1. Quiz 8 (LAST QUIZ!) 8:30-8:50am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book Quiz 4 Re-evaluation Request Due this Thursday, 3/6. Quiz 5 Re-evaluation Request Due next Thursday, 3/13. 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. Next Week Last lecture March 11 Last lecture + Information on Final, Final review sessions, among other things…

2. PHYSICS 7A Final Exam March 18, Tuesday, 10:30am - 12:30pm Location TBA Bring pen/pencils, calculator, a photo ID to sit in the final No makeup Final PHYSICS 7A Final Review Sessions Every 7A instructors (lecturers + DL instructors) will hold a 1.5hours each session on March 15,16,17 (Sat through Mon) Location and schedule are available on the course website (click on “Review Sessions”). You can go to any session.

3. Enthalpy Is a state function: - U depends only on state of system - P depends only on state of system - V depends only on state of system => H depends only on state of system (Hess’s law) Who cares?!?!

4. initial final P V initialfinal P V W = 0 Constant volumeConstant pressure Note: nothing about gasses used - works for solids and liquids too! Enthalpy *Derivation in P.84

5. spontaneous changes occur with an increase in entropy. Laws of Thermodynamics Remember conservation of energy? (if there’s no change in ∆E mechanical), ∆ U First law of Thermodynamics Ever heard of entropy? Rudolf Clausius (1822-1888) Total entropy never decreases. the system always evolves toward equilibrium. Second law of Thermodynamics

6. Thermal equilibrium T final Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat Low tempHigh temp From everyday experience, we know that this process is irreversible and spontaneous…. but WHY???

7. Microstates So far we have described systems using P, V, T,..... Incomplete information about the system A microstate is a particular configuration of atoms/molecules in the system. For example, For a box of gas, you need to specify where all the atoms are i.e., position (x,y,z), and how fast they are moving i.e., velocity (v x, v y, v z ).

8. MicrostatesConstraintsStatesMicrostates Things we worry about: Constraints: States: Tell us which microstates are allowed. Examples The volume of a box constraints the possible positions of gas atoms. The energy of the box constraints the possible speeds of gas atoms. Groups of microstates that share some average properties,i.e. A collection of states that “look” the same macroscopically. Examples gasses: P ~ average density, V~volume filled, T~average KE

9. Microstates vs states Flipping a coin 3 times: Microstates: all possible combinations of coin flips Constraints: some combinations not possible (e.g. HHTHHH) MicrostatesStates States: total number of heads Hypothesis: every microstate is equally likely. is the one with the most microstates Hypothesis: every microstate is equally likely. The state that is most likely is the one with the most microstates Prob.

10. 10 atoms in a box Microstates vs states

11. 10 atoms in a box Microstates vs states

12. 10 atoms in a box Microstates vs states

13. “Ordered microstate” equally likely as a random microstate Are we likely to find the system in “ordered state” or “random state”?? …umm almost all the microstates look “random” Microstates vs states

14. 1024 microstates, each microstate equal width Define states by “total number of heads” Different states contain different # of microstates Therefore even though each microstate is equally likely, some states are more likely than others. 10 fair coin flips

15. We can also consider our physical system to be two “sub- systems”: * Sub-system A: the first two coin flips * Sub-system B: the final eight coin flips HH HT TH TT Any of the 256 micro. 10 fair coin flips

16. where k B is Boltzman’s constant If our system is composed of two sub-systems A and B: We can add the entropy of the subsystems to get the total entropy. Entropy

17. where k B is Boltzmann’s constant ln(Omega) is always increasing. As # microstates available increase, so does the entropy. Entropy

18. Why split our system into subsystems? Splitting 10 coin flips into the first 2 flips and the remaining 8 is perverse ice (0 0 C) Water (0 0 C) But calculating heat needed to raise temperature of this system to 10 0 C we would split into subsystems: the ice and the water

19. How to calculate entropy? We should divide our box up into “atom-sized” chuncks. But how big should our velocity microstates be? ice (0 0 C) Water (0 0 C) How can we get a definite answer for the number of microstates in this system? Relating entropy to microstates is useful for conceptually understanding what entropy is. At this level, it is not useful for calculating the change in entropy

20. For slow, reversible processes: initial final P VS T initial W > 0 when Delta V 0 Q > 0 when Delta S > 0 Q < 0 when Delta S < 0 How to calculate entropy? Answered

21. For slow, reversible processes: To get to entropy we can “turn this expression around” If temperature is constant, then we can easily integrate: This last equation is not generally true; as heat enters or leaves a system the temperature often changes. (isothermal only!) How to calculate entropy? Answered Q

22. If the process is not slow or reversible, or it is very difficult you can use the fact entropy is a state function If you can find any process from the initial to final state, you can use this path to calculate ∆ S for the process in question! (As in calculation of enthalpy in DLM14) How to calculate entropy? Answered 2

23. Summary

24. STO P SLO W Why do we care about entropy? That is our next topic..... the quest for equilibrium or, “how presidential elections differ from thermodynamics”

25. Lesson: some states are more likely than others. But once the coins are flipped we know what they are going to be. Our system does not evolve in time. Solids, liquids and gasses do not stay in the same microstate -- they change in time. 10 fair coin flips

26. e.g. First coin flip is T. So I have 49 H, 1T => state is 49 Second coin flip is H. Still have 49 H => state is 49 Third coin flip is T. Now state is 48 etc....... What does our state look like as a function of “time”? 10 fair coin flips 50

27. “Short” example (400 flips) with 50 coins “Long” example (1500 flips) with 50 coins

28. “Short” example (400 flips) with 100 coins “Long” example (1600 flips) with 100 coins

29. “Interactions” (i.e. coin flips) take a certain amount of time each. After many interactions, the systems settle down “close” to the most likely value. This is what is meant by equilibrium. The system may depart from equilibrium, but large departures are rare and typically don’t last very long. Equilibrium

30. Equilibrium is the most likely state Each microstate is equally likely, so the equilibrium state has the most microstates. Therefore the equilibrium state has the highest entropy. For large (i.e. moles of atoms) systems, the system is (essentially) always evolving toward equilibrium. Therefore the total entropy never decreases: What’s equilibrium to do with Entropy? Second law of Thermodynamics

31. This is only for total entropy! ice (0 0 C=273K) air (20 0 C) heat flows this way Heat entering ice: dQ ice = T ice dS ice > 0 =>S ice increasing Heat leaving air: dQ air = T air dS air S air decreasing This is okay, because dS tot = dS ice + dS air > 0

32. Running for president? Must be a natural born U.S. citizen (or be a U.S. citizen when the constitution was written) Must be at least 35 years old Must have been a resident of the U.S. for at least 14 years. Constraints: Total number of microstates = 150,000,000 Are all microstates equally likely? Why do we assume this is true for atoms?

33. Hillary Clinton Barack Obama Counter-examples to the “rich, white, Christian man” hypothesis

34. Are all microstates equally likely? Is each microstate equally likely for a gas/solid/liquid/...... ? Rolling a (fair) diceY Presidential electionsN Your seating position in this classN Rolling a weighted diceN