dipole moment, and surface tension. Whenever possible, data for viscosity and dielectric constant are provided at two temperatures to permit interpolation for intermediate temperatures and also to permit limited extrapolation of the data. The dipole moments are often listed for different physical states. Values for surface tension can be calculated over a range of temperatures from two constants that can be fitted into a linear equation. Also extensively revised and expanded are the properties of combustible mixtures in air. A table of triple points has been added. 

In addition to H2, D2, and molecular tritium [100028-17-8] the following isotopic mixtures exist HD [13983-20-5] HT [14885-60-0] and DT [14885-61-1]. Table 5 Hsts the vapor pressures of normal H2, D2, and T2 at the respective boiling points and triple points. As the molecular weight of the isotope increases, the triple point and boiling point temperatures also increase. Other physical constants also differ for the heavy isotopes. A 98% ortho—25/q deuterium mixture (the low temperature form) has the following critical properties = 1.650 MPa(16.28 atm), = 38.26 K, 17 = 60.3 cm/mol3... 

VP = vapor pressure point CVGT, constant volume gas thermometer point TP, triple point MP, melting point FP, freezing point. Note MP and FP at 101.325 Pa (1 atm) ambient pressure. 

Properties of Light and Heavy Hydrogen. Vapor pressures from the triple point to the critical point for hydrogen, deuterium, tritium, and the various diatomic combinations are Hsted in Table 1 (15). Data are presented for the equiUbrium and normal states. The equiUbrium state for these substances is the low temperature ortho—para composition existing at 20.39 K, the normal boiling point of normal hydrogen. The normal state is the high (above 200 K) temperature ortho—para composition, which remains essentially constant. 

Liquid Heat Capacity The two commonly used liqmd heat capacities are either at constant pressure or at saturated conditions. There is negligible difference between them for most compounds up to a reduced temperature (temperature/critical temperature) of 0.7. Liquid heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. 

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. 

Temperature Tgo in the range between 3.0 and 24.5561 K is defined in terms of 3He or 4He constant volume gas thermometers (CVGT), calibrated at the triple points of Ne and H2, and at a temperature between 3.0 and 5.0 K that has been obtained from vapor pressure versus temperature relations for He. 

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 ... 

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. 

At a constant pressure higher than the triple point, heating ice changes it to liquid, then to steam. 

The melting point of ammonium hydrosulphide in a closed vessel was found by E. Briner to be 120° and, in the presence of an excess of hydrogen sulphide, the m.p. is a triple point NHiSHv HgS+NHg, and the equilibrium constant is K=0 04 at 22°. The heat of vaporization of the solid hydrosulphide, in consequence of dissociation, will be equal to the heat of formation of the solid from the component gases, viz., 22 4 Cals., as found by J. Thomsen. According to F. Isambert, the heat of vaporization between 77° and 132° is 23 Cals., and, according to J. H. van t Hoff, calculated between 9 5° and 25 1° at constant press., 22 7 Cals. J. Walker and J. S. Lumsden find that the value of this constant increases with a rise of temp., being 19 7 Cals, between 4 2° and 18°, and 22 0° between 30 9° and 44 4°. 

The four coefficients A, B, C, and D have been derived, for example, with selected hydrocarbons [25, 26], Equation 7.4.3 accurately represents the vapor pressure function over the entire temperature range between the triple point and the critical point. If the coefficients are not available for a given compound, they can be calculated. D is calculated from the pressure van der Waals constant, a, which can be estimated from group contributions. B is calculated directly from group contributions. Then the coefficients A and C can be estimated from two pv/T points (e.g., normal boiling point and critical point). This approach has been evaluated for various classes of hydrocarbons commonly encountered in petroleum technology [25, 26]. 

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. 

It is worthwhile to discuss the relative contributions of the binary and the three-particle correlations to the initial decay. If the triplet correlation is neglected, then the values of the Gaussian time constants are equal to 89 fs and 93 fs for the friction and the viscosity, respectively. Thus, the triplet correlation slows down the decay of viscosity more than that of the friction. The greater effect of the triplet correlation is in accord with the more collective nature of the viscosity. This point also highlights the difference between the viscosity and the friction. As already discussed, the Kirkwood superposition approximation has been used for the triplet correlation function to keep the problem tractable. This introduces an error which, however, may not be very significant for an argon-like system at triple point. 

Substance X has a vapor pressure of 100 mm Hg at its triple point (48°C). When 1 mol of X is heated at 1 atm pressure with a constant rate of heat input, the following heating curve is obtained ... 

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. 

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