# 21.3: Temperatures at a Phase Transition

A phase transition like melting is often done under equilibrium conditions. We have seen that both the H and the S curves undergo a dicontinuity at such a temperature, 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:

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

\[Δ_{trs}H = T_{trs}Δ_{trs}S\]

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

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