New location for the Course website

http://www.physics.ucdavis.edu/physics7/7A_2008WinCD/7A_2008WinCD.html

Also accessible from: http://www.physics.ucdavis.edu/physics7/

Quiz 6 8:30-8:50am TODAYHave your calculator ready.

Cell phone calculator NOT allowed.Closed book

Quiz 2 Re-evaluation Request Due this Thursday, 2/21.Quiz 3 Re-evaluation Request Due next Thursday, 2/28.

Turn in you original Quiz along with the Re-evaluation Request Form. Note: It is possible for your grade to be lowered after the re-evaluation.

Quiz 3 average 8.78 (Q1 8.69, Q2 7.22) , rubrics/grades posted on the website

Quiz 4 will be returned this week.

Next lecture February 26Quiz 7 will cover the material from today’s lecture and material from DLM10 (again!) and 11, excluding FNTs for DLM12.

Example H2O

Recap: Particle Model of MatterRecap: Particle Model of MatterNormal Matter : Particles Bouncing Normal Matter : Particles Bouncing Around!Around!

“Idealized” picture of water magnified one billion times

Example H2O

Recap: Particle Model of MatterRecap: Particle Model of MatterNormal Matter : Particles Bouncing Normal Matter : Particles Bouncing Around!Around!

“Idealized” picture of water magnified one billion times

Relate the energy of large objects to the energies of the individual constituents.

Liquid: Molecules can move around, but are loosely held together by molecular bonds. Nearly incompressible.

Gas: Molecules move freely through space. Compressible.

Solid: Rigid, definite shape. Nearly incompressible.

Phases under MicroscopePhases under Microscope

• The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions.

Ebond = ∑all pairs(PEpair-wise)

Particle Model of EParticle Model of EbondbondEbond for a substance is the amount of energy

required to break apart “all” the bonds

• The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions.

Ebond = ∑all pairs(PEpair-wise)

• A useful approximation of the above relation is ,

Ebond ~ (total number of nearest neighbor pairs) x ()

Particle Model of EParticle Model of Ebondbond

Don’t forget the negative sign!

Count the nearest neighbor pairs for ALL atoms in the substance!

: Depth of the pair-wise potential well for a given substance

Ebond for a substance is the amount of energy

required to break apart “all” the bonds

• The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions.

Ebond = ∑all pairs(PEpair-wise)

• A useful approximation of the above relation is ,

Ebond ~ (total number of nearest neighbor pairs) x ()

Ebond ~ {(number of nearest neighbor pairs for each atom)/2} x N x ()

Ebond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors.

Particle Model of EParticle Model of Ebondbond

Don’t forget the negative sign!

Count the nearest neighbor pairs for ALL atoms in the substance!

N:Total number of atoms in the substance

: Depth of the pair-wise potential well for a given substance

Ebond for a substance is the amount of energy

required to break apart “all” the bonds

Particle Model of EParticle Model of EthermalthermalEthermal is the energy associated with the random motions and vibrations of the particles.

• Ethermal is split between PEoscillation and KE .

Liquids and Solids

Model atoms in liquids and solids as if there were springs between the atoms.

Particle Model of EParticle Model of EthermalthermalEthermal is the energy associated with the random motions and vibrations of the particles.

• Ethermal is split between PEoscillation and KE .

• For solids and liquids,

KEall atoms = (1/2)Ethermal

PEall atoms = PEbond + PEoscillation = Ebond + (1/2)Ethermal

Liquids and Solids

Model atoms in liquids and solids as if there were springs between the atoms.

Particle Model of EParticle Model of EthermalthermalEthermal is the energy associated with the random motions and vibrations of the particles.

• Ethermal is split between PEoscillation and KE .

• For solids and liquids,

KEall atoms = (1/2)Ethermal

PEall atoms = PEbond + PEoscillation = Ebond + (1/2)Ethermal

Liquids and Solids

KEall atoms + PEall atoms

= Ethermal + Ebond

Model atoms in liquids and solids as if there were springs between the atoms.

What about Gas phase?What about Gas phase?

KEall atoms + PEall atoms

= Ethermal + Ebond

GasNo intermolecular bonds,

i.e. no springs

For monoatomic gas (e.g. He, Ne, Ar),

What about Gas phase?What about Gas phase?

KEall atoms = EthermalGas

No bonds, i.e. no springs

For monoatomic gas (e.g. He, Ne, Ar),

For non-monoatomic gas (e.g. N2, O2, CO2), we’ll

talk about it later.

Solid&Liquid: KEall atoms = (1/2)Ethermal

PEall atoms = Ebond + (1/2)Ethermal

What is Temperature in terms of EWhat is Temperature in terms of Ethermalthermal??

Gas: KEall atoms = Ethermal

QuestionQuestion

What is TemperatureWhat is Temperature

in terms of Ein terms of Ethermalthermal??

??

QuestionQuestion

What is TemperatureWhat is Temperature

in terms of Ein terms of Ethermalthermal??

Answer: Answer:

Temperature IS Thermal Energy!Temperature IS Thermal Energy!

??

But Wait a minute…

[Energy] = [Joule] [Temperature] = [Kelvin]

Answer revised: Answer revised:

Temperature is proportional to ETemperature is proportional to Ethermal. thermal.

The proportionality constant is kThe proportionality constant is kBB : : Boltzman constantBoltzman constant

kkBB = 1.38 = 1.38 10 10-23-23 Joule for every degree Joule for every degree KelvinKelvin

To be precise, energy associated with the To be precise, energy associated with the component of motions/vibrations in any component of motions/vibrations in any particular direction is (1/2)kparticular direction is (1/2)kBBT :T :

EEthermal per modethermal per mode = (1/2) k = (1/2) kBBTT

a.k.a. Equipartition of Energya.k.a. Equipartition of Energy

Liquids and Solids

Gas

Modes : Ways each particle has of storing energy

Ex. Mass-spring has one KE mode and one PE mode

““ModeMode””

Equipartition of Energy RestatedEquipartition of Energy Restated

In thermal equilibrium, EIn thermal equilibrium, Ethermal thermal is shared equally is shared equally among all the “active” modes available to the among all the “active” modes available to the particle. In other words,each “active” mode has particle. In other words,each “active” mode has the same amount of energy given by :the same amount of energy given by :

EEthermal per modethermal per mode = (1/2) k = (1/2) kBBTT

Liquids and Solids

Gas

Low temp High temp

Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat

HeatHeat

Thermal equilibriumThermal equilibriumIf the two objects are at the same temperature, no heat flows between them.

A system in thermal equilibriumin thermal equilibriumis a system whose temperature is not changing in time.

i.e. A system in thermal equilibriumin thermal equilibriumis a system whose energy per mode is not changing with time.

Tfinal

3 KEtranslational modes

Modes of an atom in solid/liquidModes of an atom in solid/liquid

Every atom can move in three directions

3 KEtranslational modes

Modes of an atom in solid/liquidModes of an atom in solid/liquid

Every atom can move in three directions

Plus 3 potential energy along

three directions

3 PE modes

3 KEtranslational modes

Modes of an atom in solid/liquidModes of an atom in solid/liquid

Every atom can move in three directions

Plus 3 potential energy along

three directions

Total number of modes is 3PE + 3KE = 6Ethermal = 6(1/2)kBT

3 PE modes

3 KEtranslational modes

Modes of an atom in monoatomic gasModes of an atom in monoatomic gas

Every atom can move in three directions

3 KEtranslational modes

Modes of an atom in monoatomic gasModes of an atom in monoatomic gas

Every atom can move in three directions

0 PE modes

Gas

No bonds, i.e. no springs

3 KEtranslational modes

Modes of an atom in monoatomic gasModes of an atom in monoatomic gas

Every atom can move in three directions

Total number of modes is 3KE = 3Ethermal = 3(1/2)kBT

0 PE modes

Gas

No bonds, i.e. no springs

3 KEtranslational modes

Modes of a molecule in diatomic gasModes of a molecule in diatomic gas

3 KEtranslational modes

2 KErotational modes

Modes of a molecule in diatomic gasModes of a molecule in diatomic gas

3 KEtranslational modes

2 vibrational modes (1 KE, 1PE)(associated with atom-atom interaction

within the molecule)

2 KErotational modes

Modes of a molecule in diatomic gasModes of a molecule in diatomic gas

3 KEtranslational modes

2 vibrational modes (1 KE, 1PE)(associated with atom-atom interaction

within the molecule)

2 KErotational modes

Total number of modes is 6KE + 1PE = 7Ethermal = 7(1/2)kBT

•Sometimes (at lower temperatures), however, not all the modes are “active”. (Freezing

out of modes)

Modes of a molecule in diatomic gasModes of a molecule in diatomic gas

KE KE modemode

PE PE modemode

TotalTotal

Solids 3

Liquids

Monatomic gasses

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3

Liquids

Monatomic gasses

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids

Monatomic gasses

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3

Monatomic gasses

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3 0

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3 0 3

Diatomic gasses

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3 0 3

Diatomic gasses 3+2+1

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

KE KE modemode

PE PE modemode

TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3 0 3

Diatomic gases 3+2+1 1 7

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

Does this explain anything about anything?

KE KE modemode

PE PE modemode TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses 3 0 3

Diatomic gasses 3+2+1 1 7

Equipartition tells us that the energy per mode is 1/2 kBT.

We have counted

number of modes

in different phases as:

When energy is added to a system, what does it mean to have more places (modes) to store energy?

KE KE modemode

PE PE modemode TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses

3 0 3

Diatomic gases 3+2+1 1 7

Equipartition tells us that the energy per mode is 1/2 kBT.

QuestionDoes it take More/Less energy to raise the temperature of diatomic gas compared to monatomic gas?

KE KE modemode

PE PE modemode TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses

3 0 3

Diatomic gasses 3+2+1 1 7

Equipartition tells us that the energy per mode is 1/2 kBT.

QuestionDoes it take More/Less energy to raise the temperature of diatomic gas compared to monatomic gas?

(a) More(b) Less(c) Equal (d) Who knows?

diatomic(no vibrations)

(10

0 C

)

All measurements at 25 Cunless listed otherwise (5

00

C)

monatomic

Well, let’s see real measurements of heat capacity…

KE KE modemode

PE PE modemode TotalTotal

Solids 3 3 6

Liquids 3 3 6

Monatomic gasses

3 0 3

Diatomic gasses 3+2+1 1 7

QuestionDoes it take More/Less energy to raise the temperature of diatomic gas compared to monatomic gas?

(a) More

C = ∆Ethermal / ∆T ∆ Ethermal per molecule = number of active modes (1/2)kB∆T

∆ Ethermal per N atoms = number of active modes (1/2)kB∆T N

Closed Book

Don’t forget to fill in your DL

section number!