Phase transition latent heat

Thermodynamic potential G has only one global minimum for P = 0 above the phase transition temperature c- This global minimum might be accompanied by two local minima, which corresponds to the metastable ferroelectric phase. The spontaneous polarization jumps to zero at the Curie temperature c from the value given in Eq. (5.47) (see Fig. 5.11). Crystal energy changes also discontinuously at this temperamre, which must be accompanied by non-zero phase transition latent heat. Such phase transition is called the first-kind phase transition because of this latent heat. 

There are several types of transitions between solid phases and latent heats and the kinetics of the transformation both depend strongly on the particular type of transformation. 

The spontaneous polarization is therefore dependent on square root of o - and goes to zero at the temperature o (Fig. 5.8). In this case, the temperature 0 is identical with the phase transition temperature c (i.e. Curie temperatme). Spontaneous polarization appears and disappears at that temperature. Also the thermodynamic potential G changes continuously at the phase transition point between paraelectric and ferroelectric phases. No latent heat is associated with the phase... 

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]. 

A Hquid crystal compound in more cases than not takes on more than one type of mesomorphic stmcture as the conditions of temperature or solvent are changed. In thermotropic Hquid crystals, transitions between various phases occur at definite temperatures and are usually accompanied by a latent heat. 

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 ... 

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 ... 

The integral terms representing AH and AH can be computed if molal heat capacity data Cp(T) are available for each of the reactants (i) and products (j). When phase transitions occur between T and Tj for any of the species, proper accounting must be made by including the appropriate latent heats of phase transformations for those species in the evaluation of AHj, and AH terms. In the absence of phase changes, let Cp(T) = a + bT + cT describe the variation of (cal/g-mole °K) with absolute temperature T (°K). Assuming that constants a, b, and c are known for each species involved in the reaction, we can write... 

Le — latent heat of evaporation. v2 — Vi = Ar = volume change accompanying unit mass of phase transition at the pressure p. 

Where pit denote the pressure and latent heat of transition in the system which does not contain the i-th phase. 

Most steam generating plants operate below the critical pressure of water, and the boiling process therefore involves two-phase, nucleate boiling within the boiler water. At its critical pressure of 3,208.2 pounds per square inch absolute (psia), however, the boiling point of water is 374.15 C (705.47 °F), the latent heat of vaporization declines to zero, and steam bubble formation stops (despite the continued application of heat), to be replaced by a smooth transition of water directly to single-phase gaseous steam. 

If a phase transition takes place between the specified and datum temperatures, the latent heat of the phase transition is added to the sensible-heat change calculated by equation 3.11. The sensible-heat calculation is then split into two parts ... 

The variation of enthalpy for binary mixtures is conveniently represented on a diagram. An example is shown in Figure 3.3. The diagram shows the enthalpy of mixtures of ammonia and water versus concentration with pressure and temperature as parameters. It covers the phase changes from solid to liquid to vapour, and the enthalpy values given include the latent heats for the phase transitions. 

Second-order phase transitions are those for which the second derivatives of the chemical potential and of Gibbs free energy exhibit discontinuous changes at the transition temperature. During second-order transitions (at constant pressure), there is no latent heat of the phase change, but there is a discontinuity in heat capacity (i.e., heat capacity is different in the two... 

This implies that the exponents and y defined above are 0 = y = 2( = d) for a first-order transition. Since the symmetry around if = 0 is preserved for finite L, there is no shift of the transition. This feature is different, however, if we consider temperature-driven first-order transitions , since there is no symmetry between the disordered high-temperature phase and the ordered low-temperature phase. In order to understand the rounding of the delta-function singularity of the specific heat, which measures the latent heat for L- oo, it now is useful to consider the energy distribution, for which again a double Gaussian approximation applies ... 

The phase transitions of water as caused by changing heat content. Slopes of the lines indicate heat capacity. Note that the latent heats are slightly temperature dependent, i.e., the latent heat of vaporization is 540 cal/g at 100°C and 533 cal/g at 110°C. 

The method of latent heat storage based on liquid-solid phase transition is available to make smaller the volume of heat storage tank, because of its higher thermal density than that of sensible heat storage. Therefore, a substance which has a large amount of latent heat of fusion is more profitable as a heat storage material. 

Fig. 5 The typical DSC diagram for solid state phase transition with latent heat red plot) or without latent heat blue plot). The scale is not the same in general the curve for a second-order transition blue plot) is associated with smaller changes of heat capacity (and therefore more difficult to detect)...

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

Ni(C2HgN2)3(N03)2 is quite different - the space group type and the lattice change at (ca. 106 K). The transition show discontinuity of the cell volume and, as expected, there is a latent heat of transition. Notably at the critical temperature the two phases are structurally different and therefore they are in equilibrium at that temperature. A minor hysteresis is observed. 

The Meissner effect is a very important characteristic of superconductors. Among the consequences of its linkage to the free energy are the following (a) The superconducting state is more ordered than the normal state (b) only a small fraction of the electrons in a solid need participate in superconductivity (c) the phase transition must be of second order that is, there is no latent heat of transition in the absence of any applied magnetic field and (d) superconductivity involves excitations across an energy gap. 

S5 — Sjv)r—o = yT- The behaviour of y in the superconducting state is different from that of the normal state y is a linear function of temperature in the normal state but its temperature dependence is exponential in the superconducting state. The superconducting transition at zero magnetic field is a second-order phase transition since there is discontinuity in specific heat but no latent heat change. 

Reconstructive phase transitions occur when major changes are made in the topology, i.e. when the bond graph is reorganized. The transitions usually observed in structures with lattice-induced strain are displacive and often second order (no latent heat). Reconstructive transitions arise when two quite different structures with the same composition have similar free energies. Unlike the displacive transitions they involve the dissolution of one structure and the recrystallization of a quite different structure. These phase transitions possess a latent heat and often display hysteresis. 

The latent-heat terms (3.112) become necessary whenever the integrand ACP undergoes discontinuous change at a phase transition, with accompanying release of hidden AH. [The latent heat contribution is automatically included if one understands J(ACV) dT as Lehesgue integration.] For numerical evaluation of the integral in (3.111), power series... 

As shown in the table, contribution 1 [Sq = 0] is the third-law convention contribution 2 is a theoretical approximation (based on the Debye heat capacity of long-wavelength vibrational modes) for the low-temperature region 0-16K, contributing only 1.3 J mol-1 K1 contribution 3 is the CP/T integral for the low-temperature solid I form of HC1 contribution 4 is the A/7, >n/7), latent heat contribution (12.1 J mol 1 K1) for the enantiomorphic solid I —> solid II phase transition at 98.36K, and so forth. 

We can also write the transition entropy ASa for this phase transition in terms of the associated latent heat AHa and transition temperature T(r as... 

The function describing the change in entropy, as a function of temperature, involves the use of a prescription that contains a formula specific to a particular phase. At each phase transition temperature the function suffers a finite jump in value because of the sudden change in thermodynamic properties. For example, at the boiling point 7b the sudden change in entropy is due to the latent heat of evaporation (see Figure 2.8). 

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