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1. Phase Transition

   Linked via "vaporization"

   The original Ehrenfest scheme classifies transitions based on which derivative of the free energy exhibits a discontinuity or singularity at the transition point ($Tc$ or $Pc$):
   First-Order Transitions: These are characterized by a finite, discontinuous jump in the first derivatives of the Gibbs free energy, namely the volume ($V = (\partial G / \partial P)T$) and the entropy ($S = -(\partial G / \partial T)P$). These transitions involve latent heat, $L = T\Delta S$, which must be supp…