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21.3: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition

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    Phase transitions (e.g. melting) often occur under equilibrium conditions. We have seen that both the \(H\) and the \(S\) curves undergo a discontinuity at constant temperature during melting, because there is an enthalpy of fusion to overcome. For a general phase transition at equilibrium at constant \(T\) and \(P\), we can say that:

    \[Δ_{trs}G = Δ_{trs}H - T_{trs}Δ_{trs}S = 0 \nonumber \]

    \[Δ_{trs}H = T_{trs}Δ_{trs}S \nonumber \]

    \[\dfrac{Δ_{trs}H}{T_{trs}}=Δ_{trs}S \nonumber \]

    For melting of a crystalline solid, we now see why there is a sudden jump in enthalpy. The reason is that the solid has a much more ordered structure than the crystalline solid. The decrease in order implies a finite \(Δ_{trs}S\). We should stress at this point that we are talking about first order transitions here. The reason for this terminology is that the discontinuity is in a function like \(S\), that is a first order derivative of \(G\) (or \(A\)):

    \[\left(\frac{\partial\bar{G}}{\partial T}\right)_P=-\bar{S} \nonumber \]

    Second order derivatives (e.g. the heat capacity) will display a singularity (+∞) at the transition point.

    Every phase transition will have a change in entropy associated with it. The different types of phase transitions that can occur are:

    \(l \rightarrow g\) Vaporization / boiling
    \(g \rightarrow l\) Condensation
    \(s \rightarrow l\) Fusion / melting
    \(l \rightarrow s\) Freezing
    \(s \rightarrow g\) Sublimation
    \(g \rightarrow s\) Deposition
    \(s \rightarrow s\) Solid to solid phase transition

    21.3: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.