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Phase Transitions in Physics: Solids, Liquids, and Gases, Study notes of Physics

University of Illinois - Urbana-Champaign Physics

A part of the lecture notes for physics 213, specifically lecture 13. It covers the topic of phase transitions, focusing on the differences between solids, liquids, and gases, and the concepts of gibbs free energy, phase diagrams, and latent heats. The document also includes questions and exercises for students.

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Physics 213: Lecture 13, Pg 1

Lecture 13

Phase Transitions

Agenda for today

•Phase equilibria and chemical potentials

•Gibbs Free Energy

•Vapor pressure of a solid

•Latent heats

•Phase diagrams

•Origins of phase separation

Reference for this Lecture:

Elements Ch 13 Lecture 14:

Broad applications

cool demos

Discover Study notes of Physics University of Illinois - Urbana-Champaign

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Download Phase Transitions in Physics: Solids, Liquids, and Gases and more Study notes Physics in PDF only on Docsity!

Physics 213: Lecture 13, Pg 1

Lecture 13 Lecture 13

Phase Transitions

Agenda for today Agenda for today

Phase equilibria and chemical potentials

Gibbs Free Energy

Vapor pressure of a solid

Latent heats

Phase diagrams

Origins of phase separation

Reference for this Lecture:

Elements

Ch 13

Lecture 14:

Broad applications

cool demos

Physics 213: Lecture 13, Pg 2

Phases: Roadmap Phases: Roadmap

We’ll start from the common observation that materials canbe found in distinct phases

E.g solid, liquid, gas.

We’ll explain how equilibria between these phases work.

Then we’ll go back and try to understand why distinctphases exist in the first place.

Physics 213: Lecture 13, Pg 4

How can solids, liquids and gases be stable at differenttemperatures?

Phase Transitions: total entropy? Phase Transitions: total entropy?

We know that at some intermediate temperature,water will be a liquid

in this case, energy to form the liquid is taken fromthe environment, reducing its entropy, but theentropy of the liquid must increase more

We know that at low enough temperatures a substancelike water is a solid

its entropy is lower than that of the liquid so it mustgive up enough energy to its environment to makethe

total

entropy

increase

when ice forms

water

ice

liquid water

ice:

S

tot

S

water

S

env

ice

liquid water:

S

tot

S

water

S

env

Physics 213: Lecture 13, Pg 5

Gibbs free energy

Most phase transitions are observed under

constant-p,T

conditions,

not constant-V,T

−

what happens if you try to freeze or boil water in a fixed-V bottle?

−

Or boil liquid N

in a fixed-volume cannon?

In this case, the entropy of the environment changes not only whenthe system

energy

changes but also when its

volume

changes

−

If the system expands into the reservoir, the reservoir loses V andhence S (OR if system does mechanical W, reservoir supplies Q)

T

G

T

TS

U

T

V

T

U

S

T

V

T

U

S

TS

H

TS

pV

U

G

where

So here, maximizing

total

S means minimizing

system

G. Variables U, V, S are of system.Fixed p, T are of reservoir.

H

U+pV,

enthalpy

Physics 213: Lecture 13, Pg 7

Phase Transitions: ACT 1 Phase Transitions: ACT 1

What happens if heat flows slowly into watercontaining some ice cubes (maintaining equilibrium)?

temperature will remain constant until ice ismelted

Q:

What happens to the energy added to thesystem while the temperature is at 0

C?

water @

C

ice

Q

A. It heats up the iceB. It heats up the waterC. It breaks up ice bonds

Physics 213: Lecture 13, Pg 8

Phase Transitions: ACT 1 Phase Transitions: ACT 1

What happens if heat flows slowly into watercontaining some ice cubes (maintaining equilibrium)?

temperature will remain constant until ice ismelted

Q:

What happens to the energy added to thesystem while the temperature is at 0

C?

water @

C

ice

Q

A. It heats up the iceB. It heats up the waterC. It breaks up ice bonds

Physics 213: Lecture 13, Pg 10

Act 2 Act 2

1) What is the change of entropy per mole

of water when ice melts (@ p = 1 atm)?Q

= 333 J/g

a) 333 J/g K

b) 300 J/mol K

c) 22 J/mol K

water @

C

ice

Q

Physics 213: Lecture 13, Pg 11

Act 2 Act 2

1) What is the change of entropy per mole of

water when ice melts (p = 1 atm)?Q

= 333 J/g

a) 333 J/g K

b) 300 J/mol K

c) 22 J/mol K

water @

C

ice

Q

= T

S;

S = Q

/T

S = 333 J/g / 273 K * 18 g/mol

= 22.2 J/mol K

That’s a loss of

of about 3 per molecule:

only about e

, or 5%, as many microstates available

to each molecule in the solid.

Physics 213: Lecture 13, Pg 13

Phase Diagrams Phase Diagrams

Notice that in almost all the(p.T) plane, only ONE phaseis stable.

On special transition lines,two phases are stable.

At very special triple points,those line cross and threephases are stable.

Physics 213: Lecture 13, Pg 14

Chemical Potentials of Solids and Liquids Chemical Potentials of Solids and Liquids

Solids have heat capacity (mostly from vibrations), so S depends on T.

( Why?)

μμμμ

decreases with T.

(How do you know it’s a decrease?)

The liquid phase is less bound than the solid (

∆

), but its S is higher.

μμμμ

starts higher, but falls more quickly with T.

To minimize G

state with the lowest

At

special values

of (p,T), different

phases can have the same

and

thus coexist.

∆ ∆

Liquid-solid equilibrium

freeze

Because the liquid and solid have about the same volume per particle,

for now we can ignore p and just consider equilibria at different T.

Physics 213: Lecture 13, Pg 16

) The substance is in state C. What will happen?

a. substance will meltb. free energy will be minimizedc. total entropy will maximize

Act 4

1) Which point corresponds to a liquid?

A B C

Point A corresponds to a liquid out of equilibrium.Point B corresponds to a liquid in equilibrium with the solid phase

∆ ∆

Physics 213: Lecture 13, Pg 17

) The substance is in state C. What will happen?

a. substance will meltb. free energy will be minimizedc. total entropy will maximize

Act 4

1) Which point corresponds to a liquid?

A B C

Point A corresponds to a liquid out of equilibrium.Point B corresponds to a liquid in equilibrium with the solid phase

∆ ∆

Physics 213: Lecture 13, Pg 19

Why Why

separate separate

gas gas

- -

liquid phases? liquid phases?

A crude van A crude van

der der

Waals picture Waals picture

At low density, a gas is nearly ideal:

p=(N/V)kT

As N/V is raised, the molecules spendtime near each other, and the net forceis attractive, reducing U. So p < (N/V)kT.

P can even drop as N/V increases!

If they get too crammed together, theinteraction potential gets positive, andbig, so p shoots up.

N/V

Which N/V can be stable?

Same p, different N/V

You can get mechanical equilibrium between two different N/V!

And the intermediate N/V aren’t stable.

The system separates into two distinct phases.

Intermediate N/V pay the lost entropy cost

without getting the lost-energy gain.

Physics 213: Lecture 13, Pg 20

WHY separate gas WHY separate gas

- -

liquid phases? liquid phases?

A crude van A crude van

der der

Waals picture Waals picture

At low density, a gas is nearly ideal:

=kTln(n/n

As N/V is raised, the moleculesspend time near each other, and thenet force is attractive, reducing U.

<kTln(n/n

can even

drop

as N/V increases!

If they get too crammed together,the interaction potential getspositive, and big, so

Phase Transitions in Physics: Solids, Liquids, and Gases, Study notes of Physics

Related documents

Partial preview of the text

Download Phase Transitions in Physics: Solids, Liquids, and Gases and more Study notes Physics in PDF only on Docsity!

Phase Transitions

Phase Transitions

Phase equilibria and chemical potentials

Gibbs Free Energy

Vapor pressure of a solid

Latent heats

Phase diagrams

Origins of phase separation

Reference for this Lecture:

Elements

Ch 13

Lecture 14:

Broad applications

cool demos

We’ll start from the common observation that materials canbe found in distinct phases

E.g solid, liquid, gas.

We’ll explain how equilibria between these phases work.

Then we’ll go back and try to understand why distinctphases exist in the first place.

We know that at some intermediate temperature,water will be a liquid

in this case, energy to form the liquid is taken fromthe environment, reducing its entropy, but theentropy of the liquid must increase more

We know that at low enough temperatures a substancelike water is a solid

its entropy is lower than that of the liquid so it mustgive up enough energy to its environment to makethe

total

entropy

increase

when ice forms

S

S

S

S

S

S

Gibbs free energy

Gibbs free energy

Most phase transitions are observed under

constant-p,T

conditions,

not constant-V,T

what happens if you try to freeze or boil water in a fixed-V bottle?

Or boil liquid N

in a fixed-volume cannon?

In this case, the entropy of the environment changes not only whenthe system

energy

changes but also when its

volume

changes

If the system expands into the reservoir, the reservoir loses V andhence S (OR if system does mechanical W, reservoir supplies Q)

T

G

T

TS

U

T

V

T

U

S

T

V

T

U

S

S

S

S

TS

H

TS

pV

U

G

where

So here, maximizing

S means minimizing

G.

Variables U, V, S are of system.Fixed p, T are of reservoir.