due to monday holiday (presidents day 2/18), 2/14 thursday dl section (1,3,4) cancelled. (dl section...

Due to Monday Holiday (Presidents Day 2/18),

2/14 Thursday DL Section (1,3,4) cancelled. (DL Section 7,10 meet as normal)

2/15 Friday DL Section 2,5,6 cancelled.

Quiz 5 10-10:20am TODAYHave your calculator ready.

Cell phone calculator NOT allowed.Closed book

Quiz 1 Re-evaluation Request Due this Thursday, 2/14.Quiz 2 Re-evaluation Request Due next Thursday, 2/21.

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 info (grades, ave score) will be posted this week. Quiz 4 graded, scores being recorded.

Next lecture February 19Quiz 6 will cover the material from today’s lecture (excluding equipartition) and material from DLM9 and 10, excluding FNTs for DLM11.

What is the world made of?What holds the world together?

Where did the universe come from?

What is the world made of?What holds the world together?

Where did the universe come from?

Particle Model of MatterParticle Model of Matter

Normal Matter : ParticlesNormal Matter : ParticlesBouncing Around!Bouncing Around!

Understand the particulate nature of matter

How big(small) is an atom, anyways?How big(small) is an atom, anyways?


1 or 2 x 10-10 m = 1 or 2Å (Angstrom) in radius


1 or 2 x 10-10 m = 1 to 2Å (Angstrom) in radius

QuickTime™ and a decompressor

are needed to see this picture.QuickTime™ and a

decompressorare needed to see this picture.

Normal Matter : ParticlesNormal Matter : ParticlesBouncing Around!Bouncing Around!

Model Bonded Atoms Model Bonded Atoms as Masses on Springas Masses on Spring~ two atomic size particles interacting via“pair-wise potential”

Richard P. Feynman... I believe it is the atomic hypothesis... that all things are made of atoms--little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another...

If all scientific information were to be lost, these wouldbe the most valuable ideas to pass on to future generations.

R.P. Feynman, Physics Nobel Laureate in 1965R.P. Feynman, Physics Nobel Laureate in 1965

r

PE

Distance between the atoms

Repulsive: Atoms push apart as they get too close

““pair-wise potential” a.k.a. Lennard-Jones Potentialpair-wise potential” a.k.a. Lennard-Jones Potential

Flattening: atoms have negligible forces at large separation.

Displacement from equilibrium y[+][-]

PEmass-spring


PEmass-spring

Question: If the mass is displaced upwards, the following is true:a)The dot moves up and to the right, and the force vector points to the left.b)The dot moves up and to the right, and the force vector points to the right.c)The dot moves up and to the left, and the force vector points to the right.d)None of the above.


direction of force

y

PEmass-spring


direction of force

PEmass-spring


PEmass-spring

On this side force pushes up

On this side force pushes down

Equilibrium

Forces from potentials point in direction

that (locally) lowers PE


PEmass-spring

Equilibrium

Potential Energy curve of a spring:

PE = (1/2) k (x)2

W (work) = PE =F||x

Force = -PE / x = - k x


PEmass-spring

Equilibrium

~Force

Potential Energy curve of a spring:

PE = (1/2) k (x)2 W (work) = PE =F||xForce = -PE / x = - k x

•Force is always in direction that decreases PE• Force is related to the slope -- NOT the value of PE• The steeper the PE vs r graph, the larger the force |F|=|d(PE)/dr|

r

PE

Distance between the atoms

Repulsive: Atoms push apart as they get too close

““pair-wise potential” a.k.a. Lennard-Jones Potentialpair-wise potential” a.k.a. Lennard-Jones Potential

Flattening: atoms have negligible forces at large separation.

PE

KE

Etot

Separation (x10-10 m)

Ene

rgy

(x10

-21 J

)

Example H2O

Particle Model of EParticle Model of Ebondbond

Particle Model of EParticle Model of Ethermalthermal

What is Ebond in terms of KE and PE of individual atom (atom pair)? What is Ethermal in terms of KE and PE of individual atom (atom pair)?

• Ebond for a substance is the amount of energy required to break apart “all” the bondsi.e. we define Ebond = 0 when all the atoms are separated

• 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 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

A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is Etot greater?

a) Situation A has a greater Etot

b) Situation B has a greater Etot

c) Both have the same Etot

d) Impossible to tell

A

B


a) Situation A has a greater Etot

A

B


b) Situation B has a greater Etot

A

B

A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is Ethermal greater?

a) Situation A has a greater Ethermal

b) Situation B has a greater Ethermal

c) Both have the same Ethermal


A

B

A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is Ethermal greater?

a) Situation A has a greater Ethermal

b) Situation B has a greater Ethermal

c) Both have the same Ethermal


A

B

KE

KE

Okay. Now let us look at the same problem from the perspective of the KE and PE of individual atoms.

initial

final


Ethermal is the energy associated with the random microscopic motions and vibrations of the particles.



• We increased Ethermal by putting more energy into the system




• KE and PE keep changing into one another as the atoms vibrate, so we cannot make meaningful statements about instantaneous KE and PE





• We can make statements about average KE and PE.





• We can make statements about average KE and PE.

• Increasing Ethermal increases BOTH KEaverage and PEaverage

Particle Model of EParticle Model of Ethermalthermal and E and Ebondbond

The energy associated with the random motion of particles

is split between PEoscillation and KE .

Mass on Spring

QuickTime™ and aH.264 decompressor

are needed to see this picture.

Energy

position

As we increase Etot we increase PEave and KEave

PEave = KEave = Etot/2

Etot

PEKE



is split between PEoscillation and KE .



is split between PEoscillation and KE . • For particles in liquids and solids, let’s not forget the part

of PE hat correspond to Ebond of the system.

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





• Ebond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors.• For solids and liquids,

KEall atoms = (1/2)Ethermal

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

=> KEall atoms + PEall atoms = Ethermal + Ebond





• Ebond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors.• For solids and liquids,

KEall atoms = (1/2)Ethermal

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

=> KEall atoms + PEall atoms = Ethermal + Ebond

• In the gas phase, there are no springs, so there is no PEoscillation or

PEbond

• If the atoms do not move too far, the forces between them can be modeled as if there were springs between the atoms.

• Each particle in a solid or liquid oscillates in 3 dimensions about its equilibrium positions as determined by its single-particle potential.

Intro to Equipartition of Energy Intro to Equipartition of Energy

• Another way of saying is, each particle has six “ways” to store the energy associated with its random thermal motion.

• We call this “way” for a system to have thermal energy as a “mode”.

Intro to Equipartition of Energy Intro to Equipartition of Energy

Closed Book

Don’t forget to fill in your DL

section number!

!!THIS QUIZ IS TWO-SIDED!!

due to monday holiday (presidents day 2/18), 2/14 thursday dl section (1,3,4) cancelled. (dl section...

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