Entropy of irreversible process

Intuitively, we know that the freezing of water below meting point, e.g -10 ℃ occurs spontaneously.

It means freezing of supercooled water is a irreversible process. Calculation of the entropy change for this process is by taking reversible detour path. Cp values of the materials involved and the latent heat give the entropy change and the enthalpy change of the system. The total entropy change is positive for this spontaneous process.