# Thermal Physics (PHYS*2240)

Code and section: PHYS*2240*01

Term: Fall 2018

Instructor: Michelle Dunlop

## Course Information

### Course Objectives

This course will introduce you to the basic ideas of thermal physics, including temperature, heat, work; and thermal, mechanical and diffusive equilibrium. We will discuss the statistical basis for entropy and thermodynamics. We will cover applications of thermodynamics to both non-interacting and interacting systems.

Courses in thermal physics (thermodynamics and statistical mechanics) form one of the core sequences in the physics undergraduate curriculum, alongside course sequences in classical mechanics, in electromagnetism, and in quantum mechanics. The objective of PHYS*2240 is to begin your journey along the thermal physics sequence (which informally includes NANO*3600, PHYS*4240, and PHYS*4150). You should enter PHYS*2240 with a standard first-year science background, including some first-year physics and calculus.

We will follow the topic selection and structure in the textbook Thermal Physics by Daniel V. Schroeder. We will cover Chapters 1-3 extensively; we will also discuss selected topics from Chapters 4 and 5. Please see the course outline at the end of this Syllabus for a detailed schedule of lecture topics. After introducing some basic thermodynamic language and mathematical tools, we will explore the first law thermodynamics: energy conservation. However, we will find that energy conservation is not sufficient to answer the big questions of thermodynamics. The idea of entropy and the introduction of a second law of thermodynamics is necessary to answer these big questions and describe thermal phenomena. The entropy concept originates from our lack of precise knowledge about which of the many, many microscopic states a system is actually in, despite our imposition of constraints on the system at a macroscopic level. We will discuss entropy from a statistical perspective. Having motivated the second law, we will explore its consequences for equilibrium, for phase transitions, and for various applications and measurable quantities. These examples will illustrate the general structure of the theory, and will highlight the universal scope of thermal physics.

You will refine your analytical and problem-solving skills through regular written assignments.

### Class Schedule and Location

Monday, Wednesday, and Friday 1:30 pm - 2:20 pm, MCKN 228
First Lecture: Friday, September 7th
Last Lecture: Friday, November 30th
The course runs for 12 weeks (35 lectures); there is no lecture on Thanksgiving (Monday, October 8th) or for the in-class term test 1. Friday, November 30th is a Thanksgiving make-up lecture.

### Course Instructor

Name Office Phone Email
Michelle Dunlop MacNaughton 330 (519) 824-4120 ext. 53985 boudream@uoguelph.ca

#### Office Hours

Usually, Monday, 2:30 pm - 3:30 pm and Tuesday, 1:30 pm - 3:00 pm. However, office hours will shift depending on whether an assignment is due on Wedensday or on Friday, or whether there is an upcoming test. Please check the course calendar on CourseLink. Please send me an email if you can’t find me and wish to schedule a meeting.

### Course Materials

#### Required Textbook

An Introduction to Thermal Physics, by D. V. Schroeder (Addison Wesley Longman, 2000).
Other, optional resources:

• C.B.P. Finn, Thermal Physics
• Thermal physics online resources and simulations: www.compadre.org/stp

### Evaluation

Assessment Weight Due Date
Assignments (5) 30% roughly every two weeks
Term Test 1 10% Wednesday, October 10th, in class
Term Test 2 20% Tuesday, November 13th, 7-9 PM, place TBD
Final Exam 40% Wednesday, December 12th, 2:30 – 4:30 pm, place TBD

A medical certificate is required if the exam is missed.

Assignment solutions that are not stapled together will receive a grade reduction of 5%. Assignments are due at the beginning of class; late assignments will receive a grade of zero.

Physics is not done in a vacuum. (OK, sometimes it is...) Students may discuss assignments amongst themselves but their written solutions must not be shared with anyone (this would be an example of plagiarism).

Plagiarism is the act of appropriating the ...composition of another, or parts or passages of his [or her] writings, or the ideas or language of the same, and passing them off as the product of one's own mind...'' (Black's Law Dictionary). A student found to have plagiarized will receive zero for the work concerned. Collaborators shown to be culpable will be subject to the same penalties.

### Course Evaluation

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the Department’s Tenure and Promotion Committee in evaluating the faculty member's contribution in the area of teaching.
The Department's teaching evaluation questionnaire invites student response both through numerically quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department’s Tenure and Promotions Committee only considers comments signed by students (choosing "I agree" in question 14). Your instructor will see all signed and unsigned comments after final grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards.

Note: No information will be passed on to the instructor until after the final grades have been submitted.

## Standard Statements

### E-mail Communication

As per university regulations, all students are required to check their University of Guelph e-mail account regularly: e-mail is the official route of communication between the University and its students.

### When You Cannot Meet a Course Requirement

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons, please email the course instructor to make arrangements.

### Drop Date

At Guelph, the last date to drop one-semester courses, without academic penalty, is Friday, November 2nd. For regulations and procedures for Dropping Courses, see the Undergraduate Calendar.

### Copies of out-of-class assignments

Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.

### Accessibility

The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community's shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identified, ongoing disability or a short-term disability, should contact Student Accessibility Services (SAS) as soon as possible.

For more information, contact SAS at 519-824-4120 ext. 56208 or visit the SAS website.

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community – faculty, staff, and students – to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring. University of Guelph students have the responsibility of abiding by the University's policy on academic misconduct regardless of their location of study; faculty, staff and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection.

Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.

### Recording of Materials

Presentations which are made in relation to course work—including lectures—cannot be recorded or copied without the permission of the presenter, whether the instructor, a classmate or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.

### Resources

The Academic Calendars are the source of information about the University of Guelph’s procedures, policies and regulations which apply to undergraduate, graduate and diploma programs.

### Course Outline

This course will introduce you to the basic ideas of thermal physics, including temperature, heat, work; and thermal, mechanical and diffusive equilibrium. We will discuss the statistical basis for entropy and thermodynamics. We will cover applications of thermodynamics to both non-interacting and interacting systems.

#### I. Equilibrium, state variables, and equations of state [Chapters 1.1, 1.2]

1. The microscopic world and the macroscopic world, temperature, thermal equilibrium
2. Kelvin scale of temperature, ideal gas equation of state, thermal expansion
3. Pressure; the isothermal atmosphere, Boltzmann factor
4. Differentials, partial derivatives, and the mathematics of functions of multiple variables
5. Interacting gas: the van der Waals equation of state, P-V diagram, isotherm
6. van der Waals fluid continued: isothermal compression, instability, phase transition (pp. 180-181)

#### II. Conservation of energy: work and heat [Chapters 1.4 – 1.6]

7. Mechanical work; quasi-static, isothermal expansion of an ideal gas
8. Work is path-dependent, energy is a state function. What is heat? First law: energy conservation
9. Quasi-static, adiabatic expansion of an ideal gas
10. Adiabatic atmosphere example. Internal energy, heat and temperature
11. Heat capacity at constant V or constant P, heat transfer example

#### III. Microstates and multiplicity: the statistical origin of entropy [Chapters 2.1 – 2.5]

12. The big question of thermodynamics, two-state system
13. Microvariables and microstates of the two-state system, counting microstates, constraints and the multiplicity function
14. Term Test 1 (in class)
15. Macrovariables and macrostates of the two-state system, Einstein solid
16. Multiplicity of the Einstein solid. Interacting systems: two Einstein solids in thermal contact
17. Two larger Einstein solids in thermal contact, most likely macrostate
18. Large systems, large numbers, behavior of the multiplicity function
19. Sharpness of the multiplicity function, two macroscopic Einstein solids in thermal contact, behaviour near the peak: peak width and franctional peak width
20. Multiplicity of a monatomic ideal gas, indistinguishability, energy hyper-surface
21. Two interacting ideal gases, behaviour of multiplicity, entropy (finally!)

#### IV. Entropy, second law, thermodynamic equilibrium, applications [Chapters 2.6, 3.1, 3.2, 3.4-3.6, 1.3, 1.6, 4.1]

22. Second Law: Increase of entropy following release of internal constraints
23. Entropy changes in ideal gas: isothermal expansion, adiabatic expansion, free expansion, mixing
24. Temperature, thermal equilibrium, heat flow and entropy
25. Behaviour of the heat capacity and entropy at low temperatures
26. Mechanical equilibrium, entropy and pressure, thermodynamic identity, relation between entropy and constant-pressure heat capacity
27. Problem solving
28. Diffusive equilibrium, chemical potential (Term Test 2 in the evening)
29. The isothermal atmosphere revisited, surface adsorption
30. Internal degrees of freedom, equipartition of energy, heat capacity data
31. Heat engines and the Carnot cycle
32. Entropy of the van der Waals fluid (pp. 180-186)

#### V. Phase Transitions and Gibbs free energy [Chapters 5.1-5.3]

33. Phase transitions, constant T, P, N, Gibbs free energy of van der Waals fluid, minimum free energy and equilibrium (pp. 170-171, 182-184)
34. Second law for constant T, P, N, thermodynamic identity, chemical potential
35. Phase transition in the van der Waals fluid, metastability and instability, jump in V and S at the liquid-gas transition
36. Slope of the phase boundary: the Clausius-Clapeyon relation (Course evaluation)

### Learning Outcomes

#### Critical and Creative Thinking

Will be assessed through five problem sets, two term tests, and a final written exam, where students will analyze problems and physical situations in thermodynamics, and apply the general thermodynamic principles discussed in class, such as energy conservation and entropy maximization, to the specific problems. For example, students will learn to analyze which variables are being varied and which are held fixed in a particular, multivariable, physical context and how this determines the appropriate theoretical treatment the problem. Students will develop an ability to critically analyze when the hypotheses underlying thermodynamic laws apply and when they do not, and how to approach a problem in either case. Problems on assignments will relate to problems discussed in class, but may involve novel aspects that the students will have to recognize and account for, through creative application of the general principles. In more complicated problems, student will need to take several simple physical laws or relationships, and properly use them in conjunction to arrive at a solution to the total problem. The problems will be selected from real-world contexts in a range of disciplines and situations where thermodynamics provides crucial insight. On tests, approximately a quarter to a third of the grade will involve conceptual problems, rather than calculations, where students directly demonstrate their physical insight and intuition.

#### Literacy

Information is provided to students through lectures and through the required textbook, and related texts mentioned on the course syllabus. Students are encouraged to consult more than one text, to find a treatment of the material that is clearest to them. Assignment problems often are in the form of word problems, and students will need to extract and evaluate the information from the wording that is relevant to solving the problem. Some assigned problems are designed to develop a student's sense of the numbers and magnitudes involved in a physical context, that is, numerical literacy. Occasionally, students are asked to find material data in publically-accessible handbooks and tables; this requires the students to interpret what data the tables contains, to determine if it was taken under relevant conditions, and to convert the data to the correct units. One emphasis of this course is the power of drawing graphs to solve problems and illustrate concepts. Students will develop their visual literacy through practice recognizing and extracting information from graphical representations, and creating accurate, illustrative graphs and sketches of their own. They will learn to appreciate that when drawing sketches of mathematical relations, the sketches must respect physical limiting cases, which they will analyze. Students should incorporate these graphs into their logical chain of reasoning.

#### Global Understanding

This course will include some discussion of the history of thermodynamics throughout the 19th and early 20th centuries, before the advent of quantum mechanics. This may include a discussion of the importance of the invention of the steam engine to the intellectual development of the field through the work of Carnot and of Clausius, and later the understanding of the microscopic basis for entropy due to Boltzmann. Paradoxes in classical thermodynamic theory that will be resolved by quantum mechanics, and will be discussed in upper-year courses, will be mentioned. History, however, is not an emphasis in the course; students will be directed to a well-crafted online documentary on the historical development of thermodynamics.

#### Communicating

An early-term tutorial will show students how to properly present a problem solution, including having students provide explanations of their thought processes, and justification for their use of particular formulae and their choice of approach to the problem. In this way, it is hoped that students develop a systematic, well-reasoned and logical approach to problem solving, and clarify their thinking, and communicating, about how the general principles of thermodynamics apply in specific contexts. By working on word problems, students will develop skill in noticing nuance in a problem, for example the difference between a quantity and a change in a quantity. Students are encouraged in class to ask many questions, for their own benefit, to practice formulating specific, scientific questions, for the benefit of their classroom peers, who likely have the same question, and for the benefit of the instructor, who can use these questions to gauge student understanding the topic, through both the question content and the language (simple, sophisticated) used to ask the question. Reading comprehension comes through the textbook, on which the lectures are closely based. Conceptual questions on tests will challenge students to formulate coherent, logical arguments, perhaps integrating several related concepts into their answer in a compelling and consistent way. Concept questions also test how accurately students have absorbed the material, and where their notions of the nuances become vague, and where they are just regurgitating dogma.

#### Professional and Ethical Behaviour

Academic integrity is emphasized from the first lecture, and throughout as students complete the assignments. Deadlines for assignments are fixed, and known to the students beforehand; the workload for this course is not light. Thus the mastery of time management and the organizational skills of the students will come to the fore. There will be little prodding, or reminders, by the instructor to hand in assignments, to remember deadlines, or to keep on top of the readings or the lectures. The students will be responsible for maintaining their own work habits and, through practice, master appropriate work habits that will aid them currently, and in their later academic and professional career.