# 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 Condensation Fusion / melting Freezing Sublimation Deposition 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.