PY 410, Statistical and Thermal
Physics, Spring 2012

Homework 1 (Due Feb. 2^{nd}),
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

Homework 2 (Due Feb 9^{th}),
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

Bl
– 27

Br – 23

G
– 18

O – 25

R – 31

Y
– 34

Please send the data by Thu, Feb. 2^{nd}.
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.! |

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

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

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

Homework 6 (Due March 22^{nd}**) – **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

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

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

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

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

Additional “*” -
level problem. Magnetic
cooling