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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/
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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.
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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
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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.
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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
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• 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
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• 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
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• 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
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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.
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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.
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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.
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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),
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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.
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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
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QuestionQuestion
What is TemperatureWhat is Temperature
in terms of Ein terms of Ethermalthermal??
??
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QuestionQuestion
What is TemperatureWhat is Temperature
in terms of Ein terms of Ethermalthermal??
Answer: Answer:
Temperature IS Thermal Energy!Temperature IS Thermal Energy!
??
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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
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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
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Modes : Ways each particle has of storing energy
Ex. Mass-spring has one KE mode and one PE mode
““ModeMode””
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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
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Low temp High temp
Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat
HeatHeat
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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
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3 KEtranslational modes
Modes of an atom in solid/liquidModes of an atom in solid/liquid
Every atom can move in three directions
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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
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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
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3 KEtranslational modes
Modes of an atom in monoatomic gasModes of an atom in monoatomic gas
Every atom can move in three directions
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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
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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
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3 KEtranslational modes
Modes of a molecule in diatomic gasModes of a molecule in diatomic gas
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3 KEtranslational modes
2 KErotational modes
Modes of a molecule in diatomic gasModes of a molecule in diatomic gas
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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
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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
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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?
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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?
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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?
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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?
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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…
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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
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Closed Book
Don’t forget to fill in your DL
section number!