The triple point

Equations (2) and (3) are physically meaningful only in the temperature range bounded by the triple-point temperature and the critical temperature. Nevertheless, it is often useful to extrapolate these equations either to lower or, more often, to higher temperatures. In this monograph we have extrapolated the function F [Equation (3)] to a reduced temperature of nearly 2. We do not recommend further extrapolation. For highly supercritical components it is better to use the unsymmetric normalization for activity coefficients as indicated in Chapter 2 and as discussed further in a later section of this chapter. 

Thermal conductivity is expressed in W/(m K) and measures the ease in which heat is transmitted through a thin layer of material. Conductivity of liquids, written as A, decreases in an essentially linear manner between the triple point and the boiling point temperatures. Beyond a reduced temperature of 0.8, the relationship is not at all linear. For estimation of conductivity we will distinguish two cases < )... 

Usually, Tj is taken as the triple point and T2 as the normal boiling point. The average error is about 5%. 

At a given temperature and pressure, a pure compound can exist in one, two or three states. The compound exists at three different states at the triple point and at two different states along the curves of vaporization, freezing and sublimation. Refer to Figure 4.6. 

At the triple point, the free energies of each phase are equal ... 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

The normal melting point of a substance is the temperature at which solid and hquid are in equilibrium at atmospheric pressure. At the triple point, the pressure is the equilibrium vapour pressure of the system (solid liquid - vapour) and the temperature differs from the melting point. The difference is, however, quite small—usually only a fraction of a degree—since the line TV departs only slightly from the vertical within reasonable ranges of pressure. 

It is clear that if the vapour at a pressure below the triple point is reduced sufficiently in temperature, it will condense directly to the solid form, or, sublimation will ensue. In order that a solid may pass directly... 

Condensation takes place on the cold surface directly as the solid because the pressure is below that at the triple point. 

If the triple point pressure of a solid is below one atmosphere, it will melt if the heating is conducted rapidly so that the vajiour pressure can exceed that at the triple point. If camphor is heated in a closed space, the vapour pressure increases and when the value of 360 mm. is reached, the solid will melt further heating results in an increase in the vapour pressure and the camphor will boil when the vapour pressure is 760 mm. 

For most practical purposes the temperature and pressure at the triple point may be regarded as not differing appreciably from the melting point and the vapour pressure at the melting point respectively. 

Temperature kelvin K Defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 

The ultimate definition of thermodynamic temperature is in terms of pV (pressure X volume) in a gas thermometer extrapolated to low pressure. The kelvin (K), the unit of thermodynamic temperature, is defined by specifying the temperature of one fixed point on the scale—the triple point... 

Defining fixed points of the International Temperature Scale of 1990 (ITS-90). Except for the triple points, the assigned values of temperature are for equilibrium states at a pressure of one standard atmosphere (101 325 Pa). 

The working temperature, 77 K, is well below the triple point of krypton, 116 K, but if the solid is taken as the reference state the isotherm shows an unusually sharp upward turn at the high-pressure end. The usual practice, following Beebe, is therefore to take p° as the saturation vapour pressure of the supereooled liquid (p° = 2-49 Torr at 77-35 K and 27-5 Torr at 90-2 K). 

Molten Salt Distillation. Hafnium tetrachloride is slightly more volatile than zirconium tetrachloride, but a separation process based on this volatility difference is impractical at atmospheric pressures because only soHd and vapor phases exist. The triple point for these systems is at about 2.7 MPa (400 psia) and 400°C so that separation of the Hquids by distillation would necessarily require a massive pressurized system (13). 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

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... 

Temperatures on the ITS-90 are expressed in terms of the ratio of the resistance of the SPRT at temperature to the resistance at the triple point of water. The resistance ratio W(V is calculated as... 

Properties. Thallium is grayish white, heavy, and soft. When freshly cut, it has a metallic luster that quickly dulls to a bluish gray tinge like that of lead. A heavy oxide cmst forms on the metal surface when in contact with air for several days. The metal has a close-packed hexagonal lattice below 230°C, at which point it is transformed to a body-centered cubic lattice. At high pressures, thallium transforms to a face-centered cubic form. The triple point between the three phases is at 110°C and 3000 MPa (30 kbar). The physical properties of thallium are summarized in Table 1. 

Pure zirconium tetrachloride is obtained by the fractional distillation of the anhydrous tetrachlorides in a high pressure system (58). Commercial operation of the fractional distillation process in a batch mode was proposed by Ishizuka Research Institute (59). The mixed tetrachlorides are heated above 437°C, the triple point of zirconium tetrachloride. AH of the hafnium tetrachloride and some of the zirconium tetrachloride are distiUed, leaving pure zirconium tetrachloride. The innovative aspect of this operation is the use of a double-sheU reactor. The autogenous pressure of 3—4.5 MPa (30—45 atm) inside the heated reactor is balanced by the nitrogen pressure contained in the cold outer reactor (60). However, previous evaluation in the former USSR of the binary distiUation process (61) has cast doubt on the feasibHity of also producing zirconium-free hafnium tetrachloride by this method because of the limited range of operating temperature imposed by the smaH difference in temperature between the triple point, 433°C, and critical temperature, 453°C, a hafnium tetrachloride. 

Static Pressure Synthesis. Diamond can form direcdy from graphite at pressures of about 13 GPa (130 kbar) and higher at temperatures of about 3300—4300 K (7). No catalyst is needed. The transformation is carried out in a static high pressure apparatus in which the sample is heated by the discharge current from a capacitor. Diamond forms in a few milliseconds and is recovered in the form of polycrystalline lumps. From this work, and studies of graphite vaporization/melting, the triple point of diamond, graphite, and molten carbon is estimated to He at 13 GPa and 5000 K (Fig. 1)... 

---