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Lecture # 5

Lecture # 5. Cassandra Paul Physics 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…. Case 1. M 1. M 2. m 1. m 2. KE trans. PE gravity. KE trans. PE gravity. Speed.

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Lecture # 5

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  1. Lecture # 5 Cassandra Paul Physics 7A Summer Session II 2008

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

  3. The ‘Race’ Explained….

  4. Case 1 M1 M2 m1 m2 KEtrans PEgravity KEtrans PEgravity Speed Speed Height Height m1 +d ½ M1 (vf2-0) +M1g(hf-0)+ ½ m1 (vf2-0) + m1g(hf-0)=0 M1 -d ½ M1 vf2 +M1g(-d)+ ½ m1vf2 + m1g(d)=0 Combining PE and KE terms (M1+m1)½vf2 + (m1-M1)gd =0 PE’s are the same for both systems (mass difference is the same) m2 So KE’s must be the same for both systems M2 But… M+m is bigger for case 1, therefore: vf must be smaller to make up for it! Case 2

  5. 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)

  6. Like Billiards or Jezzball

  7. 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!

  8. Intro Particle Model of Matter A graphical representation of the energies associated with particles

  9. Lennard-Jones (pair-wise) potential

  10. We know the shape… but what exactly is this a graph of? • The potential energy of one atom with respect to a system of particles. • The potential energy of a system (many particles) • The potential energy of one particle with respect to another particle • The total energy of one particle with respect to a system of atoms • The total energy of one atom with respect to another

  11. Remember the Anchor But Cassandra when is one particle ever ‘anchored’ in space? Good question! It’s not, but our graph is always drawn with respect to one particle at the origin, even if the origin is moving

  12. Potential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential Energy r ro  ~ 10-10m = 1Å   r (atomic diameters)  Do not need to memorize   ~ 10-21 J pair-wise  is the atomic diameter  is the well depth ro is the equilibrium separation

  13. Forces and the Potential Force = -d(PE)/dx Repulsive Attractive Or, negative change in y over change in x Force has a magnitude of slope, and the direction of decreasing PE!

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

  15. Let’s do a closed system…

  16. Etot = KE + PE KE = 0 -3ε = KE + -3ε -3ε = KE + -4ε KE = 1ε -3ε = KE + -7ε KE = 4ε KE = 5ε -3ε = KE + -8ε KE = 4ε -3ε = KE + -7ε -3ε = KE + -4ε KE = 1ε Etot -3ε = KE + -1ε KE = -1ε KE can’t be negative!!!!!

  17. Turning Points Where the Etot intersects the PE curve, there are ‘turning Points.’ Etot The particle oscilates between These two points.

  18. 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? • 1ε • 3ε • -1ε • 2.88σ • Impossible to tell i f

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

  20. OK let’s draw an Energy System Diagram: System: Two Particles, one bond Initial: v=0, r=1.12σ Final: v~0 r=3σ Work PEpair-wise f ΔPE = Work Energy Added Wait! We don’t have an equation for PE pair-wise! It’s ok, we have something better… a graph! i PEf – PEi = Work 0ε – (-1ε) = Work Work = 1ε

  21. 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

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