Phase transition Vaporization

There are a number of characteristics of the type of phase transitions we have considered so far. In practice, these characteristics are often used to determine data points for phase equilibrium lines. One of the obvious characteristics is a discontinuity in enthalpy as a function of temperature. Consider a sample of ice at -100°C and a pressure of 1 bar. The enthalpy changes smoothly as the temperature is increased until the system reaches 0°C, the melting temperature. At this point, there is a jump in the enthalpy corresponding to the enthalpy of melting. After all the ice has melted, the temperature can be increased and the enthalpy will be a new but different function of the temperature. Since the heat capacity, Cp, is the derivative of the enthalpy with respect to temperature, Cp as a function of temperature is also discontinuous at the phase transition. Vaporization of liquid water at 100°C and 1 bar leads to a sharp increase in volume. Thus, volume is a discontinuous function at a phase transition. The same holds for entropy. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

The enthalpy over a temperature range that includes phase transitions, melting, and vaporization, is represented by ... 

Figure 4.3b is a schematic representation of the behavior of S and V in the vicinity of T . Although both the crystal and liquid phases have the same value of G at T , this is not the case for S and V (or for the enthalpy H). Since these latter variables can be written as first derivatives of G and show discontinuities at the transition point, the fusion process is called a first-order transition. Vaporization and other familiar phase transitions are also first-order transitions. The behavior of V at Tg in Fig. 4.1 shows that the glass transition is not a first-order transition. One of the objectives of this chapter is to gain a better understanding of what else it might be. We shall return to this in Sec. 4.8. 

Denotes phase transition from liquid to vapor Denotes residual thermodynamic property Denotes a total value of a thermodynamic property V Denotes vapor phase... 

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Goldwire, Jr., H. C., H. C. Rodean, R. T. Cederwall, E. J. Kansa, R. P. Koopman, J. W. McClure, T. G. McRae, L. K. Morris, L. Kamppiner, R. D. Kiefer, P. A. Urtiew and C. D. Lind. 1983. Coyote series data rejwrt LLNL/NWC 1981 LNG spill tests, dispersion, vapor bum, and rapid-phase-transition. Lawrence Livermore National Laboratory Report UCID-I9953. Vol. 2. 

Clausius-Clapeyron Equation. This equation was originally derived to describe the vaporization process of a pure liquid, but it can be also applied to other two-phase transitions of a pure substance. The Clausius-Clapeyron equation relates the variation of vapor pressure (P ) with absolute temperature (T) to the molar latent heat of vaporization, i.e., the thermal energy required to vajxirize one mole of the pure liquid ... 

In the CO2 phase diagram of Figure 8.1, we considered only (solid + liquid), (vapor + solid) and (vapor + liquid) equilibria. A (solid + solid) phase transition has not been observed in C(>,m but many substances do have one or more. Equilibrium can exist between the different solid phases I, II, III, etc., so that... 

Phase transitions and vapor pressure calculation for Pu-noble metal... 

All the energy supplied is used to drive the phase transition, such as the conversion of liquid into vapor, rather than to raise the temperature. The T in the denominator of Eq. 1 is therefore a constant and may be set equal to the transition temperature (in kelvins). 

As we saw in Section 5.1, a single substance can exist in different phases, or physical forms. The phases of a substance include its solid, liquid, and gaseous forms and its different solid forms, such as the diamond and graphite phases of carbon. In one case—helium—two liquid phases are known to exist. The conversion of a substance from one phase into another, such as the melting of ice, the vaporization of water, and the conversion of graphite into diamond, is called a phase transition (recall Section 6.11). 

Solvent Injection The solvent injection technique involves the injection of solutions of lipid in solvents with high vapor pressure (ether, fluorocarbons, ethanol) into excess aqueous phase under reduced pressure. In general, the aqueous phase is maintained above the phase transition of the lipids (Te) and a reduced pressure... 

Vapor Pressure Equations of Adamantane and Diamantane for Eiquid-Vapor and Solid-Vapor Phase Transitions... 

Figure 6. Vapor-liquid-solid (plastic crystal) phase diagram of adamantane. The phase transition from plastic crystal to rigid crystal phase occurs at 208.6K (l/T = 0.004794K ). This diagram is based on the data of Table II.

The theoretical foundation for describing critical phenomena in confined systems is the finite-size scaling approach [64], by which the dependence of physical quantities on system size is investigated. On the basis of the Ising Hamiltonian and finite-size scaling theory, Fisher and Nakanishi computed the critical temperature of a fluid confined between parallel plates of distance D [66]. The critical temperature refers to, e.g., a liquid/vapor phase transition. Alternatively, the demixing phase transition of an initially miscible Kquid/Kquid mixture could be considered. Fisher and Nakashini foimd that compared with free space, the critical temperature is shifted by an amoimt... 

With the critical exponent being positive, it follows that large shifts of the critical temperature are expected when the fluid is confined in a narrow space. Evans et al. computed the shift of the critical temperature for a liquid/vapor phase transition in a parallel-plates geometry [67]. They considered a maximum width of the slit of 20 times the range of the interaction potential between the fluid and the solid wall. For this case, a shift in critical temperature of 5% compared with the free-space phase transition was found. From theoretical considerations of critical phenomena... 

Another type of physical explosion can occur upon rapid vaporization of a liquid when contacted with a significantly hotter material (e.g., water added to vessel containing hot oil). This is also referred to as a rapid phase transition explosion. In addition to blast, physical explosions can also generate fragments when initially confined. 

Rapid Phase Transition Explosion Rapid vaporization of a liquid when contacted with a significantly hotter material. 

In pharmaceutical systems, both heat and mass transfer are involved whenever a phase change occurs. Lyophilization (freeze-drying) depends on the solid-vapor phase transition of water induced by the addition of thermal energy to a frozen sample in a controlled manner. Lyophilization is described in detail in Chapter 16. Similarly, the adsorption of water vapor by pharmaceutical solids liberates the heat of condensation, as discussed in Chapter 17. 

---