PY 410, Statistical and Thermal Physics, Spring 2012

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

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.

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. 16th) problems from Reif: 2.1, 2.2, 2.4, 2.8, 2.10  Solutions

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

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

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

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

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

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

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