PHY4513 Thermal and Statistical Physics

Spring 2008

Instructor: Dr. Huan-Xiang Zhou

Time: Tuesday and Thursday 11:00 am -12:15 pm

Classroom: UPL 109

Textbook

Course Description

Thermal and Statistical Physics deals with the properties of systems containing large numbers (~1023) 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 1 – 2 pm, KLB 419, or by appointment by e-mail (zhou@sb.fsu.edu) or phone (645-1336).

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 NA = 300, NB = 200, and qtotal = 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/kB (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 3NkBT/2.

Review Materials

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 DG for producing 2 moles of NH3.  In comparing against the tabulated value of DG (p. 405 of textbook), note that the latter value is for producing 1 mole of NH3.

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 H2O 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) kBlnW for an isolated system and (b) (UF)/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 eA is occupied by i particles and eB is occupied by j particles. The probability for eA being unoccupied is the sum of the probabilities for 00 and 01; similarly the probability for eB being occupied is the sum of the probabilities for 01 and 11.

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