PY 410, Statistical and Thermal Physics, Spring 2012

 

Syllabus

Lecture1

Lecture2

Lecture3

Homework 1 (Due Feb. 2nd), problems from Reif: 1.1; 1.4 (analyze the answer at large N), 1.5, 1.9, 1.10, 1.12, 1.14

Additional Problem.* A person throws dice N times. Find the probability distribution of the maximum score for different N. Write down your results explicitly in a table for N=1,2,3 (use decimal numbers not fractions). Discuss the asymptotical form of this distribution when N is large. Solutions

Lecture4

Homework 2 (Due Feb 9th), problems from Reif: 1.16, 1.17, 1.18, 1.23, 1.26*, 1.28* Solutions

M&M problem. This problem consists of three parts

1. Each of you will get a Pack of M&M mini. Each pack contains candies of six colors: Blue (Bl), Brown (Br), Green (G), Orange (O), Red (R) and Yellow (Y). You will need to count number of candies of each color and send the data to a designated person. The sample data you need to send should look like this
Bl27
Br – 23

G – 18
O – 25
R – 31

Y – 34

Please send the data by Thu, Feb. 2nd. Please do not invent the data; it is important that you do actual counting.

2. Now you can eat your candies, discard them, or share with your friends.

3. After all data is collected you will get back a table containing the results from the whole group. Each of you need to independently perform the statistical analysis of the data and answer the following questions.

      Estimate the variance and the mean for the number of candies of each color. Are these results consistent with the Poisson distribution?

      Estimate the variance of the sum of B-candies (i.e. blue + brown). Is it approximately equal to the sum of variances? Are the blue and brown colors statistically independent?

      Estimate the variance of the total number of candies (i.e. blue + brown + green + orange + red + yellow). Are all colors statistically independent? Explain your result.

      Plot the distribution function (in mathematica, excel, or any other software) for all colors (or all colors except red) from all students, i.e. the horizontal axis should be the number of candies and the vertical axis is the normalized frequency of occurrence of this number. The total number of data points should be 6 x number of analyzed packs. Fit this distribution to the Poisson distribution and Gaussian distribution. Which if the distributions work better? Argue why.

 

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

Q

Total

Blue

43

26

27

24

25

27

32

35

31

27

38

27

25

27

31

24

32

29

530

Blue

Brown

28

38

30

42

30

29

36

30

31

34

27

39

40

34

36

32

36

36

608

Brown

Green

22

30

33

27

35

25

30

28

33

26

30

20

30

33

31

27

34

29

523

Green

Orange

33

19

36

38

32

30

18

30

28

40

32

37

27

37

26

29

35

28

555

Orange

Red

43

46

41

39

41

54

47

34

35

41

45

36

47

41

34

45

42

47

758

Red

Yellow

33

39

33

31

36

36

31

42

39

32

27

41

33

23

40

28

21

30

595

Yellow

Total

202

198

200

201

199

201

194

199

197

200

199

200

202

195

198

185

200

199

3569

Total (all colors)

note: 12/18 packs have red as max.!

 

 

Lecture5

Lecture6

 

Homework 3 (due Feb. 16th) problems from Reif: 2.1, 2.2, 2.4, 2.8, 2.10 Solutions

 

Lecture7

Lecture8

 

Homework 4 (due Feb. 23rd) problems from Reif: 3.1, 3.3, 3.4; Problem 4* Solutions

Lecture9

Lecture10

 

Homework 5 (due Mar 1st) problems from Reif: 2.11, 3.5, 3.6 Solutions

 

Lecture11

Lecture12

 

Homework 6 (Due March 22nd) – problem 1 on page 5, problem 4 on page 6, and problem 3 on page 7 in the notes (lecture 11), Solutions Problems from Reif: 4.1, 4.2, 5.1, 5.2, 5.3, 5.4. Solutions

 

Lecture13

Lecture14

 

Homework 7 (Due March 29th) Reif : 5.5, 5.7, 5.8, 5.9. Prove that the Carnot engine realizes the heat engine with maximum efficiency. Solutions

 

Lecture15

Lecture16

 

Homework 8 (Due April 5th) Reif: 6.1, 6.2, 6,3, 6.4, 6.5, 6.7 Solutions

 

Lecture17

Lecture18

 

Homework 9 (Due April 12th) Reif 6.8, 6.10, 6.11, 6.12, 6.13*, 6.14* Solutions

 

Lecture19

Lecture20

 

Homework 10 (Due April 26th) Reif: 9.1, 9.2, 9.5, 9.7, 9.9., 9.12

Additional * - level problem. Magnetic cooling

 

Lecture21

Lecture22