Lecture # 5

Cassandra PaulPhysics 7A

Summer Session II 2008

• Quickly discuss ‘the race’• Ideal gases• What is Lennard-Jones/Pair-wise potential?• Particle Model of Bond Energy

The ‘Race’ Explained….

M1M1

m1m1

Case 1

Case 2M2

m2

+d

-d

KEtransSpeed

PEgravityHeight

KEtransSpeed

PEgravityHeight

½ M1 (vf2-0) +M1g(hf-0)+ ½ m1 (vf

2-0) +m1g(hf-0)=0

½ M1 vf2 +M1g(-d)+ ½ m1vf

2 + m1g(d)=0

(M1+m1)½vf2 + (m1-M1)gd =0

Combining PE and KE terms

PE’s are the same for both systems (mass difference is the same)

So KE’s must be the same for both systems

But… M+m is bigger for case 1, therefore: vf must be smaller to make up for it!

M1 M2 m2m1

Ideal Gas

• In Intro Chemistry we always dealt with ‘Ideal’ gasses. What does that actually mean?

• Ideal gases:– Have no intermolecular forces– Have perfectly elastic collisions with each other

(and the sides of containers)

Like Billiards or Jezzball

What was the point of the N2 Activity?

• What did we calculate?• Spacing of atoms is about 10σ.• At what point of the pair-wise potential do

atoms/molecules have zero PE and Zero force?• 3σ!• What do we take away from this?• The ideal gas approximation is useful for gases!

Intro Particle Model of Matter

A graphical representation of the energies associated with particles

Lennard-Jones (pair-wise) potential

We know the shape… but what exactly is this a graph of?

A. The potential energy of one atom with respect to a system of particles.

B. The potential energy of a system (many particles)C. The potential energy of one particle with respect

to another particleD. The total energy of one particle with respect to a

system of atomsE. The total energy of one atom with respect to

another

Remember the Anchor

But Cassandra when is one particle ever ‘anchored’ in space?

But Cassandra when is one particle ever ‘anchored’ in space?

Good question! It’snot, but our graphis always drawn with respect to oneparticle at the origin,even if the origin is moving

Energy

r (atomic diameters)

r

is the atomic diameter

ro

is the well depth ro is the equilibrium separation

Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential

pair-wise

~ 10-21 J

~ 10-10m = 1Å

Do not need to memorize

Forces and the Potential

Repulsive Attractive

Force = -d(PE)/dx

Or, negative change in y over change in x

Force has a magnitude of slope,and the direction ofdecreasing PE!

If the curve only tells us about PE, how do we find KE and Etot?

Let’s do a closed system…

Etot

Etot = KE + PE

-3ε = KE + -3ε

-3ε = KE + -4ε

KE = 0

KE = 1ε

-3ε = KE + -7ε KE = 4ε

-3ε = KE + -8ε KE = 5ε

-3ε = KE + -7ε KE = 4ε

-3ε = KE + -4ε KE = 1ε

-3ε = KE + -1ε KE = -1ε

KE can’t be negative!!!!!

Etot

Turning Points

Where the Etot intersects thePE curve, there are ‘turning Points.’

The particle oscilates between These two points.

How much work does it take to move one particle from rest at equilibrium (1.12σ), to 3σ

with a minute (negligible but non zero) velocity?

A. 1εB. 3εC. -1εD. 2.88σE. Impossible

to tell

i f

Same idea as before:

Initial: at 1.12σ, v=0PE + KE = Etot-1ε + 0 = -1ε• Now what?Is this a closed system?NO! Adding energy:Final: at 3σ, v~0• So new Etot = 0Must add 1ε to get there.

OK let’s draw an Energy System Diagram:

PEpair-wise

System: Two Particles, one bondInitial: v=0, r=1.12σFinal: v~0 r=3σ

Wait! We don’t have an equation for PE pair-wise!

It’s ok, we have something better… a graph!

Work

ΔPE = Work

PEf – PEi = Work

0ε – (-1ε) = Work Work = 1ε

EnergyAdded

i

f

DL sections

• Swapno: 11:00AM Everson Section 1• Amandeep: 11:00AM Roesller Section 2• Yi: 1:40PM Everson Section 3• Chun-Yen: 1:40PM Roesller Section 4