A. Scardicchio, ICTP

This lesson continues the study of the phase transitions of the van der Waals fluid in the vicinity of the critical point. As in the previous lesson, the van der Waals equation of state was expanded to third order in the variables *?X=X-X _{c}, *where

*X*represents the three state variables

*P, V*and

*T*. A comprehensive analysis of the behaviour of the fluid in the

*?P-*plane followed.

*?T*The equilibrium states of the system around the critical point can be analyzed by minimizing the enthalpy state function. For * ?T* > 0 (the region of only one fluid phase) the enthalpy has one absolute minimum while for

*< 0 there are two local minimums that correspond to the liquid and vapor phases. In the latter case, for given*

*?T**,*

*(?T**one of the two is the absolute minimum and corresponds to the equilibrium state of the system. The exception to this are the states that belong to the phase transition line. There, the enthalpy has the same value in both minima signaling the coexistence of the two phases.*

*?P)*Finally, the **classification of phase transitions** was introduced. It is based on the behavior of the derivatives of the state functions with respect to the state variables at the transition points.