Statistical Mechanics Assignments

Oberlin College Physics 410

Spring 2024

This World Wide Web page written by Dan Styer, Oberlin College Department of Physics and Astronomy ;
http://www.oberlin.edu/physics/dstyer/StatMech/Assignments/assignments.html;
last updated 19 April 2024.

Statistical Mechanics home page

Technical note: To access the links marked (PDF) you must first download the free Adobe Acrobat Reader or Open Standard software.

Assignment 1 (due Friday, 9 February): Problems 1.1, 1.2, 1.3, and 1.5.

Model Solutions 1:

Problem 1.1 The rotating water glass (PDF)
Problem 1.2 Compressibility, expansion coefficient (PDF)
Problem 1.3 Heat capacity as a susceptibility (PDF)
Problem 1.5 Human genetics (PDF)

Assignment 2 (due Friday, 16 February): Problems 2.6, 2.8, 2.9, 2.11, and D.1. (Look at problems 2.4, 2.10, and D.2.)

Model Solutions 2:

Problem 2.6 Lost in space (PDF)
Problem 2.8 Accessible regions of phase space (PDF)
Problem 2.9 Accessible configurations of a spin system (PDF)
Problem 2.11 The logarithm (PDF)
Problem D.1 Volume of a d-dimensional sphere (PDF)

Assignment 3 (due Friday, 23 February): Problems 2.12, 2.15, 2.23, 2.24, and 2.27. (Look at problems 2.16 through 2.21.)

Model Solutions 3:

Problem 2.12 Entropy of a spin system (PDF)
Problem 2.15 Other worlds (PDF)
Problem 2.23 Chemical potential of an ideal gas (PDF)
Problem 2.24 Ideal paramagnet, take three (PDF)
Problem 2.27 Entropy as a function of mass (PDF)

Assignment 4 (due Friday, 1 March): Problems 3.5, 3.16, 3.17.

Model Solutions 4:

Problem 3.5 Work in terms of p and V (PDF)
Problem 3.16 Acceptable forms for the entropy (PDF)
Problem 3.17 Heat capacities for the ideal gas (PDF)

Assignment 5 (due Friday, 8 March): Take home exam.

Model Solutions for Exam (PDF)

Assignment 6 (due Friday, 15 March): Problems 3.30, 3.32, 3.34, 3.35, and 3.37.

Model Solutions 6:

Problem 3.30 Magnetic systems (PDF)
Problem 3.32 Heat capacity at constant pressure (PDF)
Problem 3.34 Heat capacities in a magnetic system (PDF)
Problem 3.35 Isothermal compressibility (PDF)
Problem 3.37 Isothermal vs. adiabatic compressibility (PDF)

SPRING BREAK

Assignment 7 (due Friday, 5 April): Problems 4.3, 4.9, 4.10, and 4.13. (Look at problem 4.12.)

Model Solutions 7:

Problem 4.3 Entropy in the canonical ensemble (PDF)
Problem 4.9 Fluctuation-susceptibility relation for a magnetic system (PDF)
Problem 4.10 Two definitions of magnetization (PDF)
Problem 4.13 Parametric differentiation in quantum mechanics (PDF)

Assignment 8 (due Friday, 12 April): Problems 4.6, 4.7, 5.6, and 5.7. (Look at problems 4.8 and 4.15.)

Model Solutions 8:

Problem 4.6 Number fluctuations in the grand canonical ensemble (PDF)
Problem 4.7 Classical monatomic ideal gas in the grand canonical ensemble (PDF)
Problem 5.6 Schottky anomaly (PDF)
Problem 5.7 Simple harmonic oscillator (PDF)

Assignment 9 (due Friday, 19 April): Oral exam. (The oral exam will concern the ideal paramagnet. I recommend that you review your solutions to problems 2.9 and 2.12. You may also want to examine these tips for oral exams (PDF).)

Assignment 10 (due Friday, 26 April): Problems 6.12 and 6.20. (Look at problems 6.11 and 6.13.)

Model Solutions 10:

Problem 6.12 Isothermal compressibility of quantal ideal gases (PDF)
Problem 6.20 Thermodynamics of the fermion gas (PDF)

Assignment 11 (due Friday, 3 May): Problems 6.22, 6.24, 7.4, and 7.5. (Look at problems 6.25 and 7.1.)

Model Solutions 11:

Problem 6.22 White dwarf stars (PDF)
Problem 6.24 Thermodynamics of the Bose condensate (PDF)
Problems 7.4 and 7.5 Debye frequency; Debye model energy and heat capacity (PDF)

Assignment 12 (due Friday, 10 May): Problem 9.1.

Model Solutions 12:

Problem 9.1 Denaturization of DNA (PDF)

Final Exam from 2019 (PDF)

Model Solutions for Final Exam from 2019 (PDF)