1. Physics 176: Lecture 2 Tuesday, 1/18/2011 Before you take your seat: Pick up PRS transmitter Pick up 1-min questionnaire

2. Please Ask Questions! PLEASE feel free to ask questions during lecture but please also be patient if I feel it would be best to discuss your question with you after lecture, so as not to break the flow of the lecture.

3. Another Demo: A Supersaturated Medium ● Medical gel packs: phase transition of a supercooled material ● Why do you have to click the disk to initiate?

4. Phase Transitions: Metaphor For How Complexity Arises

5. Interesting Transitions to Think About: ● Origin of life: inert chemical soup to something else. Likely or not? ● Cells combining to form animals and plants. ● Neurons combining to form brains, is consciousness a phase transition? ● Computers combining to form networks.

6. Why Thermal Physics Is So Interesting ● Emergence versus reduction: why is the world so interesting? ● Subject involves different approach than mechanics, electrodynamics and quantum: develop insights through conceptual models rather than finding solutions to fundamental equations.

7. State The State of a Physical System ● One of the most important concepts in science: set of numbers that is sufficient and necessary to predict all known properties using sets of equations. ● State of a system is hard to determine, e.g., photon state was discovered in steps: direction, energy (color), polarization. ● Mechanics: state of N point particles is 6N numbers, position vector and velocity vector for each particle at given time. ● E&M: state of is knowledge of E and B fields everywhere at given time, infinite amount of info. ● QM: state is a unit vector, typically specified by passing particles through various filters.

8. Need to Know State Explains Why Star Trek Teleportation is in Trouble

9. Equilibrium Leads to Great Conceptual Simplification for Macroscopic Objects ● In classical mechanics, have to specify position and velocity vectors for each particle, doom for Avogadro's number of particles 10 23. (Current computers simulate 10 8 particles.) ● For quantum mechanics, have to specify wave function  (t,x 1,x 2,...) for all particles at given time, doom again. ● For E&M, have to specify E and B fields at all points in space at given time, doom again if many charges and currents. have to specify just two variables such as T and P ● But for macroscopic systems in equilibrium, have to specify just two variables such as T and P. Crazy paradox: how can things simplify so much with so many particles? ● In classical mechanics, have to specify position and velocity vectors for each particle, doom for Avogadro's number of particles 10 23. (Current computers simulate 10 8 particles.) ● For E&M, have to specify E and B fields at all points in space at given time, doom again if many charges and currents. ● For quantum mechanics, have to specify wave function  (t,x 1,x 2,...) for 10 23 particles at given time, doom again. have to specify just three variables such as T, V, and P ● But for a macroscopic system in equilibrium, have to specify just three variables such as T, V, and P. Crazy: how can things simplify so much with so many particles?

10. Why So Few Numbers for Equilibrium? ● It is a subtle consequence of conservation laws and statistical averaging. ● It is not obvious why this reduction occurs, e.g., fails for glasses and granular media. (Hand out granular flow demos)

11. Practical Criteria For Thermodynamic Equilibrium ● Consists of many components ● Temperature constant in time and space. ● Pressure constant unless external field present. ● Properties time independent up to rigid translation and rotation (no relative motion) ● Properties independent of history of system, this can be hard to achieve. NOTE: Most systems in universe are nonequilibrium! ● Consists of many components (macroscopic) ● Temperature constant in time and space. ● Pressure constant unless external field present. ● No relative motion: properties time independent up to rigid translation and rotation ● Properties independent of history of system (this can be hard to achieve). NOTE: Most systems in universe are nonequilibrium!

12. Short Question: Example of Time-Independent Nonequilibrium System?

13. Nonequilibrium Systems are Hard! Spiral Defect Chaos State of Convecting Fluid

14. Where we are heading? ● Chapter 1: concepts of equilibrium, relaxation time, temperature, ideal gas, work, heat, and heat capacity. First law of thermodynamics. (Mainly review.) ● Chapter 2: microstates of a macrostate, multiplicity W, entropy S, why entropy spontaneously increases, why equilibrium corresponds to maximum entropy (2 nd law). Three models: paramagnet, Einstein solid, ideal gas. ● Chapter 3: 1/T = dS/dE, chemical potential, applications to heat capacities. ● Jump to Chapters 6 and 7 to do some statistical physics then return to Chapters 4 and 5.

15. Time Scale to Attain Equilibrium Scales with Size L of System Time scales to equilibrate over region of size L: More subtle time scales: quantum tunneling means all solids act like liquids over long times (100 times age of universe), protons eventually decay, etc. Let's be reasonable here...

16. PRS: Can One Boil Water With Boiling Water? Plastic cup of water is suspended in middle of pot of boiling water. Then after a while: (a) Tcup > 100 o C and water boils (b) Tcup = 100 o C and water boils (c) Tcup = 100 o C and water doesn't boil (d) Tcup < 100 o C and water doesn't boil.