Announcements 9/26/11 Exam review session: Friday, 4 pm, room C460 Reading assignment for Wednesday:

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. 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. The entropy of any system decreases in all real

processesb. The entropy of any system increases in all real

processesc. The entropy of the Universe decreases in all real

processesd. 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 lefta. microstate = A spades, K spd, Q spd, J spd, 10 spdb. macrostate = ?c. How many microstates make up that macrostate?

Hand on righta. microstate = 2 spades, 3 diam, 7 heart, 8 clubs, Q

diamb. macrostate = ?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. Microstate = ?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, Eint

Observation: doesn’t depend on path

Something is a state variable! Assumption: path is well defined, T exists whole time

“Internally reversible”

AB

P

V

B

A

dQ

T

“Proof” by example, monatomic gas Path 1: ACB Path 2: ADB

(DB = isothermal)

ln ln 2

ln ln 2

ln ln 4

ln1ln 2

C CV

V C A V

A A

B BP

P B C P

C C

D DP

P D A P

A A

B BB Don

D D

nC dTdQnC T T nC

T T

nC dTdQnC T T nC

T T

nC dTdQnC T T nC

T T

nRT V VworkdQ QdQ nR

T T T T T

A

BP

V

C

D

V1 2V1 4V1

P1

2P1

Path 1: AC + CB

Path 2: AD + DB

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!

B

AB

A

dQS

T

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 V2? T2? P2? How to find S?

S for adiabatic?

Adiabats = constant entropy contours (“isentropic” changes)

Wait… isn’t “free expansion” an adiabatic process?

before after

S of Universe S of gas doesn’t depend on path (state

variable):

What about S of surroundings? What about Stotal = Sgas + Ssurroundings?

AB

P

V

path1 path 2

B

AB

A

dQS

T

S S

(See HW problem 12-4)

Thermodynamics Song http://www.uky.edu/~holler/CHE107/media/f

irst_second_law.mp3(takes 4:13)