Transcript PowerPoint

Lectures 1 – Course Overview
Monday January 7th (start Ch. 1 on Wed. 9th)
•Organization of the course
•Course web page
•Breakdown of the grade
•Schedule of topics and exams
•Syllabus
•Overview of the course
•History
•Outline of topics
Reading:
All of chapter 1 (pages 1 - 23)
I will assign the 1st homework set on Wed.
The PHY4523 course web site
http://www.phys.ufl.edu/~hill/teaching/2008/4523/index.htm
•All information is posted here
•Syllabus, homework and exam policies, etc..
•Homework assignments (incl. deadlines) and solutions
•Course schedule with tentative exam dates
•Solutions to exams and practice tests
•A link to my PHY3513 course web page
•Weekly homework assignments: no excuse for NOT
getting 80-100% on these. The deadlines vary from
week to week. No late homework accepted.
•Homework assignments will be graded by a graduate
TA. However, all questions about grading should be
directed to the instructor (Hill).
•I will give short unannounced quizzes in roughly 30% of
the lectures. We will use the SRS (HiTT). Remotes will
be provided, but you are free to use your own also.
PHY4523 written exams
http://www.phys.ufl.edu/~hill/teaching/2005/3513/index.htm
In-class exams: there will be three of these (in NPB
1002), each lasting 50 minutes, and starting promptly at
11:45am. The tentative dates for these exams are:
You MUST take all 3 of these exams (see web site for
policy on make up exams, or come and talk to instructor).
Final: There will be a cumulative 2 hour final exam (in NPB
1002) during finals week. You MUST take this exam.
The best two scores out of the 3 in-class exams will be worth
a total of 34% (17% each) towards your final grade. The final
exam will be worth 34% towards your final grade.
About the text book
Introductory Statistical Mechanics, by R. Bowley and M. Sanchez
•If not available at the UF bookstore, try other bookstores
around Gainesville.
•We will cover only the first 10 chapters.
•If you still have the book by Ashley Carter, this can serve as
an excellent supplementary text.
•This is the first time I have used the book by Bowley and
Sanchez, so I cannot comment on accuracy of, e.g. solutions.
•Take some time to study the appendices at the end of the
book. In particular, Appendices C to E will be essential for this
course and homework problems may be assigned from this
material. You will also find useful integrals in Appendix B.
•Homework assignments mainly from end of chapter problem
sets. Numerical answers to ALL of the problems are given in
Appendix G, including written solutions to the odd-numbered
problems.
About the course and the instructor
•In terms of the concepts, the pace should be comfortable.
However, the level of mathematical sophistication is
substantially higher than in PHY3513.
•There is plenty of time for class discussion. PLEASE DON’T BE
SHY. Speak up!! Ask questions. This adds to the learning
experience and to the overall enjoyment of the lectures. Don’t
be afraid to ask me crazy questions. I am not afraid to admit
that I do not know the answer.
•Lectures typically include: PowerPoint slides with important
ideas (posted on-line); worked examples on the board (not
posted on-line); some demonstrations; discussion; and quizzes.
•Feel free to come to my office (NPB2263) or lab (NPB B158) at
any time to discuss anything related to the course. I will also
make every effort to be in my office during office hours.
•I have some travel during this semester, and will arrange well
qualified cover on these occasions.
PHY4523 grading
http://www.phys.ufl.edu/~hill/teaching/2008/4523/index.htm
• For those of you who have taken PHY3513 with me, note
that these percentages are a bit different; there is
slightly more emphasis on exams in this course.
• After the 2nd exam, I will be prepared to discuss your
performance with you individually, and what grade(s) you
may be tracking for.
• This is the first time that I have taught this course, so I
cannot predict what score will correspond to what grade.
However.......
An example of PHY4523 grading
PHY 3513 (Fall 2006)
Number of students
4
Mean 78%
Median 81%
3
B
C+
B+
A
2
D
PHY 3513, 2006:
15
A
(40%)
8
B+
(22%)
6
B
(16%)
5
C
(14%)
1
D
(3%)
Note 83% A/B+/B
1
0
50 55 60 65 70 75 80 85 90 95 100
Score (%)
PHY 3513, 2007:
11
A
(37%)
6
B+
(20%)
9
B
(30%)
3
C
(10%)
1
D
(3%)
Note 87% A/B+/B
DO THE HOMEWORK & COME TO CLASS
PHY 3513 (2005-2007)
~100 data points
100
• Clear correlation
between homework
and exam scores.
• Nevertheless, the
exams require
understanding, i.e.
you will not get away
with memorization of
homework problems.
Overall Grade
90
80
70
60
50
40
20
30
40
50
60
70
80
90
100
110
Score on Homework
•IF YOU ARE HERE ONLY FOR THE GRADE, THE
CHANCES ARE HIGH THAT YOU WILL DO POORLY.
Statistical Mechanics
An Overview
The early history: thermodynamics and statistical physics
The early history: thermodynamics and statistical physics
*
The dawn of quantum mechanics and quantum statistics
*
Heike Kamerlingh Onnes became the 1st physicist to liquify helium.
The dawn of quantum mechanics and quantum statistics
The dawn of quantum mechanics and quantum statistics
Statistical Mechanics
What will we cover?
A review of classical thermodynamics (1st 2 chapters)
•Temperature, 1st law, functions of state, etc
•Entropy and the 2nd law, irreversible processes
Probability and Statistics
PHY 3513 (Fall 2006)
Number of students
4
Mean 78%
Median 81%
3
B
C+
B+
A
2
D
1
0
50 55 60 65 70 75 80 85 90 95 100
Score (%)
Probability and Statistics
PHY2048 - Fall 2002
18
Mean 63±0.5
Sigma 27.5±1.5
Area 470±33
Number of students
16
14
458 students
12
10
8
6
4
2
00
0
20
40
60
Final score (%)
80
100
Probability and Statistics
PHY2048 - Fall 2002 (test 2)
Number of students
120
Mean 3.03±0.09
Sigma 3.41±0.32
Area 561±75
100
80
522 students
60
40
20
0
0
1
2
3
4
5
Score (out of 8)
Gaussian statistics:
  x  x 2 
1
f  x 
exp  

2
2 
 2

6
7
8
Probability and Entropy
Suppose you toss 4 coins. There are 16 (24)
possible outcomes. Each one is equally
probably, i.e. probability of each result is
1/16. Let W be the number of
configurations, i.e. 16 in this case, then:
1
p1  ;
W
Ptot   pi  W  p1  1
i
Boltzmann’s hypothesis concerning
entropy:
S  kB ln W
where kB = 1.38 × 1023 J/K is Boltzmann’s
constant.
The connection to thermodynamics
Maxwell-Boltzmann speed distribution function
 m 
f  v   4 

2

kT


3/ 2

v 2 exp mv 2 / 2kT

1/ 2
 2kT 
vm  

 m 
1/ 2
 8kT 
v 

 m 
1/ 2
vrms
 3kT 


m


Equation of state:
1
2
1 2 2
2
PV  Nmv   N  mv   N   NkT
3
3
2
 3
The bridge to thermodynamics through Z
Z   exp   E j / kT ; js represent different configurations
j
  1/ kT
Quantum statistics and identical particles
Indistinguishable events
Heisenberg
uncertainty
principle
The indistinguishability of identical particles has a profound effect on
statistics. Furthermore, there are two fundamentally different types of
particle in nature: bosons and fermions. The statistical rules for each
type of particle differ!
Applications
Specific heats:
Insulating solid
Diatomic molecular gas
Fermi and Bose gases