CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 178
7.2.1 Phase transitions of the first and second order
It follows from the condition of phase equilibrium (7.1) that during phase transitions the Gibbs
energy is a continuous function of temperature and pressure. If the first derivatives of the Gibbs
energy, i.e. entropy and volume [see 3.41] are discontinuous at a phase transition,
S(1) 6 =S(2) a V(1) 6 =V(2), (7.5)the process is classified as afirst-order phase transition.
If the first derivatives of the Gibbs energy are continuous while its second derivatives, i.e.
the isobaric heat capacity [see (3.18)] and the isothermal compressibility coefficient [see (2.10)]
are discontinuous,
S(1)=S(2), Cp(1) 6 =C(2)p a V(1)=V(2), β(1) 6 =β(2), (7.6)the process is classified as asecond-order phase transition.
Note:Melting, sublimation, boiling and (in most cases) transformation of crystalline mod-
ifications represent first-order phase transitions. Glass transitions, some transformations
of crystalline modifications, or the transition from the ferromagnetic to the diamagnetic
state represent second-order phase transitions.