Physics 7A – Lecture 5 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg Prof. Robin D. Erbacher 343 Phy/Geo Bldg

AnnouncementsAnnouncements Next Monday is a HOLIDAY. No lecture. DLs canceled M-W. Check calendar for specifics. Quiz 3 is today, focusing on material from DLMs 5-9. Join this Class Session with your PRS clicker! My office hours moved: 10-11:30 am Tuesdays. Check Physics 7 website frequently for updates. Turn off cell phones and pagers during lecture.

Three New Energy Systems

Examples: Mechanical Phenomena E movement (KE) Egravit y E sprin g Rear shock absorber and spring of BMW R75/5 Motorcycle

Energy Conservation E therma l E bond E movement (KE) E gravit y E electri c E sprin g We’ve now learned about five different types of energy systems we can use in our conservation equations and Energy Interaction Diagrams. Steam engine E nuclea r Nuclear power plant There are many different forms of energy (energy systems):     

Graphing Energies What are the x-axis, y axis? Units? x axis (independent variable: height) y axis (dependent variable: PE grav ) Which quantity (energy) is the easiest to graph? E tot ? PE grav ? What about KE? Where should the origin (0) be placed? Where does it most make sense? Should the floor be 0m?

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring Clicker: 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.

Potential Energy v. Displacement Displacement from equilibrium y[+][-] direction of force yy PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] direction of force PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring On this side force pushes up On this side force pushes down Equilibrium Forces from potentials point in direction that (locally) lowers PE

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring Equilibrium Potential Energy curve of a spring:  PE = ½ k (  x) 2 W (work) =  PE = -F ║  x Force = -  PE /  x = - k x Putting work into the system increases the energy. Here, work is force through a distance

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring Equilibrium Potential Energy curve of a spring:  PE = ½ k (  x) 2 W (work) =  PE = -F ║  x Force ≈ -  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 ~Force

What Does This Have to Do With the Real World? Why does it take more energy to vaporize than to melt? What is Ebond? We will model real atoms of liquids and solids as oscillating masses and springs Particle Model of Matter Three-phase model of matter Energy-interaction model Mass-spring oscillator Particle model of matter  Particle model of bond energy  Particle model of thermal energy Thermodynamics Ideal gas model Statistical model of thermodynamics r

Particle Model of Matter

Of What is the World Made? What is the world made of? What holds the world together? Where did the universe come from?

The Atomic Hypothesis 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 would be the most valuable ideas to pass on to future generations. R.P. Feynman, Physics Nobel Laureate in 1965

Normal Matter: Particles Bouncing Around! Fermilab Bubble Chamber Photo Atoms in DNA Subatomic particles

Particle Model of Matter We will model real atoms of liquids and solids as oscillating masses and springs. r Goal : To understand macroscopic phenomena (e.g. melting, vaporizing) and macrocopic properties of matter such as phases, temperature, heat capacities, in terms of microscopic constituents and its behavior.

Model: Bonded Atoms as Masses on Springs Atom 1 (anchored) Atom 2 (bonded) ~ two atomic size particles interacting via “pair- wise potential” a.k.a. Lennard-Jones Potential

Microscopic Picture of Matter Particle: atomic sized object. Attractive forces, Repulsive forces…obvious, but need specifics. (bowl and ball) Center-to-center: here is ‘r’, not surface to surface. (studs) Equilibrium: same as spring, pendulum, ball-in-bowl… Pair-wise Potential Energy: between 2 particles (see above). Single Particle Potential Energy: sum from all interactions with neighbors.

Potential Energy Between Two Atoms “pair-wise potential” a.k.a. Lennard-Jones Potential separation r Distance between the atoms (r) (units of  – atomic diameter) Equilibrium separation r o Potential Energy

Equilibrium Separation r o (mass-spring oscillator analogy) Displacement from equilibrium y[+][-] PE mass-spring

Potential Energy Between Two Atoms separation r Distance between the atoms (r) (units of  – atomic diameter) Equilibrium separation: r o The force the two particles exert on each other is zero. If the particles move from this separation, larger or smaller, The force pushes/pulls them back. Equilibrium separation r o Potential Energy

“Pairwise” Atom-Atom Potential a.k.a Leonard-Jones Potential separation What happens as the separation between atoms increases from equilibrium ? r Distance between the atoms, r Equilibrium separation r o Potential Energy

Slope of PE Curve: Force |F|=|d(PE)/dr| (mass-spring oscillator analogy) Displacement from equilibrium y[+][-] PE mass-spring direction of force

“Pairwise” Atom-Atom Potential a.k.a Leonard-Jones Potential separation r Distance between the atoms, r Equilibrium separation r o Potential Energy As the atom-atom separation increases from equilibrium, force from the potential increases. ~ attracting each other when they area little distance apart

“Pairwise” Atom-Atom Potential a.k.a Leonard-Jones Potential separation Flattening: atoms have negligible forces at large separation. r Distance between the atoms, r Repulsive: Atoms push apart as they get too close. Equilibrium separation r o Potential Energy

Total Energy = PE + KE E tot 10 Separation ( m) Energy ( J)

Separation ( m) Energy ( J) E tot

Separation ( m) Energy ( J) E tot

PE KE E tot Separation ( m) Energy ( J)

This is what is meant by a “bond” - the particles cannot escape from one another

Atom-Atom Potential separation r Distance between the atoms, r The bond is an abstraction: Atoms that don’t have enough energy cannot escape the potential (force), so we treat them as bound until we add enough energy to free them. Total energy between atoms Potential Energy E total

The bond is an abstraction: Atoms that don’t have enough energy cannot escape the potential (force), so we treat them as bound until we add enough energy to free them.

Clicker: What is “breaking a bond”? If a bond is “broken” in an atom-atom potential, which of the following must be true: A. E tot  0 B. E tot  0 C. PE  0 D. PE  0 E. KE  0  

r Energy ( J) Distance between the atoms, r E tot When E tot ≥ 0, What is true about KE at very large r? Clicker:Pair-wise potential a)KE < PE b)KE = PE c)KE ≈ E tot

Pair-wise Potential Energy  roro * ‘Not to scale’ Can you see the forces and energy systems?  = atomic radius r o = equilibrium separation

Energy r (atomic diameters) r   is the atomic diameter roro   is the well depth r o is the equilibrium separation  pair-wise  ~ J  ~ m = 1Å Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential

 roro Atoms bound together? Bonds Formed? Squeezing? Bonds breaking?

Phases Under the Microscope (ahhh…now things are starting to tie together!) 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.

Molecular Model If the atoms in the molecule do not move too far, the forces between them can be modeled as if there were springs between the atoms. The potential energy acts similar to that of a simple oscillator.

Slightly Different Situation… How is this situation different? Double ‘k’. Same equilibrium. Else same…

Consider three atoms arranged as shown. What is the potential seen by the center atom? (Hint: what is the potential for each of the bonds separately? Now combine them.) Hint: what is r value of the equilibrium position? How can you extend this linear model to 3-dimensions? What will the potential look like? Three Interacting Particles: Activity LCR “-” r “+”

Three Interacting Particles Center atom potential (from left atom)

Three Interacting Particles Center atom potential (from right atom)

Three Interacting Particles Center atom potential (from both atoms)

Multiple Atom System E bond for a substance is the amount of energy required to break apart “all” the bonds i.e. we define E bond = 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. E bond = ∑ all pairs (PE pair-wise )

Next Time: More on Molecular Models, and Macroscopic Properties