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Quiz 6 8:30-8:50am TODAY Have 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 26 Quiz 7 will cover the material from today’s lecture and material from DLM10 (again!) and 11, excluding FNTs for DLM12.

Example H 2 O Recap: Particle Model of Matter Normal Matter : Particles Bouncing Around! “Idealized” picture of water magnified one billion times

Example H 2 O Recap: Particle Model of Matter Normal Matter : Particles Bouncing 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 Microscope

The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions. E bond = ∑ all pairs (PE pair-wise ) Particle Model of E bond E bond 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. E bond = ∑ all pairs (PE pair-wise ) A useful approximation of the above relation is, E bond ~  (total number of nearest neighbor pairs) x (  ) Particle Model of E bond 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 E bond 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. E bond = ∑ all pairs (PE pair-wise ) A useful approximation of the above relation is, E bond ~  (total number of nearest neighbor pairs) x (  ) E bond ~  {(number of nearest neighbor pairs for each atom)/2} x N x (  )  E bond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors. Particle Model of E bond 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 E bond for a substance is the amount of energy required to break apart “all” the bonds

Particle Model of E thermal E thermal is the energy associated with the random motions and vibrations of the particles. E thermal is split between PE oscillation and KE. Liquids and Solids Model atoms in liquids and solids as if there were springs between the atoms.

Particle Model of E thermal E thermal is the energy associated with the random motions and vibrations of the particles. E thermal is split between PE oscillation and KE. For solids and liquids, KE all atoms = (1/2)E thermal PE all atoms = PE bond + PE oscillation = E bond + (1/2)E thermal Liquids and Solids Model atoms in liquids and solids as if there were springs between the atoms.

Particle Model of E thermal E thermal is the energy associated with the random motions and vibrations of the particles. E thermal is split between PE oscillation and KE. For solids and liquids, KE all atoms = (1/2)E thermal PE all atoms = PE bond + PE oscillation = E bond + (1/2)E thermal Liquids and Solids KE all atoms + PE all atoms = E thermal + E bond Model atoms in liquids and solids as if there were springs between the atoms.

What about Gas phase? KE all atoms + PE all atoms = E thermal + E bond Gas No intermolecular bonds, i.e. no springs For monoatomic gas (e.g. He, Ne, Ar),

What about Gas phase? KE all atoms = E thermal Gas No bonds, i.e. no springs For monoatomic gas (e.g. He, Ne, Ar), For non-monoatomic gas (e.g. N 2, O 2, CO 2 ), we’ll talk about it later.

Solid&Liquid: KE all atoms = (1/2)E thermal PE all atoms = E bond + (1/2)E thermal What is Temperature in terms of E thermal ? Gas: KE all atoms = E thermal

Question What is Temperature in terms of E thermal ? in terms of E thermal ? ? ?

Question What is Temperature in terms of E thermal ? in terms of E thermal ? Answer: Temperature IS Thermal Energy! ? ?

But Wait a minute… [Energy] = [Joule][Temperature] = [Kelvin] Answer revised: Temperature is proportional to E thermal. The proportionality constant is k B : Boltzman constant k B = 1.38  Joule for every degree Kelvin

To be precise, energy associated with the component of motions/vibrations in any particular direction is (1/2)k B T : E thermal per mode = (1/2) k B T a.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 “Mode”

Equipartition of Energy Restated In thermal equilibrium, E thermal is shared equally among all the “active” modes available to the particle. In other words,each “active” mode has the same amount of energy given by : E thermal per mode = (1/2) k B T Liquids and Solids Gas

Low tempHigh temp Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat Heat

Thermal equilibrium If the two objects are at the same temperature, no heat flows between them. in thermal equilibrium A system in thermal equilibrium is a system whose temperature is not changing in time. in thermal equilibrium i.e. A system in thermal equilibrium is a system whose energy per mode is not changing with time. T final

3 KE translational modes Modes of an atom in solid/liquid Every atom can move in three directions

3 KE translational modes Modes of an atom in solid/liquid Every atom can move in three directions Plus 3 potential energy along three directions 3 PE modes

3 KE translational modes Modes 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 = 6 E thermal = 6  (1/2)k B T 3 PE modes

3 KE translational modes Modes of an atom in monoatomic gas Every atom can move in three directions

3 KE translational modes Modes of an atom in monoatomic gas Every atom can move in three directions 0 PE modes Gas No bonds, i.e. no springs

3 KE translational modes Modes of an atom in monoatomic gas Every atom can move in three directions Total number of modes is 3KE = 3 E thermal = 3  (1/2)k B T 0 PE modes Gas No bonds, i.e. no springs

3 KE translational modes Modes of a molecule in diatomic gas

3 KE translational modes 2 KE rotational modes Modes of a molecule in diatomic gas

3 KE translational modes 2 vibrational modes (1 KE, 1PE) (associated with atom-atom interaction within the molecule) 2 KE rotational modes Modes of a molecule in diatomic gas

3 KE translational modes 2 vibrational modes (1 KE, 1PE) (associated with atom-atom interaction within the molecule) 2 KE rotational modes Total number of modes is 6KE + 1PE = 7 E thermal = 7  (1/2)k B T Sometimes (at lower temperatures), however, not all the modes are “active”. (Freezing out of modes) Modes of a molecule in diatomic gas

KE mode PE mode Total Solids3 Liquids Monatomic gasses Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids33 Liquids Monatomic gasses Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids Monatomic gasses Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids3 Monatomic gasses Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses3 Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses30 Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses303 Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses303 Diatomic gasses3+2+1 Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as:

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses303 Diatomic gases Equipartition tells us that the energy per mode is 1/2 k B T. We have counted number of modes in different phases as: Does this explain anything about anything?

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses303 Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. 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 mode PE mode Total Solids336 Liquids336 Monatomic gasses 303 Diatomic gases Equipartition tells us that the energy per mode is 1/2 k B T. Question Does it take More/Less energy to raise the temperature of diatomic gas compared to monatomic gas?

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses 303 Diatomic gasses Equipartition tells us that the energy per mode is 1/2 k B T. Question Does 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) (100 C) All measurements at 25 C unless listed otherwise (500 C) monatomic Well, let’s see real measurements of heat capacity…

KE mode PE mode Total Solids336 Liquids336 Monatomic gasses 303 Diatomic gasses Question Does it take More/Less energy to raise the temperature of diatomic gas compared to monatomic gas? (a) More C = ∆E thermal / ∆T ∆ E thermal per molecule = number of active modes  (1/2)k B ∆T ∆ E thermal per N atoms = number of active modes  (1/2)k B ∆T  N

Closed Book Don’t forget to fill in your DL section number!