DSC 76 x5855
kcrosby@carthage.edu
https://www.carthage.edu/live/profiles/98-kevin-crosby
Office Hours: MWF 10:30-11:30; TR 2:30-3:30

Course Prerequisites

Completion of PHY 2210 with a grade of C- or better
Concurrent Enrollment in MTH 2020.

This is an advanced course in statistical mechanics and thermodynamics. You will need to have proficiency with ordinary linear differential equations, partial derivatives, complex numbers, and standard integration techniques. Soap carving, shadow puppetry, downhill zorbing, and peacock husbandry are also useful skills.

Textbooks and other Resources

Required Texts:

• An Introduction to Thermal Physics, Daniel V. Schroeder (Addison Wesley Longman, 2000)

Software Used in the Course:

• Mathematica/Wolfram Alpha (occasionally)
• Excel (often)

Course Description

Why were all the Kings’ horsemen never able to put Humpty Dumpty back together again? Why do all things wind down and die? And what’s with the cosmological inevitability of heat death and the cold silent end of everything? These are questions that have a lot to do with the seeming one-way direction of time, which has everything to do with thermal physics and the surprising connections between entropy and time. We will wrestle with these questions in this course while also learning how they apply directly to the design of rocket engines, chemical reactions, the weather, and myriad physical phenomena about which you should be wondering.

Thermal Physics comprises two approaches to the study of matter. Thermodynamics discovered first, describes the behavior of composite systems (systems comprised of atoms or other discrete entities – gases, solids, etc.) in terms of a few simple laws that predict the evolution of the system, its energy, and its interaction with other entities. Equilibrium Statistical mechanics uses probability theory to explain the thermodynamic behavior of such systems and provide powerful tools for predicting the thermodynamic properties of substances. Statistical Mechanics and Thermodynamics are complementary approaches to understanding the behavior of matter and we will learn to apply both to a wide variety of interesting problems in this course.

Thermal Physics is the study of everything at a temperature above absolute zero. Which is everything. We will study atoms, molecules, stars, galaxies, and even find insights into exotic states of matter such as neutron stars and superfluid helium using the tools we learn in this course. Thermal Physics finds applications across the spectrum of scientific inquiry, from protein folding to the distribution of matter in the universe. This course will Introduce the concepts, formalism, and applications of classical and quantum statistical mechanics, including thermodynamics, and illustrate some of the modern applications this branch of physics.

A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown. -A. Einstein

My memory for figures, otherwise tolerably accurate, always lets me down when I am counting beer glasses.” -L. Boltzmann.

Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously. (Opening lines of “States of Matter”, by D.L. Goodstein).

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Learning Goals

My objective for this course is that you will understand the key concepts of thermodynamics and equilibrium statistical mechanics and that you will master the application of these concepts to the canonical problems of these disciplines. The learning outcomes that support these objectives are the following.

The successful student will be able to

1. define, quantify, and relate measures of temperature and energy.
2. identify the appropriate solution formalism for canonical problems in thermodynamics and solve those problems.
3.  Apply fundamental probability and combinatoric theory to physical and mathematical systems to derive thermodynamic behavior.
4. Derive equations of state from an understanding of thermodynamic states and state variables.
5. Calculate thermodynamic properties of model systems using the microcanonical, the canonical, and the grand canonical ensembles.
6. Write with increased mathematical sophistication over the course of the semester.

Requirements

Meetings and Attendance

We meet from 9:00-9:15 MWF in DSC 53. This course is flipped. That is, the lectures are available in video form and we we will spend class time working problems, covering homework, and doing case study exercises. I expect that you will have watched the whiteboard video for the day and read the relevant text material before class. Class exercises and discussions will be structured around the reading assignments. Plan to spend approximately 3 hours of work reviewing lecture videos, reading text, and working problems for each hour of in-class activity.

As you know by now, attendance and active participation in class are essential to success in physics courses.  Please come to class with questions and reading notes! Participation in class discussions is an important element of the course grade and is measured by the extent to which you can both ask questions that are relevant to the topic at hand and contribute knowledge and insight to the discussions. Participation is 5% of the course grade.

Homework

There are 60 homework problems assigned in this course.  Homework is due each Monday. The homework problems represent 20% of the course grade.  As such, your write-ups should reflect a considerable investment of your time in crafting detailed and complete solutions. Solutions should be of sufficient explanatory detail to make it clear that you understand the mathematics and concepts. USE WORDS TO DESCRIBE YOUR LOGIC. Equations alone are not sufficient to convey meaning. The mathematics should be logically developed in a clear and complete sequence of steps with words. Problem solutions that consist entirely of equations and numbers will receive no credit. Problem assignments are on the course schedule.  I do not accept late homework.

While collaboration is encouraged, each student should submit homework write-ups that reflect their own understanding of the problems. Significant similarities between homework submissions from two students may be grounds for failure of the assignment by both parties. It is appropriate to include notes in your solutions crediting the insights of others, such as “Abby suggested that I use ideal gas law at this step to eliminate the volume term,” or “I consulted the website www.thermal.com” for help on understanding this step.”

It is trivial to find solutions to most textbook problems on the web. However, struggling independently on lots of homework problems is an essential exercise for your brain in its path toward becoming a physicist. Using the work of others in your homework is no different than trying to build muscle mass by watching others lift your weights. Do the work. Don’t plagiarize. It’s obvious and sad when you do and the standard repercussions apply.

5 point scoring rubric for homework

Each homework problem will be graded on a 5 point scale described below.  Remember that homework is the essential activity in this course.  Doing lots and lots of problems is the only way to master this material. I won’t make extensive comments on your homework assignments because I will be providing detailed solutions for each problem for you to cross-check your work.

Score 5: Advanced Level  Your work is unusually exemplary and goes beyond my expectations for this particular problem.  This score is rarely achieved and represents more than just “getting it right.” It usually entails a detailed description (in words) of the process, solution, and implications of the solution. A creative approach to the problem is evident and you have surprised me with your solution. I love being surprised.

Score 4: Fully Meeting Expectations  Your work is essentially correct and free of most major errors.  Your work meets my expectations. It is rigorous, uses words to explain your logic, and is cleanly presented.

Score 3: Mostly Correct Your process is mostly clear and essentially correct. There may be small mechanical errors or errors in thinking but you’re on the right track. You should quickly check the posted solutions and resolve any differences that might exist.

Score 2: Nearly Meeting Expectations  Your work is missing some important components or has some important errors that need to be resolved before you can progress.  Please take a careful look at the posted solution guide and try to resolve differences between your understanding of the problem and mine.

Score 1: Attempted But on the Wrong Track You made an attempt at the problem but were unable to identify and use the relevant principle or concept to attack the problem. Take a look at the solution guide and then arrange a few minutes to talk individually with me as soon as possible.

Score 0: Insufficient Effort  Your work was not submitted according to the directions or no meaningful attempt is evident in your work.

Quizzes

There will be weekly quizzes based on the assigned homework. Quizzes will be administered at the beginning of class each Monday. Each quiz will consist of one single question drawn from the text reading and/or homework assigned the previous week and one qualitative (did you read the chapter?) question from the assigned reading for the current week. Quizzes represent 10% of the course grade. Quizzes cannot be made-up though I will drop the lowest two quizzes from your average.

Exams

There will be two in-class exams and a comprehensive final exam. Each exam is equally weighted and is 20% of the overall course grade. Exam questions are based on the learning outcomes for the course and are representative of the types of problems covered in class and in the homework. The exams are closed book/closed note format. You may bring in a single 8-1/2 x 11″ sheet of notes (both sides) for each exam. Calculators are permitted but phones may not be used during exams. Exams may not be made up. If a medical emergency causes you to miss an exam, the missed points will be added to your Final Exam. Documentation is required.

Case Studies

There are 3-4 Case Studies in this course drawn from current or historical events and important applications of the material in various related fields (astrophysics, medicine, space flight). The Case Studies should be worked on both in class and outside of class and require a written solution in the form of a short (3-5 page) paper with sufficient physical and mathematical insights to demonstrate your understanding of the material covered. The Case Studies represent 5% of the course grade.

Computers

I will make use of physics simulations and other computer teaching tools in the course.   Many of the homework problems require the use of Mathematica and/or Excel.  Interactive computer-based exercises may be assigned.  If you have a laptop, please bring it to class.

Grading and Policies

• Exams 60%
• Homework  20%
• Quizzes 10%
• Case Studies 5%
• Participation 5%

Academic Honesty

Students are bound by the terms of the Carthage College Academic Honesty Contract in the Student Handbook. Any act of academic dishonesty is a sufficient cause for failure of the course.