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Phase transitions

Phase transitions. Qualitative discussion: the 1-component system water. specific volume. Clausius-Clapeyron Equation. Heat Reservoir R. T=const. Consider a system of liquid & vapor phases in equilibrium at given P and T. P=const. vapor phase contains N 2 particles.

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Phase transitions

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

  2. Clausius-Clapeyron Equation Heat Reservoir R T=const. Consider a system of liquid & vapor phases in equilibrium at given P and T P=const. vapor phase contains N2 particles constant # of particles N=N1+N2 liquid phase contains N1 particles P and T fixed System in a state of minimum Gibbs free energy Gibbs free energy/particle = chemical potential

  3. N2= N - N1 with const. for Let´s discuss G  minimum for g1>g2, g1<g2 and g1=g2 Index 1: liquid Index 2: vapor g1>g2 G at minimum for N1=0 N2=N (only vapor phase) 1 g1<g2 G at minimum for N1=N N2=0 (only liquid phase) 2 g1=g2 G at minimum for all N1, N2 with N1+N2=N 3 equilibrium of vapor & liquid phase

  4. P=const g g1(T,P)=1 g2(T,P)=2 T0 T P=P(T) = g2(T,P) g1(T,P) At the phase transition “vaporization curve” Note: g1=g2  1=2(see equilibrium conditions) How does the pressure change with temperature for two phases in equilibrium

  5. 1  T defining the transition line g1(T,P(T)) = g2(T,P(T)) With -s1 v1 -s2 v2 and we see From dg=-s dT+vdP volume/particle entropy/particle Latent heat: heat needed to change system from phase 1 to phase 2 = = Clausius-Clapeyron equation T=const. at phase transition

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