Phase transitions Qualitative discussion: the 1-component system water specific volume

Clausius-Clapeyron Equation Consider a system of liquid & vapor phases in equilibrium at given P and T Heat Reservoir R T=const. P=const. liquid phase contains N 1 particles vapor phase contains N 2 particles N=N 1 +N 2 constant # of particles P and T fixed System in a state of minimum Gibbs free energy Gibbs free energy/particle = chemical potential

with N 2 = N - N 1 const. for Let´s discuss G  minimum for g 1 >g 2, g 1 <g 2 and g 1 =g 2 Index 1: liquid Index 2: vapor 1 g 1 >g 2 G at minimum for N 1 =0N 2 =N (only vapor phase) 2 g 1 <g 2 G at minimum for N 1 =NN 2 =0 (only liquid phase) 3 g 1 =g 2 G at minimum for all N 1, N 2 with N 1 +N 2 =N equilibrium of vapor & liquid phase

P=const T g g 1 (T,P)=  1 g 2 (T,P)=  2 T0T0 At the phase transition g 1 (T,P) = g 2 (T,P) P=P(T) “vaporization curve” How does the pressure change with temperature for two phases in equilibrium Note: g 1 =g 2   1 =  2 ( see equilibrium conditions )

volume/particle With g 1 (T,P(T))= g 2 (T,P(T))  T defining the transition line From dg=-s dT+vdP we see entropy/particle and -s 1 -s 2 v1v1 v2v2 Latent heat: heat needed to change system from phase 1 to phase 2 Clausius-Clapeyron equation T=const. at phase transition 1