Clapeyron equation melting transition

Equation (9) is valid for evaporation and sublimation processes, but not valid for transitions between solids or for the melting of solids. Clausius-Clapeyron equation is an approximate equation because the volume of the liquid has been neglected and ideal behaviour of the vapour is also taken into account. 

A liquid freezes to give a solid at the freezing phase transition temperature under a specified pressure, which is usually taken as 1 atm (or conversely a solid melts at the melting temperature which is equal to the freezing temperature). For this phase transition, the Clapeyron equation (Equation (279)) becomes... 

The transition point, like the melting point, is affected by pressure. Depending on the relative values of the specific volumes of the two polymorphs, an increase in pressure can either raise or lower the transition temperature. However, since this difference in specific volumes is ordinarily very small, the Clausius—Clapeyron equation predicts that the magnitude of dT/dP will not be great. 

The vapor pressure equation for the alpha phase is derived by evaluating free energy functions for the solid and the gas at 25 K intervals from 1000 to 1750 K and the transition temperature. For the liquid phase, values are evaluated at 50 K intervals from 1800 to 3600 K and the melting point. For the beta phase, values were evaluated at the transition and melting point temperatures and fitted to the Clausius-Clapeyron equation (Table 15). 

The relation between the chain melting transition in the three-dimensional aqueous systems and in monolayers was also analysed in this work. It was then assumed that the heat of transition (calculated from the Claussius-Clapeyron equation) and the molecular area in the monolayer are the same as in the fully hydrated aqueous phases. A discrepancy in the transition temperature between the monolayer and bilayer phases obtained in this way was explained as an effect of the external pressure applied. 

Compared to vaporization, the influence of pressure on the melting point is small. In general, the influence of pressure on a phase transition process is given by the Clapeyron equation ... 

Solution The Clapeyron equation. Equation 4.28, provides the relation between temperature and pressure for a phase transition. We need to consider how it ap>plies in the case of a solid-to-liquid (or liquid-to-solid) phase transition. The approximation of Equation 4.32 to the molar volume for a phase transition is based in part on the fact that for a solid or a liquid, the molar volume is largely independent of temperature, as well as being a value much less than the molar volume of a gas. This means that for fusion or melting, the change in the molar transition volume in Equation 4.28 is usually well approximated as a constant (independent of T). The following steps are carried out with this approximation, as well as with the assumption that the transition enthalpy is independent of temperature. 

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