On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

Abstract

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.

The Critical Temperature of Aluminum

“…Notice that Roman et al [33] modified by Velasco et al [34] give a correlation formula different from those of Meyra et al and Watson, but it leads to the same form given by Eq. 3 for T c : the resulting values are therefore the same as those of Table 2.…”

A predictive vapor-pressure equation

“…showing that the Riedel equation was probably the best, simplest choice among the considered vapor-pressure equations. Furthermore, since our result, equation (32), is a fully predictive equation, it should be compared with equations of the same kind. TABLE 1 Critical pressure P c , critical temperature T c , reduced triple point temperature T tr , reduced normal boiling temperature T br , and the natural logarithm of the reduced triple point pressure P tr for the substances considered in this work (data from NIST) …”

“…Thus, equation (32) with the parameters a 1 and b 0 given by equations (28) and (35), respectively, provides a simple equation for the vapor-pressure along the whole coexistence curve. Application of equation (32) needs the reduced triple point constants P tr and T tr , and the reduced normal boiling temperature T br as input data.…”

“…The dimensionless temperature (19) has been considered by several authors to correlate experimental data of the enthalpy of vaporization [28][29][30], the liquid saturation density [31], and the vaporpressure [4,3,5,8,14,15] of several substances. It has also been used by us [32] to analyze the apparent universal behavior of some thermodynamic properties along the coexistence curve. Equation (18) suggests the introduction of the variable /ðtÞ T r ln P r T tr ln P tr ; ð20Þ…”

“…Application of equation (32) needs the reduced triple point constants P tr and T tr , and the reduced normal boiling temperature T br as input data. Therefore, the proposed equation does not include any empirical parameter and can be considered as a fully predictive equation.…”