Announcements 9/26/11
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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
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Which of the following is a version of the Second Law of
Thermodynamics?
a. The entropy of any system decreases in all real processes
b. The entropy of any system increases in all real processes
c. The entropy of the Universe decreases in all real processes
d. The entropy of the Universe increases in all real processes
Second Law
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Clausius: Heat spontaneously flows from hot to
cold, not the other way around
Why? Order.
Which hand is more likely?
p.413a
Microstates vs Macrostates
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Hand on left
a. microstate = A spades, K spd, Q spd, J spd, 10 spd
b. macrostate = ?
c. How many microstates make up that macrostate?
Hand on right
a. microstate = 2 spades, 3 diam, 7 heart, 8 clubs, Q diam
b. macrostate = ?
c. How many microstates make up that macrostate?
The most common macrostates are those that…
p.413a
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Probability  Heat flow
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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
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For the air in this room, right now:
a. Microstate = ?
(Just called the “state”)
b. Macrostate = ?
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.
Hold this thought until next time
A New State Variable
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State variables we know: P, V, T, Eint
P
B
A
V
B
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Observation:

A
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dQ
doesn’t depend on path
T
 Something is a state variable!
Assumption: path is well defined, T exists whole time
 “Internally reversible”
P
2P1
P1
“Proof” by example, monatomic gas
C
B

A
V1 2V1

D
V
4V1
Path 1: AC + CB
C
Path 2: AD + DB
C

nCV dT
dQ

 nCV ln TC TA   nCV ln 2
T
T

nCP dT
dQ

 nCP ln TB TC   nCP ln 2
T
T
A
B
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Path 1: ACB
Path 2: ADB
(DB = isothermal)
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C
D

A
B

C
D

dQ

T

workon  nRT ln VB VD 
dQ 1
Q

dQ   

  nR ln 2
T
T
T
T
T
A
B
D

A
nCP dT
 nCP ln TD TA   nCP ln 4
T
B

D
Equal?
Entropy: S
B
S AB

dQ

T
Advertisement: On Wed I will explain
how/why this quantity is related to
microstates & macrostates
A
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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!
S for isothermal?
S for const. volume?
S for const. pressure?
S for “free expansion”
before
after
What is V2? T2? P2?
How to find S?
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S for adiabatic?
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Adiabats = constant entropy contours
(“isentropic” changes)
Wait… isn’t “free expansion” an adiabatic
process?
S of Universe
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S of gas doesn’t depend on path (state variable):
B
S AB
P
B
A

dQ

T
A
Spath1  Spath 2
V
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What about S of surroundings?
What about Stotal = Sgas + Ssurroundings?
(See HW problem 12-4)
Thermodynamics Song
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http://www.uky.edu/~holler/CHE107/media/first_
second_law.mp3
(takes 4:13)