AS for Phase Changes

The enthalpy of fusion for H2O is AHfusio = 6.01 kj/mol (a positive value because melting is an endothermic process). Thus, we can use Equation 19.2 to calculate ASfusion for melting 1 mol of ice at 273 K  

Notice (a) that we must use the absolute temperature in Equation 19.2 and (b) that the units for AS, J/K, are energy divided by absolute temperature, as we expect from Equation 19.2. 

Elemental mercury is a silver liquid at room temperature. Its normal freezing point is —38.9 °C, and its molar enthalpy of fusion is = 2.29 kJ/moL What is the entropy change of the system when 50.0 g 

Before using Equation 19.2, we must first convert the given Celsius temperature to kelvins  

Check The entropy change is negative because our q value is negative, which it must be because heat flows out of the system in this exothermic process. 

---

For chemical reactions, just as for phase changes, at equilibrium, microscopic processes continue but in a balance which gives no macroscopic changes. 

Some of the physical properties of metal tetrakis-boro-hydrides, which are primarily determined by their solid-state structure, are listed in Table 1. The polymeric Th, Pa, and U borohydrides are of much lower volatility than the monomeric Zr, Hf, Np, and Pu compounds. The intermolecular bonds connecting molecules together decrease their volatility substantially since these bonds break when the solid vaporizes (12). A plot of log p(mmHg) vs 1/T yields the equation log p(mmHg) = -A/T + B, where T is in K. Values of A and B allow the calculation of the heats (AH) and entropies (AS) for phase-change processes as shown in Table 1. The actinide ions in the polymeric compounds are 14 coordinate however, in the gaseous state they are 12 coordinate (12). 

Restructuring of a surface may occur as a phase change with a transition temperature as with the Si(OOl) surface [23]. It may occur on chemisorption, as in the case of oxygen atoms on a stepped Cu surface [24]. The reverse effect may occur The surface layer for a Pt(lOO) face is not that of a terminal (100) plane but is reconstructed to hexagonal symmetry. On CO adsorption, the reconstruction is lifted, as shown in Fig. XVI-8. 

Tlic heat duty is best calculated with a process simulation program hi will account for phase changes as the fluid passes throiigli ilic ctioke. It will balance the enthalpies and accurately predict the change m tcnipcrature across the choke. Heat duty should be checked for vanoits combinations of inlet temperature, pressure, flow rate, and outlet temper ature and pressure, so as to determine the most critical combination. 

A cryogenic calorimeter measures Cp,m as a function of temperature. We have seen that with the aid of the Third Law, the Cp,m data (along with AHm for phase changes) can be integrated to give the absolute entropy... 

The slope of the line allows for the determination of the enthalpy of vaporization of water, A//Vap, and the y intercept yields the entropy of vaporization, A. S vap As both the enthalpy and the entropy of water increase as the phase change liquid — vapor occurs, the slope and y intercept of the Clausius-Clapeyron equation are negative and positive, respectively. At 373 K these thermodynamic quantities have values of AHvap = 40.657 kJ mol-1 and ASvap = 109.0 J K-1 mol-1. The leavening action due to water vapor or steam arises from the increased amount of water vapor that forms as pastry temperatures initially rise in the oven and then from the increased volume of the water vapor as temperatures continue... 

The implications for films cast from mixtures of enantiomers is that diagrams similar to those obtained for phase changes (i.e., melting point, etc.) versus composition for the bulk surfactant may be obtained if a film property is plotted as a function of composition. In the case of enantiomeric mixtures, these monolayer properties should be symmetric about the racemic mixture, and may help to determine whether the associations in the racemic film are homochiral, heterochiral, or ideal. Monolayers cast from non-enantiomeric chiral surfactant mixtures normally will not exhibit this feature. In addition, a systematic study of binary films cast from a mixture of chiral and achiral surfactants may help to determine the limits for chiral discrimination in monolayers doped with an achiral diluent. However, to our knowledge, there has never been any other systematic investigation of the thermodynamic, rheological and mixing properties of chiral monolayers than those reported below from this laboratory. 

Even if one of the processes is not chemical but is categorized as a phase change, for example, evaporation, the extended De Donder s equation (Equation 13.17), is known to be valid. Any large magnitude of entropy production rate (diS/dt) due to evaporation might give a correlation such as... 

DSC measures the amount of heat released by a sample as the temperature is increased or decreased at a controlled uniform rate, and so can investigate chemical reactions and measure heats of reaction for phase changes (Figure 2.30). 

Calculation of the Entropy Change AS, for Phase Transitions at Constant Temperature, T and Pressure, P... 

If a phase change takes place in a closed system, you must evaluate A(7 = A// - A(PK) for the phase change to substitute into the energy balance equation. For phase changes such as... 

Now consider a finned-tube unit with the same I.D. and O.D. tubes. Service conditions are kept identical—i.e., fluid velocities, temperatures, etc., are constant. The increases in ho and over plain-tube exchangers are assumed negligible, especially for phase-change applications, such as condensation or evaporation on the fins. Thus ... 

As discussed in the previous section, the work of Coleman and Garimella [22] identified several other regimes and patterns however, for pressure drop model development, it will be shown that this broad categorization suffices. In the absence of other valid transition criteria for phase-change flow in small hydraulic diameter circular channels, these criteria were also assumed to apply for circular channels of equivalent diameters under consideration here. 

The ceiling temperature T can be considered the upper temperature at which a pyrolytic process will reach equilibrium. It may be seen, therefore, as a recommended temperature for pyrolysis. However, in practice, the application for macromolecules of the above relations is not straightforward. The theory was developed for ideal systems (sometimes in gas phase), and although in principle this theory should hold true for any system, its application to condensed phases or polymeric materials may be accompanied by effects difficult to account for (phase change, melting, cage effect [2], etc.). The reaction rate could also be low at calculated Tq values. For this reason, temperatures 50° C or 100° C higher than Tq must frequently be used as practical values of the temperature used in pyrolysis. 

The option to use alternative forms of a function depending on the value of logical variables that outline the state of the process. A typical example is the calculation of p-V-T relations as the phase changes from gas to liquid. To fix on the appropriate form, the problem must be treated as an optimization problem in which feasibility is required on each cycle for each state with the logical variables treated as constraints for a state. Alternatively, the code can guess the state and if the logical constraints are violated, another guess can be made. 

The definition of bond energies is limited to the bond-breaking process only, and does not include any provision for changes of state. Thus, it is valid only for substances in the gaseous state. The calculations of this section therefore apply only when all substances in the reaction are gases. If liquids or solids were involved, then additional information such as heats of vaporization and fusion would be needed to account for phase changes. 

---