Temperature scaling, equilibrium phase

The international temperature scale is based upon the assignment of temperatures to a relatively small number of fixed points , conditions where three phases, or two phases at a specified pressure, are in equilibrium, and thus are required by the Gibbs phase rule to be at constant temperature. Different types of thermometers (for example, He vapor pressure thermometers, platinum resistance thermometers, platinum/rhodium thermocouples, blackbody radiators) and interpolation equations have been developed to reproduce temperatures between the fixed points and to generate temperature scales that are continuous through the intersections at the fixed points. 

The KTTS depends upon an absolute zero and one fixed point through which a straight line is projected. Because they are not ideally linear, practicable interpolation thermometers require additional fixed points to describe their individual characteristics. Thus a suitable number of fixed points, ie, temperatures at which pure substances in nature can exist in two- or three-phase equilibrium, together with specification of an interpolation instrument and appropriate algorithms, define a temperature scale. The temperature values of the fixed points are assigned values based on adjustments of data obtained by thermodynamic measurements such as gas thermometry. 

Fig. 2. Logarithmic activity diagram depicting equilibrium phase relations among aluminosilicates and sea water in an idealized nine-component model of tire ocean system at the noted temperatures, one atmosphere total pressure, and unit activity of H20. The shaded area represents (lie composition range of sea water at the specified temperature, and the dot-dash lines indicate the composition of sea water saturated with quartz, amotphous silica, and sepiolite, respectively. The scale to the left of the diagram refers to calcite saturation foi different fugacities of CO2. The dashed contours designate the composition (in % illite) of a mixed-layer illitcmontmorillonitc solid solution phase in equilibrium with sea water (from Helgesun, H, C. and Mackenzie, F T.. 1970. Silicate-sea water equilibria in the ocean system Deep Sea Res.).

In practice it is the International Practical Temperature Scale of1968 (IPTS-68) which is used for calibration of scientific and industrial instruments-t This scale has been so chosen that temperatures measured on it closely approximate ideal-gas temperatures the differences are within the limits of present accuracy of measurement. The IPTS-68 is based on assigned values of temperature for a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at these temperatures. Interpolation between the fixed-point temperatures is provided by formulas that establish the relation between readings of the standard instruments and values of the international practical temperature. The defining fixed points are specified phase-equilibrium states of pure substances, t a given in Table 1.2. 

The absolute position of the equilibrium point on the temperature scale depends upon the magnitude of the potential energy factor and upon the disparity in degree of randomness between the two phases. 

Another important projection of the PvT-diagram is the PT-graph (see Figure 2.5). In this projection, the dew-point line coincides with the boiling point in the vapor pressure curve. Similarly, solidus and liquidus curve coincide in the melting curve. The phase transition between the solid state and the gaseous state is described by the sublimation curve. Vapor pressure curve, melting curve, and sublimation curve meet at the triple point, where the three phases vapor, liquid, and solid coexist in equilibrium. The triple point of water is very well known and can be reproduced in a so-called triple point cell. It is used as a fix point of the International Temperature Scale ITS-90 [4] (Tt, = 273.16 K or = 0.01"C, Ptr = 611.657 0.01 Pa). The vapor pressure curve ends at the critical point no liquid exists above the critical temperature T. ... 

Notice, that d = 1 corresponds to the equilibrium phase coexistence temperature. The values d = 9/8 and = 0 are the upper and lower limits of the metastable nematic and isotropic states, respectively. The quantity <5k = 1 — T /Tk which sets a scale for the relative difference of the temperature from the equilibrium phase transition is known from experiments to be of the order 0.1 to 0.001. On the other hand, it is related to the coefficients occurring in the potential function according to... 

Two particular temperature scales are used extensively. The ideal-gas temperature scale is defined by gas thermometry measurements, as described on page 42. The thermodynamic temperature scale is defined by the behavior of a theoretical Carnot engine, as explained in Sec. 4.3.4. These temperature scales correspond to the physical quantities called ideal-gas temperature and thermodynamic temperature, respectively. Although the two scales have different definitions, the two temperatures turn out (Sec. 4.3.4) to be proportional to one another. Their values become identical when the same unit of temperature is used for both. Thus, the kelvin is defined by specifying that a system containing the solid, liquid, and gaseous phases of H2O coexisting at equilibrium with one another (the triple point of water) has a thermodynamic temperature of exactly 273.16 kelvins. We... 

FIG. 7 The unary C12MG phase diagram manifold. The temperature scale is to the left (outside the diagram). Each arm corresponds to a particular crystal structure the left arm is the equilibrium diagram. The transformations that occur among polymorphs are indicated by dashed arrows. 

Figure 2.10. The calibration point in the thermodynamic temperature scale is the triple point of water where phase equilibrium exists between ice, water and water vapour in a closed system these three phases can only coexist in equilibrium at one particular temperature 273.16 K.

---