PVT Behavior of Pure Substances

A qualitative observation of PVT behavior of pure substances indicates continuity in... 

The qualitative observation of PVT behavior of pure substances indicates a continuity in the isotherm at the critical point on a PV diagram. The existence of an inflection point on the critical isotherm at the critical pressure implies that the first and second derivatives of the pressure with respect to the volume are equal to zero at the critical point ... 

Figure 3.2 indicates the complexity of the PVT behavior of a pure substance and suggests the difficulty of its description by an equation. However, for the gas region alone relatively simple equations often suffice. For an isotherm such as Tj we note from Fig. 3.2 that as P increases V decreases. Thus the PV product for a gas or vapor should be much more nearly constant than either of its members. This suggests the representation of PV along an isotherm by a power series expansion in P ... 

The PVT behavior of a pure substance may also be described on a pressure-volume diagram, as shown in Figure 1.2. The variation in volume with pressure at various fixed temperatures is represented by the isotherms. If the temperature of the isotherm is above the critical, the pressure decreases continuously as the volume increases and no phase change takes place. The critical temperature isotherm is also continuous but has an inflection point at the critical pressure. On sub-critical... 

The PvT behavior of a pure substance can be described by so-called equations of state (EOS). In general, an equation of state is a relationship between P. v, and T. They can be formulated in diflferent ways, for example, volume-explicit (v=f(T,P)) or, most commonly, pressure-explicit (P = /(T, v)). An equation of state combined with the general thermodynamic correlations offers the possibility to calculate all thermodynamic properties of the substance. The simplest equation of state for describing the PvT behavior of gases is the ideal gas law ... 

This integral can be calculated directly by a volume-explicit equation of state, which is suitable to describe the PvT behavior of a pure substance. In a very similar way, the relationship for (h - h" ) can be derived ... 

If the relationship between the pressure P, the molar volume v, the absolute temperature T and, additionally, the ideal gas specific heat capacity Cp of a pure substance are known, all thermodynamic properties of this substance can be calculated. The typical PvT behavior is shown in Figure 2.1 in a three-dimensional diagram. All thermodynamically stable states are represented by the surface. Depending on the values of the state variables P, v, T the substance exists as a solid (S), liquid (L), or a vapor phase (V) or as a combination of two or three phases. They can be characterized as follows. 

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