Vaporization, heat phase-coexistence

In our heat transfer experiments, bulk fluid conditions were chosen to be just below the phase coexistence curve on either side of the lower consolute point. Thus, on heating at constant pressure, either evaporation of a liquid or condensation (retrograde) of a vapor took place once a small excess of test section surface temperature over bulk fluid temperature occurred. To be specific, the retrograde condensation region of the vapor--liquid phase coexistence curve of Figure 1 is the region of positive slope to the right of the LCST. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

In the two-phase region, vapor and liquid coexist, and vapor and liquid have the same temperature (thermal equilibrium) and pressure (mechanical equilibrium). When they are in equilibrium with each other, vapor and liquid are called saturated vapor and saturated liquid, respectively. If a saturated liquid is further heated at constant pressure, the temperature does not rise any more but stays constant. Instead, vapor is generated until all liquid is vaporized. Similarly, if saturated vapor is cooled down, the temperature stays constant, and the vapor condenses and forms a saturated liquid. Figure 2.8 illustrates the well-known behavior of water at P = 1.013 bar, when it is heated up from = 50 to 1 2 = 150 C. 

In P-r space, we see only two remarkable features the vapor pressure curve, indicating the conditions under which the vapor and liquid coexist, and the critical point, at which the distinction between vapor and liquid disappears. We indicate in this figure the critical isotherm 7 = Tc and the critical isobar P = Pc. If the liquid is heated at a constant pressure exceeding the critical pressure, it expands and reaches a vapor-like state without undergoing a phase transition. Andrews and Van der Waals called this phenomenon the continuity of states. 

Uranium hexafluoride (UF ), also called hex, is probably the best known and most widely investigated compound of uranium mainly because it is the only uranium compound with significant vapor pressure at ambient temperatures and therefore an essential raw material for most commercial isotope enrichment processes. UFg is a white monoclinic crystalline solid that sublimes directly to a gas (reaches atmospheric pressure at 56.5°C), but when heated in a closed vessel will melt at 64.05°C, which is the triple point where the solid, liquid, and gas phases coexist, as shown in Figure 1.8. This is probably one of the most weU-recognized phase diagrams in the chemical literature. 

The quantity AvapTf is the molar enthalpy change for the reversible process in which liquid changes to gas at a temperature and pressure at which the two phases coexist at equilibrium. This quantity is called the molar enthalpy of vaporization. Since the pressure is constant during the process, Ayap f is equal to the heat per amount of vaporization (Eq. 5.3.8). Hence, AyapTif is also called the molar heat of vaporization. 

The transition from the liquid to the gaseous state is called evaporation or vaporization. The reverse is referred to as condensation or, in terms of rainfall, precipitation. If heated to 100°C in a closed container at 1 atm pressure, the two phases of water will coexist in the equilibrium given in Eq. 2.4. 

For very many liquids, the entropy of vaporization at the normal boiling point is approximately 21 cal/mole °C water is not typical. The units for changes in entropy are the same as those for molar heat capacity, and care must be used to avoid confusion. When referring to an entropy change, a cal/mole °C is often called an entropy unit, abbreviated e.u. In order to avoid later misunderstanding, note now that this method of calculating AS from A HIT is valid only under equilibrium conditions. For transitions, for example, this method can be used only at temperatures where the two phases in question can coexist in equilibrium with each other. 

If a mixture of ice and water at 1 atm pressure and 0°C is placed in an insulated container and all of the air is pumped away and the container sealed, what will happen As was shown in the previous section, at pressures lower than 1 atm, the melting point of ice is above 0°C. Water will, therefore, be solid at 0°C and reduced pressure. However, when some liquid water freezes, its latent heat is released and the temperature of the system is slightly increased. Equilibrium is reestablished at the higher temperature and reduced pressure. The pressure in the system is the vapor pressure of both liquid and solid water slightly above 0 K. The new equilibrium point of the system is called the triple point of water and is at 0.0098°C and 611 Pa. Three phases—solid, liquid, and gas—coexist at the triple point, and the chemical potential of water in each of the phases must be equal ... 

Experiment 3 pressure is 4.588 torr. Again we start with ice as the only component in the cylinder at —20°C. In this case the pressure exerted on the ice by the piston is 4.588 torr. As the cylinder is heated, no new phase appears until the temperature reaches 0.0098°C. At this point, called the triple point, solid and liquid water have identical vapor pressures of 4.588 torr. Thus at 0.0098°C and 4.588 torr all three states of water are present. In fact, only under these conditions can all three states of water coexist. 

For the hydrocarbon--CO2 systems studied here, at pressures above the critical pressure (7.383 MPa) and above the critical temperature (304.21 K) of C02 the isobaric x,T coexistence plots of liquid and vapor phases form simple closed loops. The minimum occurs at the lower consolute point or the Lower Critical Solution Temperature (LCST). Since pressure is usually uniform in the vicinity of a heat transfer surface, such diagrams serve to display the equilibrium states possible in a heat transfer experiment. 

The van der Waals equation describes the critical phenomena of vapour to supercritical gas or fluid. Below critical temperature Tc gas which coexists with the liquid phase is called a vapour. Vapor has own saturated vapour pressure Pq. Then we can use the relative pressure P/Pq for description of adsorption. Fundamentally, physical adsorption is valid for vapours [10]. As the molecule-surface interaction of physical adsorption is weak, a sufficient intermolecular interaction corresponding to heat of vapourization is necessary for predominant physical adsorption. Micropore filling is a physical adsorption enhanced by overlapping of the molecule-surface interaction potentials from opposite pore walls and the adsorptive force is the strongest in physical adsorption. Nevertheless, micropore filling is a predominant process only for vapour. 

The coexisting liquid and vapor streams associated with phase separation may be brought about by phase creation or by phase addition. Phase creation is accomplished by heat transfer to and from the column as in distillation, where heat is added in the reboiler to vaporize some of the liquid, and heat is removed in the condenser to condense some of the vapor. Phase addition is accomplished by sending an auxiliary stream to the column a liquid absorbent to an absorber or a stripping vapor stream to a stripper. 

The ac heat capacity and vapor pressure isotherm experiments of CO on exfoliated graphite foam [112] allowed the detailed investigation of the narrowing of the commensurate solid-fluid coexistence region as the tricritical point is approached see Fig. 51 for this part of the phase diagram and Fig. 52 for the calorimetric data corresponding to the paths I to VII marked in the phase diagram. The vapor pressure isotherms indicate that the transition... 

Fig. 5. Proposed phase diagram of Ar on graphite. S, L, V and F represent, respectively, solid, liquid, vapor and fluid phases. Solid circles near 55 K at submonolayer coverages correspond to positions of heat-capacity anomaly arising from liquid-vapor transition. Other circles are signatures of melting. Dashed hnes are speculative. At submonolayer coverages, Ar solid melts via a weak first-order transition at a triple-point temperature (47.2 K) to a liquid-vapor coexistence region. The liquid phase appears to be orientationally ordered below 54 K. The positions of the broad anomalies centering near 49.5 K, due to the gradual decrease of this order, are not shown. Unless indicated otherwise, the uncertainty in the peak position of the heat-capacity anomaUes is comparable to or smaller than the size of the circles (from Ref 42).

PI 3.2 Estimate the heat capacity of acetic acid along the vapor-liquid coexistence curve for both phases using the vapor pressure and ideal gas heat capacity correlations given in Appendix A and the dimerization and tetramerization constants from Table 13.6. 

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