Announcements 2/2/11
Exam review session (tentative): Friday, 3-4:30 pm
a. I will send email tomorrow with final date/time, and
room location. (Vote today if you haven’t yet!)

Reading assignment for Friday:
a. Section 22.8 – Especially the marble example (Ex.
22.7, in my edition), but not 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.

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 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
Time for some physics humor

Xkcd comic:

Thermodynamics song:
a.
http://www.uky.edu/~holler/CHE107/media/first_second_law.mp3
Second Law



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

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


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 Friday
A New State Variable

State variables we know: P, V, T, Eint
P
B
A
V
B

Observation:

A

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

Path 1: ACB
Path 2: ADB
(DB = isothermal)

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 Friday I’ll (try to)
explain how/why this quantity is
related to microstates & macrostates
A



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 “free expansion”
before
after
What is V2? T2? P2?
How to find S?


S for adiabatic?


Adiabats as constant entropy contours
(“isentropic” changes)
Wait… isn’t “free expansion” an adiabatic
process?
S for isothermal?
S for const. volume?
S for const. pressure?
S of Universe

S of gas doesn’t depend on path (state variable):
B
S AB
P
B
A

dQ

T
A
Spath1  Spath 2
V


What about S of surroundings?
What about Stotal = Sgas + Ssurroundings?
(See HW problem 12-4)