Entropy of phase change

Box 4.1 Parameters Used to Estimate Entropies of Phase Change Processes... 

Related Calculations, This procedure can be used to obtain the entropy of phase change for any compound. If heat-of-vaporization data are not available, the molar entropy of vaporization for nonpolar liquids can be estimated via an empirical equation of Kistyakowsky ... 

Phase changes, which convert a substance from one phase to another, have characteristic thermodynamic properties Any change from a more constrained phase to a less constrained phase increases both the enthalpy and the entropy of the substance. Recall from our description of phase changes in Chapter 11 that enthalpy increases because energy must be provided to overcome the intermolecular forces that hold the molecules in the more constrained phase. Entropy increases because the molecules are more dispersed in the less constrained phase. Thus, when a solid melts or sublimes or a liquid vaporizes, both A H and A S are positive. Figure 14-18 summarizes these features. 

The third law of thermodynamics states that, for a perfect crystal at absolute zero temperature, the value of entropy is zero. The entropy of a molecule at other temperatures can be computed from the heat capacities and heats of phase changes using... 

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

If the heat capacity is not constant, it must be used as a function of temperature for Equation (1.70), for which the integration must then be carried out. When the temperature nears the absolute zero temperature, Cp=aT3 where a = 2.27x 10 4cal mol1 K-4. If there are some phase changes before reaching the temperature T, the entropy of phase transitions must be incorporated into the calculation for the absolute entropy ... 

In a displacive phase transition, the positions of atoms are ordered in both phases, but the position changes from a less symmetric site to a more symmetric one as the crystal undergoes the phase transition. Order-disorder transitions are distinguished from displacive transitions by, among other properties, a large entropy of phase transition, dielectric dispersion at low frequencies, and directly, by crystal structure revealing two or more sites fractionally occupied by the same atom. 

Simple kinds of phase change, such as melting and vaporization, are characterized by considerable changes of volume, and also of entropy and enthalpy, at the point of transition. Thus, whereas the chemical potentials of the two phases are equal when they are at equilibrium together, their volumes, entropies and enthalpies are far from equal. 

In the ordinary type of phase change, if fiy s, v, etc., are plotted as functions of temperature and pressure, we obtain curves as shown diagrammatically in Fig. 21. The chemical potential itself shows a change of gradient at the point of phase change, but no discofUinuUy. The latter is manifested in the entropy, volume and all other higher derivatives of the chemical potential. X... 

Apart from the discontinuous changes of entropy and volume, an important feature of these normal types of phase change is that the values of Cp and k do not usually change at all rapidly as the transition... 

Other types of phase change have been discovered which show quite a different character. In these there seems to be no difference of volume between the two forms of the substance and also little or no difference in entropy or enthalpy, i.e. zero or almost zero latent heat. The transition is manifested simply by a sharp change in the heat capacity and compressibility. These properties also vary rather rapidly as the transition point is approached. 

The new theories pointed out that LCST behavior is characteristic of exothermic mixing and negative excess entropy (25). This last is caused by den-sification of the polymers on mixing. The entropy of volume change, which ordinarily is relatively small compared to other quantities, comes to the fore in polymer-polymer blends (24). While an introduction to phase separation in polymer blends is presented here, a more detailed development of polymer blends in general is given in Chapter 13. 

However, the difference A /z -A /z represents the enthalpy A /z° accompanying the phase change of the component in question between P and P . Similarly, the difference A 5°-A 5 represents the opposite of entropy associated with the same transformation. The slope of the straight line PP is therefore given by the opposite of the ratio of the enthalpy of phase change of the compound involved to the corresponding entropy ... 

A new volume of Landolt-Bomstein appeared in 1961. This deals with calorimetric quantities and is concerned with elements, alloys, and compounds, and with reaction enthalpies. Subjects covered include the experimental and theoretical basis of thermochemistry, standard values of molar enthalpies, entropies, enthalpies of formation, free energies of formation, and enthalpies of phase change. Planck, Einstein, and Debye functions, anharmonicity, and internal rotation are considered. The final section presents thermodynamic data for mixtures and solutions. 

Standard entropies at 298.15 K are evaluated from measurements of heat capacities at constant pressure and enthalpies of phase changes from low temperatures to 298.15 K, assuming the third law of thermodynamics is applicable to the substance. The entropy at 298.15 K is given by an expression such as... 

The present review describes recent developments in the experimental techniques for low-temperature (10 to 400 K) calorimetry and in the measurement of heat capacities of organic compounds during the past ten years. Data on heat capacities, enthalpies of phase changes, and entropies of organic compounds published before 1960 can be found in Landolt-Bornstein, Zahlenwerte und Funktionen, II. Band, 4. Teil (Berlin, Springer-Verlag, 1961). See also Chapter 2. 

The physical meanings of many thermodynamic parameters such as specific heat, enthalpy, entropy, and the Gibbs function were discussed, and several methods for determining their values for nonreacting and reacting liquid- and gas-phase mixtures were discussed. The heat of formation, sensible enthalpy, and latent heat of phase change make up the total enthalpy of a substance at a given temperature ... 

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

Figure 1.4. Temperature dependence of the change in Gihhs energy, enthalpy and entropy upon transfer of ethane and butane from the gas phase to water. The data refer to transfer from the vapour phase at 0.101 MPa to a hypothetical solution of unit mole fraction and are taken from ref. 125.

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

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