# 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.