PHY 341/641 Thermodynamics and Statistical Mechanics

MWF 12 and 2 Online and face-to-face http://www.wfu.edu/~natalie/s21phy341/

Instructor: Natalie Holzwarth Office:300 OPL e-mail:natalie@wfu.edu

Course schedule for Spring 2021

Reading assignments are for the An Introduction to Thermal Physics by Daniel V. Schroeder.

The HW assignment numbers refer to problems in that text if written in black and to original problems as described in link.

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Lecture date
Reading
Topic
HW
Due date
1 Wed: 01/27/2021 Chap. 1.1-1.3 Introduction and ideal gas equations 1.21 01/29/2021
2 Fri: 01/29/2021 Chap. 1.2-1.4 First law of thermodynamics 1.17 02/03/2021
3 Mon: 02/01/2021 Chap. 1.5-1.6 Work and heat for an ideal gas
4 Wed: 02/03/2021 Chap. 1.1-1.6 Review of energy, heat, and work 1.45 02/05/2021
5 Fri: 02/05/2021 Chap. 2.1-2.2 Aspects of entropy
6 Mon: 02/08/2021 Chap. 2.3-2.4 Multiplicity distributions 2.24 02/10/2021
7 Wed: 02/10/2021 Chap. 2.5-2.6 Entropy and macrostate multiplicity 2.26 02/12/2021
8 Fri: 02/12/2021 Chap. 2.1-2.6 Review of entropy and macrostates 2.32 02/15/2021
9 Mon: 02/15/2021 Chap. 3.1-3.2 Temperature, entropy, heat 3.10a-b 02/17/2021
10 Wed: 02/17/2021 Chap. 3.3-3.4 Temperature, entropy, heat 3.23 02/19/2021
11 Fri: 02/19/2021 Chap. 3.5-3.6 Temperature, entropy, heat 3.28 02/22/2021
12 Mon: 02/22/2021 Chap. 4.1-4.3 Ideal engines and refrigerators 4.1 02/24/2021
13 Wed: 02/24/2021 Chap. 4.3-4.4 Real engines and refrigerators 4.20 02/26/2021
14 Fri: 02/26/2021 Chap. 5.1 Free energy 5.5 03/01/2021
15 Mon: 03/01/2021 Chap. 5.1-5.2 Thermodynamic relations 1.46c-e 03/03/2021
16 Wed: 03/03/2021 Chap. 5.3 Phase transformations 3.33 03/05/2021
17 Fri: 03/05/2021 Chap. 5.4 Multicomponent systems 5.14a-e 03/08/2021
18 Mon: 03/08/2021 5.5 Dilute solutions #16 03/10/2021
19 Wed: 03/10/2021 5.6 Chemical equilibria #17 03/12/2021
20 Fri: 03/12/2021 Chap. 1-5 Review
Mon: 03/15/2021 No class APS March Meeting Take Home Exam
Wed: 03/17/2021 No class APS March Meeting Take Home Exam
Fri: 03/19/2021 No class APS March Meeting Take Home Exam
21 Mon: 03/22/2021 Chap. 6.1 & 6.5 Microcanonical and canonical ensembles
22 Wed: 03/24/2021 Chap. 6.1-6.2 Canonical distributions #18 03/26/2021
23 Fri: 03/26/2021 Chap. 6.1-6.7 Canonical distributions 6.49 03/29/2021
24 Mon: 03/29/2021 Chap. 6.1-6.7 Canonical distributions #20 03/31/2021
25 Wed: 03/31/2021 App. A & Chap. 7.1 Quantum mechanical effects #21 04/02/2021
26 Fri: 04/02/2021 Chap. 7.1-7.2 Quantum mechanical effects
27 Mon: 04/05/2021 Chap. 7.3 Bose and Fermi statistics #22 04/09/2021
Wed: 04/07/2021 No class Holiday
28 Fri: 04/09/2021 Chap. 7.3 & 7.4 Bose and Fermi statistics #23 04/12/2021
29 Mon: 04/12/2021 Chap. 7.3 Fermi examples #24 04/16/2021
30 Wed: 04/14/2021 Chap. 7.5 Bose examples and lattice vibrations
31 Fri: 04/16/2021 Chap. 7.6 Bose condensation
32 Mon: 04/19/2021 Chap. 7.6 & 8.1 Interacting particles #25 04/21/2021
33 Wed: 04/21/2021 Chap. 8.1 Interacting particles #26 04/23/2021
34 Fri: 04/23/2021 Chap. 8.2 Spin magnetism
35 Mon: 04/26/2021 Chap. 8.2 Spin magnetism
36 Wed: 04/28/2021 Review
37 Fri: 04/30/2021 Review
37 Mon: 05/03/2021 Review
38 Wed: 05/05/2021 Review

PHY 341/641 -- Assignment #16

March 8, 2021

Continue reading Chapter 5 in Schroeder .

  1. Suppose you desolve 0.1 kilograms of KCl salt into 10 liters of pure water. Estimate the boiling point and freezing point of the solution measured at atmospheric pressure.

PHY 341/641 -- Assignment #17

March 10, 2021

Finish reading Chapter 5 in Schroeder .

  1. Consider the equilbrium reaction given in Eq. 5.98 of Schroeder . Assume that you can represent the number of N2 molecules in terms of the parameter χ and constant N0 by N0(1-χ). Find a consistent representation for the number of H2 and NH3 molecules so that you can estimate the fraction of ammonia molecules which are present at standard temperature pressure. Your textbook gives values for the needed parameters. (You may want to use graphics software for your estimation.)

PHY 341/641 -- Assignment #18

March 24, 2021

Continue reading Chapter 6 in Schroeder .

Consider a single particle which can be in one of 3 states having energies U1=0, U2=Δ, and U3=2Δ according to a canonical distribution.

  1. Write an expression for the partition function of this system.
  2. Write an expression for the heat capacity at constant volume for this system.
  3. Using convenient units, make a plot of the heat capacity of this system.

PHY 341/641 -- Assignment #20

March 29, 2021

Complete reading Chapter 6 in Schroeder .

Consider a system of Avogadro's number of Ne atoms (atomic mass 20.180) in a container of volume 1 m3 in equilibrium with a heat bath at temperature T=300 K.

  1. Find the most probable speed of a Ne atom.
  2. Find the fraction of Ne atoms which have a speed equal or larger than the most probable speed.

PHY 341/641 -- Assignment #21

March 31, 2021

Read Appendix A and start reading Chapter 7 in Schroeder .

Consider three different states A,B,C each with a different energy and three particles 1,2,3. Enumerate the possible distinct distributions of the particles among the states and their corresponding energies for the following cases:

  1. The three particles are distinguishable
  2. The three particles are indistinguishable and obey Bose statistics
  3. The three particles are indistinguishable and obey Fermi statistics

PHY 341/641 -- Assignment #22

April 5, 2021

Continue reading Chapter 7 in Schroeder .

This is an exercise illustrating the use of the Dirac delta function δ(x). Assume that all integrals are performed over the range of -∞ < x < ∞ and that f(x) has values and zeros within the same range. "a" and "b" denote positive real numbers. Evaluate the following integrals performed over the full range of x having the form ∫ dx G(x) δ(b-f(x)) where G(x) and f(x) are specified below:

  1. G(x)=x and f(x)=ax
  2. G(x)=x2 and f(x)=ax
  3. G(x)=x and f(x)=ax2
  4. G(x)=x2 and f(x)=ax2

PHY 341/641 -- Assignment #23

April 9, 2021

Continue reading Chapter 7 in Schroeder .

  1. In class, we evaluated the Grand potential for an ideal Fermi gas in the limit that T is approximately 0 K. From this result, we can estimate the internal energy U and the pressume P at very low temperature. Show that this estimate is consistent with the results presented in Section 7.3 of Schroeder.

PHY 341/641 -- Assignment #24

April 12, 2021

Continue reading Chapter 7 in Schroeder .

Consider an ideal Fermi gas of spin 1/2 particles confined in a two dimensional plane of length L and area A. Each particle has mass m and there are N particles. The spatial quantum states of the particles can be enumerated with the integers nx and ny for -∞ ≤ nx,y ≤ ∞ according to

εnxny = h^2/(2mL2) (nx2 +ny2).

  1. Find the density of states g(ε) for this system. Do not be surprised to find that it does not depend on ε.
  2. Evaluate the chemical potential μ at T=0K.
  3. Evaluate the Grand potential Ω at T=0K.
  4. Evaluate the internal energy U at T=0K.

PHY 341/641 -- Assignment #25

April 19, 2021

Complete Section 7.6 and start reading Section 8.1 in Schroeder .

Suppose that you have an ideal Bose gas of 87Rb atoms with a number density of 2.5 x 1020 atoms/m3. Each atom has a mass of 1.44 x 10-25 kg. Other constants that you may want to use for this problem are the Boltzmann constant of k=1.380649 x 10-23 J/K and Planck's constant of h=6.62607015 x 10-34 J s. Additionally, you will need to evaluate the function that we defined in class whose integral can be evaluated with software (Maple, Mathematica, etc.) or it can be evaluated from a convergent infinite series g3/2(z)=∑m=1∞ zm m-3/2.

  1. Find the critical temperature Tc for forming a Bose condensate in this system.
  2. Find the chemical potential for this system at T=0.00001 K.

PHY 341/641 -- Assignment #26

April 21, 2021

Complete reading Section 8.1 in Schroeder .

Choose some appropriate values for the Lennard-Jones potential form for your favorite atom (r0 and Φ0).

  1. For three different temperatures T evaluate the second virial coefficient B(T) using Maple, Mathematica, or other software of your choice.
  2. Qualitatively, what controls the sign of the second virial coefficient?
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Last modfied: Sunday, 24-Jan-2021 18:03:35 EST