Announcements 9/26/11 Exam review session: Friday, 4 pm, room C460 Reading assignment for Wednesday: a. a.Section 22.8 – Especially read the marble example (Ex. 22.7, in my edition), but don’t worry about the “Adiabatic Free Expansion: One Last Time” example (Ex. 22.8, in my edition). b. b.The “What is entropy?” handout posted to website – Read up through Example 1. Please spend at least ~10 minutes glancing over it, or you will likely be really confused in class on Friday. xkcd

Reading quiz Which of the following is a version of the Second Law of Thermodynamics? a. a.The entropy of any system decreases in all real processes b. b.The entropy of any system increases in all real processes c. c.The entropy of the Universe decreases in all real processes d. d.The entropy of the Universe increases in all real processes

Second Law Clausius: Heat spontaneously flows from hot to cold, not the other way around Why? Order. Which hand is more likely?

Microstates vs Macrostates Hand on left a. a.microstate = A spades, K spd, Q spd, J spd, 10 spd b. b.macrostate = ? c. c.How many microstates make up that macrostate? Hand on right a. a.microstate = 2 spades, 3 diam, 7 heart, 8 clubs, Q diam b. b.macrostate = ? c. c.How many microstates make up that macrostate? The most common macrostates are those that…

Probability  Heat flow You separate a deck into two halves: one is 70% red, 30% black; the other is 30% red, 70% black. What will happen if you randomly exchange cards between the two?

Thermodynamics For the air in this room, right now: a. a.Microstate = ? b. b.Macrostate = ? Hold this thought until next time The state the air is in will be “very close” to the one that has the most number of microstates. Next time: Entropy of a state  #Microstates in the state The state the air is in will be “very close” to the one with the highest entropy. (Just called the “state”)

A New State Variable State variables we know: P, V, T, E int Observation: doesn’t depend on path  Something is a state variable! Assumption: path is well defined, T exists whole time  “Internally reversible” A B P V

“Proof” by example, monatomic gas Path 1: A  C  B Path 2: A  D  B (D  B = isothermal) A B P V C D V1V1 2V 1 4V 1 P1P1 2P 1 Path 1: A  C + C  B Path 2: A  D + D  B Equal?

Entropy: S Assume S = 0 is defined somewhere. (That’s actually the Third Law, not mentioned in your textbook.) Integral only defined for internally reversible paths, but… S is a state variable! …so it doesn’t matter what path you use to calculate it! Advertisement: On Wed I will explain how/why this quantity is related to microstates & macrostates

 S for isothermal?  S for const. volume?  S for const. pressure?

 S for “free expansion” What is V 2 ? T 2 ? P 2 ? How to find  S?  S for adiabatic? Adiabats = constant entropy contours (“isentropic” changes) Wait… isn’t “free expansion” an adiabatic process? beforeafter

 S of Universe  S of gas doesn’t depend on path (state variable): What about  S of surroundings? What about  S total =  S gas +  S surroundings ? A B P V (See HW problem 12-4)

Thermodynamics Song second_law.mp3 second_law.mp3 (takes 4:13)