Pressure-volume diagram: pure substance

The results of the process described in Figure 2-2 may be presented in the form of a pressure-volume diagram. Figure 2-9 shows two isotherms of a typical pressure-volume diagram for a pure substance. Processes 1-3 and 4-5 correspond to the processes indicated in Figure 2-3. 

Fig. 2-9. Typical pressure-volume diagram of a pure substance showing two isotherms 13 below critical temperature, 45 above critical temperature.

We will first consider phase diagrams. Then we will define the critical point for a two-component mixture. This will be the correct definition for multicomponent mixtures. Also, we will look at an important concept called retrograde condensation. Then the pressure-volume diagram will be discussed, and differences between pure substances and two-component mixtures in the two-phase region will be illustrated. Finally, the effects of temperature and pressure on the compositions of the coexisting liquid and gas will be illustrated. 

Already we have seen that the critical temperature isotherm on a pressure-volume diagram for a pure substance has a horizontal point of inflection as it passes through the critical pressure. The data of Figure 2-10 clearly show this. Thus, for a pure substance at the critical point... 

Phase Diagram for a Pure Substance — Use of Phase Diagrams — Vapor Pressure of a Pure Substance Pressure-Volume Diagram for a Pure Substance -Density-Temperature Diagram for a Pure Substance Two-Component Mixtures 61... 

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... 

Figure 33 FT diagram showing the vapor-pressure curve for a pure substance and constant-volume lines in the single-phase regions.

Figure 6.1 Phase diagram temperature/pressure of carbon dioxide. There exists for each pure substance a relation between three variables temperature T, pressure P and volume V, known as the equation of state. The diagram above is the projection (P/T)for COj. The critical point is located at 31 °C and 7.4MPa (lMpa= 10 Pa, or 10 bar). Getting round the critical point renders it possible to go from the liquid state to the gaseous state without a discontinuity of phase.

At T = 0 K, where any transformation of a pure substance tends to be isoen-tropic, phase stability can be related to the enthalpy and a phase transition occurs at those points in the phase diagram where two phases have equal enthalpy. Erom the computational point of view, it is possible to explore a range of crystalline volumes by isometric lattice deformations and obtain the corresponding values of pressure and, consequently, of enthalpy. It is intended that nuclei are allowed to relax to their equilibrium geometry after... 

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. 

As an example, let the system contain a fixed amount n of a pure substance divided into liquid and gas phases, at a temperature and pressure at which these phases can coexist in equilibrium. When heat is transferred into the system at this T and p, some of the liquid vaporizes by a liquid-gas phase transition and V increases withdrawal of heat at this T and p causes gas to condense and V to decrease. The molar volumes and other intensive properties of the individual liquid and gas phases remain constant during these changes at constant T and p. On the pressure-volume phase diagram of Fig. 8.9 on page 208, the volume changes correspond to movement of the system point to the right or left along the tie line AB. 

Figure 4.26. A pressure-volume phase diagram for a pure substance.

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 ... 

For the regions of the diagram in Figure 2.1 where only a single phase exists, a relation is implied between the three quantities P, V, and 7. Such a relation is referred to as the PVT equation of state. It relates pressure, molar volume, and temperature for a pure, one-component substance in the equilibrium state. An equation of state may be used to solve for any one of the three quantities P, V, and 7 as a function of the other two. For instance, V can be viewed as a function of temperature and pressure, V = f(T,P). Thus ... 

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