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Phase transitions - PowerPoint PPT Presentation


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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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Presentation Transcript
slide1

Phase transitions

Qualitative discussion: the 1-component system water

specific volume

slide3

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

slide4

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

slide5

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

slide6

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