Syllabus

Physics 404

Introduction to Thermodynamics and Statistical Mechanics

Spring 2004

 

Meeting Time: Tues./Thurs. 12:30-1:45 P.M.

               Place: Room 1402, Physics

 

Instructor: J.R. Anderson; Office - Physics 2346

Office Phone - (301)-405-6142

 

Text:                Thermal Physics (1997 printing), by Charles Kittel and Herbert Kroemer

 

Supplementary Texts: Elements of Classical Thermodynamics by A.B.Pippard.

Heat and Thermodynamics  by M.W. Zemansky and H.R. Dittman

Statistical Physics by F. Reif

Thermal Physics by R. Baierlein

 

Grading:          Homework will count for about 30% of your grade.      Homework will be assigned approximately weekly and will be due at the beginning of class on days to be announced. You are responsible for knowing the homework assignments and due dates. Late homework will be accepted - with a  valid excuse.

There will be two hour exams, each of which will count for about 20% of the course grade.

The final exam will cover the entire course and will         account for about 30% of the course grade.

                        Absence from exams will be dealt with according to Standard University Policy.

 

Course Outline (Tentative): Chapters 1-10 and 12 of your text; any additional time will be devoted to special topics from the text, for example the Boltzmann transport equation or semiconductors.

 

Office Hours:  To be arranged later to fit with your schedules and mine. You are welcome to telephone or drop by anytime or to make an appointment.

 

Advice: "The statistical approach which the text uses depends upon your understanding a tightly-

reasoned sequence of   ideas, with essential concepts introduced from the beginning. Keep up with the class, ask questions, come to office hours, and do the homework." Feedback from you is important. Let me know if I am going too fast. Since this is a small class, we can be very informal and you may ask questions and comments at any time.        


Physics 404

Semester Schedule (First Approximation)

Spring 2004

 

  Date               Reading                                    Homework**                Date Due

 (Day/Month)   Assignment*                                                                  (Day/Month)

                        (Chapt.)

 27/1-2/2          Intro. and Ch-1                        #1                                  3/2

 3/2-9/2            Ch-1 & Ch-2                           #2                                  10/2

 10/2-16/2        Ch-2 &Ch-3                            #3                                  17/2

 17/2-23/2        Ch-3 & Probability                   #4 (Prob.)                      24/2

 24/2-1/3          Ch-4 & Review                        #5                                  2/3

 4/3                  Exam I

 9/3-15/3          Ch-5                                        #6                                  16/3

 16/3-29/3        Ch-6                                        #7                                  30/3

 30/3-5/4          Ch-7                                        #8                                11/4

 6/4-8/4            Review & Exam II (8/4)

 13/4-19/4        Ch-8                                          #9                                20/4

 20/4-26/4        Ch-9                                          #10                              27/4

 27/4-3/5          Ch-10                                        #11                              4/5

 4/5-10/5          Ch-12                                        #12                              11/5

 11/5                Review

 18/5                Final Exam (Scheduled for 1:30 P.M.-3:30 P.M. in Phys. 1402***)

 

* All assignments are from Kittel and Kroemer unless specified otherwise.

** Homework assignments, preliminary version, are given below. Any modifications in homework assignments will be announced in class. You are responsible for knowing the correct assignments. The majority of the problems will be from Kittel and Kroemer.

*** By unanimous agreement of all, including me, the date and time of the final exam may be changed.

 

Homework Assignment 1. Read the relevant chapters in your introductory physics text and answer the following questions

 

1. Briefly describe the absolute temperature scale.

 

2. The volume expansion of liquid mercury is given by

 

                        Vt = V0(1 + 1.8182 x 10-4t + 7.8 x 10-9t2),

 

where t is the true temperature in 0C and V0 is the volume at 00C. If the mercury is placed in a quartz tube (quartz has essentially zero volume thermal expansion), and the change in length of the mercury used as a thermometric parameter (the             length changes now being volume changes, in effect), calculate Dt = tHg -t at 250, 500, and 750C (tHg is the temperature      measured by the Hg thermometer. (Hint: This is an easy problem with a calculator.)

 

3.         a) Define heat capacity and specific heat. What are the SI          dimensions of those quantities?

            b) How would you measure the heat capacity of water, using a thermos bottle, a thermometer, a waterproof 100 W resistor, a battery, and electrical meters?

 

4. A hypothetical gas thermometer experiment (using an ideal constant volume gas thermometer) gave the following data for the fixed points:

 

                        Pice = 760.00 mm Hg and Psteam = 1039.00 mm Hg.

 

            The thermometer was then placed in liquid hydrogen boiling under atmospheric pressure, and a pressure of 56.17 mm Hg was      found .

            a) Using the two-fixed-point method and assuming an ideal gas, calculate the Celsius temperature of the boiling point of liquid hydrogen and the value of absolute zero given by these             data. From these, calculate the absolute temperature of the    boiling point of liquid hydrogen.

            b) Use the single-fixed-point or Giauque proposal to calculate   both the boiling point of hydrogen and the boiling point of             steam from the above data and compare with part a) and 1000C,           respectively. (The Giauque proposal consists in setting a        single fixed point, the triple point of water, at 273.16 K.            Assume the reference pressure P0 is 760 mm of Hg.)

 

5. State the first law of thermodynamics, defining any symbols you use in an equation.

 

6. Show the configurations that give the degeneracies indicated by the parentheses in Fig. 1.1 of K & K for the two lowest-lying levels of

            a. Li (2) and (6)

            b. B. (6) and (12).

Use the Hund's Rule hypothesis and refer to a modern physics   text on atomic spectra if you need help.

 

7.         a. If the number of spins N is an odd number, show that Eq. 14 of Chapter 1 in K&K is still valid.

            b. What are the values of s in this case?

            c. Evaluate g(N,s) for all allowed values of s if N = 5.

 

8.         Calculate the maximum value of g(N,s) in Chapt. 1 by the exact formula (Eq. 37) and by the approximate formula (Eq. 35) and compare the results. Make the calculation for all even values of N up to and including 20. Show your results in a table with the four columns shown below:

            N         g(exact)            g(approx.)        [g(approx.)-g(exact)]/g(exact)

 

            What can you conclude about the validity of the approximation? 


Homework 4

1. What is the probability of getting either a seven or a six when throwing two dice?

2. What is the probability of first drawing the king of clubs and then drawing any one of the three remaining kings from a deck of 52 cards?

3.         a) How many ways can you choose five objects from a set of twelve objects if the order of the choice is important?

             b) How many ways can you choose five objects from a set of twelve objects if the order of the choice is not important?

            c) In how many ways can you choose from twelve objects, three subgroups containing three, four, and five objects, respectively. Assume that the order is not important.

 

4.         a) What is the probability that five people have different birthdays? Assume any year has 365 days.

            b) Give an expression for the probability that r people do not have the same birthday.

            c) From b) find the value of r such that the probability of at least two of the r people having the same birthday is greater than 1/2.

 

5. The semiconductor chip manufacturing industry finds that it is extremely important to minimize the number of defective chips that result from any process. This can be illustrated by the following example. Suppose in a batch of 100 chips 5 are defective. If, for a device consisting of 5 chips, the 5 are chosen at random from this batch, what is the probability that the device does not contain a defective chip? What is the probability if there are 10 defective chips in the batch of 100?

 

6. If the letters of the word "banana" are arranged in a line at random, what is the probability that the line begins with "aaa"?

 

7. Assume a deck of cards consists of 52 cards and a poker hand is five cards dealt randomly.

            a) What is the number of ways you can get 4 of a kind? From this result find the probability of getting 4 of a kind.

            b) What is the probability of being dealt a full house (three of a kind and a pair)?

8. Is the expression,

             dx = cos(yz)dy + (y cos(yz)/z - sin (yz)/z2) dz,

an exact differential? If so, find x.

9. An unextended spring is in equilibrium. Then a mass m is placed at the end of this spring and the force of gravity causes the spring to extend by z to a new equilibrium position. Assume the spring constant is K.

            a) Obtain a formula for the extension of the spring z when it is in equilibrium.

            b) What is the change in potential energy of m?

            c) What is the increase in the internal energy of the spring?

            d) How much heat is released? Assume the process takes place at room temperature.

 

Homework 2

1. Kittell & Kroemer, Chapt. 2, Prob. 1

 

2. Kittell & Kroemer, Chapt. 2, Prob. 2

 

3. Kittell & Kroemer, Chapt. 2, Prob. 3

 

4. Kittell & Kroemer, Chapt. 2, Prob. 4

 

5. Kittell & Kroemer, Chapt. 2, Prob. 5

 

6. A block of metal is slightly confined by its surroundings. Initially, it is at a temperature of 200C and a pressure of one atmosphere. When the temperature rises by 12 0C, its volume is observed to increase by one part in 104. What is its final pressure? Assume b = 5x10-5 deg-1 and KT = 6.7x10-7 atmos-1.

 

Homework 3

1. Kittel & Kroemer, Chapt. 3, Prob.1

            a. Find the free energy from the partition function.

            b. Find U and s from F.

            c. From part b. find Cv. This is the Schottky anomaly for a two-state system.

            d. Sketch U(t)/e and Cv versus t/e as shown in Fig. 3.4 and show the limits for t/e =0 and

t/e ®¥.

            e. Estimate the value of t/e at which the maximum in Cv occurs              and discus the physical reason for this maximum.

2. Kittel & Kroemer, Chapt. 3, Prob. 9

 

3. Kittel & Kroemer, Chapt. 3, Prob. 2

            Use the generalization of Prob. 2 above that the partition of       N independent distinguishable systems is

            Z(1+2+3+...+N) = Z(1)Z(2)Z(3)....Z(N).

 

4. Kittel & Kroemer, Chapt. 3, Prob. 3

            It is not necessary to convert this partition sum to an integral. The sum can be evaluated exactly. Note that esx = [ex]s.

 

5. Kittel & Kroemer, Chapt. 3, Prob. 4

 

6. Kittel & Kroemer, Chapt. 3, Prob. 6

 

7. Kittel & Kroemer, Chapt. 3, Prob. 11 

Homework 5a

1. K&K, Chapt. 4 #1

2. K&K, Chapt. 4 #2

3. K&K, Chapt. 4 #7