Enthalpy first-order transitions

Phase transitions at which the entropy and enthalpy are discontinuous are called first-order transitions because it is the first derivatives of the free energy that are disconthuious. (The molar volume V= (d(i/d p) j is also discontinuous.) Phase transitions at which these derivatives are continuous but second derivatives of G... 

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. 

If one of these quantities experiences a discontinuous change, i.e. if AS 0 or AV 0, then the phase transition is called a first-order transition according to Ehrenfest. It is accompanied by the exchange of conversion enthalpy AH = TAS with the surroundings. 

Considerable spread is also observed in reported enthalpies of transition in single-component systems. As an example, the reported enthalpy of the first-order transition giving the fast ionic conductor phase of Agl at 420 K are compared in Table 10.5. In general, the agreement between the results obtained by adiabatic or... 

We now distinguish solid state transformations as first-order transitions or lambda transitions. The latter class groups all high-order solid state transformations (second-, third-, and fourth-order transformations see Denbigh, 1971 for exhaustive treatment). We define first-order transitions as all solid state transformations that involve discontinuities in enthalpy, entropy, volume, heat capacity, compressibility, and thermal expansion at the transition point. These transitions require substantial modifications in atomic bonding. An example of first-order transition is the solid state transformation (see also figure 2.6)... 

Figure 4.1 Variation of (a) the free energy and enthalpy with temperature and (b) the free energy and volume with pressure in a first-order transition.

Figure 20 shows the phase diagram of polyethylene119). The existence range of the condis crystals increases with pressure and temperature. The enthalpy of the reasonably reversible, first order transition from the orthorhombic to the hexagonal condis phase of polyethylene is 3.71 kJ/mol at about 500 MPa pressure 121) which is about 80 % of the total heat of fusion. The entropy of disordering is 7.2 J/(K mol), which is more than the typical transition entropy of paraffins to their high temperature... 

So-called first-order transitions include evaporation or fusion, where volume (V), entropy (S), and enthalpy (H) all exhibit a discontinuity upon differentiation of Eq. (18.5) with respect to state variables pressure (p), or temperature (7). 

With each type of transition, AG = 0, in other words the G(T) curves for both phases intersect, and slightly below and above the transition temperature the free enthalpies are equal. The various derivatives of the free enthalpy may, however show discontinuities. With a first-order transition such as melting, this is the case with with the first derivatives like V and S and also with H. 

Simple molecules may occur in three states, the solid, the liquid and the gaseous state. The transitions between these phases are sharp and associated with a thermodynamic equilibrium. Under these conditions, phase changes are typical first-order transitions, in which a primary thermodynamic function, such as volume or enthalpy, shows a sudden jump. 

Since AG = 0 for the first-order transition at p and P, we have for the enthalpy change... 

The evaluation of solid-state transitions involves first the recognition of the type of transition, which may not always be obvious. A first-order transition such as fusion involves a discontinuous change of enthalpy and entropy at the transition point, whereas second-order transitions involve only discontinuities in heat capacity. Because of impurities and other factors, first-order transitions often do not occur sharply at one temperature instead, they spread a little on either side and are sometimes difficult to distinguish fromA-type second-order transitions. 

In these equations T, T2. .. represent equilibrium first order transition temperatures and AH, AH-. .. the corresponding equilibrium transition enthalpies. is the enthalpy of the material analyzed at 0 K. 

In first order transitions, such as melting, there is a discontinuity in the volume-temperature plot (see Fig. 2.22) or enthalpy-temperature plot at... 

The thermal variation of specific heat measured by adiabatic calorimetry is showninfig 1 At about 347 K a jump of occurs which corresponds to a first order transition. This is confirmed by 0. S. C. measurement which gives an enthalpy of transition AH = 1160+ 100 cal/mole. This transition which presents an endothermic signal is however irreversible, at least down to 4 K, To obtain the initial phase it is necsssary to crystallize again the trensformed product in eceto-nitrile. However the irreversibility is not due to solvent inclusion as evidenced by mass spectroscopy analysis,... 

The thermodynamics of the I-N phase transition has been extensively investigated for resolving the issue concerning the order of the transition. Following the Ehrenfest scheme, a phase transition is classified into a first-order transition or a second-order one, depending upon the observation of finite discontinuities in the first or the second derivatives of the relevant thermodynamic potential at the transition point. An experimental assessment of the order of the I-N transition has turned out to be not a simple task because of the presence of only small discontinuities in enthalpy and specific volume. It follows from high-resolution measurements that I-N transition is weakly first order in nature [85]. 

In first order transitions, siich as melting, there is a discontinuity in the volume-temperature plot (see Fig. 2.19) or enthalpy-temperature plot at the transition temperature. In second-order transitions, only a change in slope occurs and there is thus a marked change in the first derivative or temperature coefficients, as illustrated in Fig. 2.20. The glass transition is not a first-order transition, as no... 

Figure 2.2 illustrates the change of enthalpy of silicon with temperature. In the case of a first order transition there is a discontinuity in the course of enthalpy. At this point Cp is infinite (see Section 1.7.3). 

There are many more studies of the enthalpy increments of thoria which are summarised with other relevant references in Table VII-3. Three earlier, less precise studies are noted in [1975RAN], but have not been considered. Fischer et al. [1981F1S/F1N] first showed that thoria undergoes a transition at a temperature aroimd 3000 K. Although this was presumed to be a disordering transition, their data were represented sufficiently accurately as a first-order transition at 2950 K, with a small transition enthalpy. More recently, Ronchi and Hiemaut [1996RON/HIE] have studied this transition in detail, and showed that it is indeed second-order. Their results are discussed more in detail below, and in Appendix A. 

Some thermodynamic functions can be deduced from the knowledge of the specific heat. They are the enthalpy, the internal energy and the entropy. The first function appears as the latent heat in first-order transitions like the ferromagnetic-antiferromagnetic transition or where the magnetic transition is related to a structural transition. 

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