a first-order phase transition

Boil a kettle and, at 100 C, something abrupt happens: liquid turns to vapour, absorbing a large gulp of heat (the latent heat) while the temperature stubbornly refuses to rise until all the water is gone, and the density jumps a thousandfold. Melting, freezing, boiling and sublimation are all first-order phase transitions — transitions marked by a discontinuity and a latent heat, in which the two phases genuinely coexist at the transition.

In the Ehrenfest classification a transition is first-order when the Gibbs free energy G is continuous but its first derivatives jump. Since entropy S = -(dG/dT)_p and volume V = (dG/dp)_T are those first derivatives, both change discontinuously: the entropy jump delta S gives a nonzero latent heat L = T delta S, and the volume jumps by delta V. At the transition the chemical potentials of the two phases are equal (that is why they coexist), while their slopes differ.

First-order transitions bring hysteresis and metastability: you can superheat a liquid above its boiling point or supercool it below its freezing point because forming the new phase requires nucleating an interface, which costs energy. This is everyday physics — ice, steam, crystallization — and the Clausius-Clapeyron equation is precisely the slope of a first-order coexistence line. Contrast with a continuous (second-order) transition, which has no latent heat and no coexistence.