**PHY4513 Thermal and Statistical Physics**

Spring 2008

Instructor: Dr. Huan-Xiang Zhou

Time: Tuesday and
Thursday

Classroom: UPL 109

**Textbook**

An Introduction to Thermal Physics by Daniel V. Schroeder, published by Addison Wesley Longman, 2000.

**Course Description**

Thermal and Statistical Physics
deals with the properties of systems containing large numbers (~10^{23})
of particles. Thermodynamics concerns
general principles governing such systems without probing the behaviors of the
individual particles; statistical mechanics aims to predict macroscopic
properties from the intrinsic behaviors of individual particles and their
interactions. This course will introduce
the basic principles and illustrate their applications.

**Office Hour**

Tuesday

**Grading**

Homework (25%), two mid-terms (20% each), and final exam (35%). Second mid-term and final exam are cumulative. Homework is to be completed independently; copying of homework will result in a zero for both parties. Prior approval is required for turning in any homework late.

The cutoffs for A-, B-, C-, and D are 90, 70, 50, and 40, respectively.

**Course Contents**

Chapter 1: Sections 1 to 6

HW1: 1.3,
1.7(a), 1.10, 1.12, 1.18 Solution

HW2: 1.27,
1.31, 1.36, 1.43, 1.48, 1.49 Solution

Chapter 2: Sections 1 to 6

HW3: 2.3,
2.6, 2.8(a)-(d), 2.15, 2.21, 2.23 Solution

HW4: 2.27, 2.29*,
2.35, 2.36, 2.37 Solution

2.29*: A system of two Einstein
solids has *N*_{A} = 300, *N*_{B} = 200, and *q*_{total}
= 100. Compute the entropy of the most
probable macrostate.

Chapter 3: Sections 1 to 6

HW5: 3.1*, 3.5,
3.10, 3.28, 3.35* Solution

3.1*: Only find results in *e*/*k*_{B}
(i.e., no need to do so in Kelvins).

3.35* hint: find the two integral
values of *q* that would bracket the
original multiplicity.

HW6 [**bonus**]: 3.8, 3.11, 3.14, 3.31, 3.37* Solution

3.37* hints: Total energy *U** = *U*
+ *Nmgz*,
where *U* is the internal energy
arising from the translation of the molecules.
Substitute *U* = *U** – *Nmgz* into the expression for
entropy. Find *m* by taking derivative with respect to *N*. At the end, substitute *U** – *Nmgz* = *U* by 3*Nk*_{B}*T*/2.

**Review Materials**

Page 1 Page 2 Page 3 Page 4 Page 5

**First mid-term:** February 7 Problems
with Solutions

Chapter 4: Sections
1 and 2 Solution

HW7: 4.2, 4.4, 4.5, 4.7, 4.8, 4.10,
4.11

Chapter 5: Sections 1 to 3

HW8: 5.1,
5.2*, 5.5(a)-(c), 5.6(a)-(d) Solution

5.2*: Calculate D*G* for producing
2 moles of NH_{3}. In comparing against the tabulated value of D*G* (p. 405 of
textbook), note that the latter value is for producing 1 mole of NH_{3}.

HW9: 5.9*,
5.11*, 5.20, 5.21, 5.23(a)&(c) Solution

5.9* hint: first sketch entropy as a
function of temperature. Then use *S* = –(¶*G*/¶*T*)_{P}_{, N} to sketch *G* as
function of *T*. Under constant *P* and *N*, S is the slope
in the *G* versus *T* plot.

5.11* hint: for part (b), recall
that the maximal electric work is the negative of the change in Gibbs free
energy when one mole of hydrogen gas is consumed (to make one mole of water).

HW10: 5.24,
5.25, 5.28, 5.29, 5.32* Solution

5.32(a) hint: think about the latent
heat of melting and the densities of liquid water and ice. The volume *V* of one mole of H_{2}O is the inverse of density.

**Second mid-term:** March 6 Problems
with Solutions

Chapter 6: Sections 1 and 7

HW11: 6.2,
6.3, 6.6, 6.15, 6.22 Solution

HW12: 6.31,
6.33, 6.43*, 6.44*, 6.50 Solution

6.43 hint: the familiar expressions
for entropy are (a) *k*_{B}lnW for an
isolated system and (b) (*U* – *F*)/*T*
for a system at constant temperature and volume.

6.44 hint: first relate *F* to *Z*
and then recall *m* = (¶*F*/¶*N*)_{T}_{, V}.

Chapter 7: Sections
1 to 2 Solution

HW13: 7.1, 7.2, 7.8, 7.11, 7.12*,
7.13

7.12 hint: the possible microstates
are: 00, 01, 10, and 11, here “*ij*” means that *e*_{A} is occupied by *i* particles and *e*_{B} is occupied by *j*
particles. The probability for *e*_{A} being unoccupied is the sum of the probabilities for 00 and
01; similarly the probability for *e*_{B} being occupied is the sum of the probabilities for 01 and 11.

**Final exam:** April 21, 5:30-7:30 pm, UPL 109