Latent Heat Update Steps

[1] Update the adiabatic coefficient $c_{adi,m}$ to include latent heat using equation eq:effective-adiabatic-coefficient with current adiabatic coefficient $c_{adi,m}$ to define the adiabatic coefficient prior to this update step, latent heat of fusion $L_m$ and equation eq:partial-melt-fraction-pressure to calculate the partial derivative of melt fraction with respect to pressure with marker temperature $T_m$ and pressure $P_m$.

[2] Update marker heat capacity $C_{p,m}$ to include latent heat using equation eq:effective-heat-capacity with current heat capacity $C_{p,m}$ to define the heat capacity prior to this update step, latent heat of fusion $L_m$ and equation eq:partial-melt-fraction-temperature to calculate the partial derivative of melt fraction with respect to temperature with marker temperature $T_m$ and pressure $P_m$.