Thermal Physics (PHYS*2240)

Code and section: PHYS*2240*01

Term: Fall 2020

Instructor: Daryl Good


Course Information

Course Objectives

This course will introduce you to the basic ideas of thermal physics, including tem- perature, 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

Lectures are scheduled for Monday, Wednesday, and Friday 12:30 pm - 1:20 pm, online.  However, I will only be giving 1 lecture (sometimes 2) a week live on Zoom during this scheduled time.  The other lectures will be prerecorded videos that I will post on CourseLink.  You should still make yourself available for all the scheduled lecture timeslots each week since I will be holding office hours or tutorials or midterm exams during the timeslots that are not used for live lectures.

First Lecture: Friday, September 11th
Last Lecture: Friday, December 4th 

The course runs for 12 weeks (36 lectures); there is no lecture on Thanksgiving (Monday, October 12th). Friday, December 4th is a Thanksgiving make-up lecture.

Course Instructor

Name:     Daryl Good
Office:  MacNaughton 330 (I will never be there)

Office Hours

Online availability via Zoom on Monday, Wednesday, and Friday 12:30 pm - 2:00 pm, when a lecture, midterm exam or tutorial is not scheduled.  I will not be presenting any new material at office hours, but you are free to ask me questions. Please send me an email if you can't find me and wish to schedule a meeting.

Course Website

CourseLink: Login via

Required Textbook

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

Other, optional resources

  • C. B. P. Finn, Thermal Physics 
  • C. J. Adkins, Equilibrium Thermodynamics 
  • Thermal physics online resources and simulations:


Assessment % of Grade Due Date
Assignments (5)  30% roughly every two weeks
Term Test 1  15% Wednesday, October  14th (tentatively),  online during lecture time slot
Term Test 2 20% Monday, November 16th (tentatively), online during lecture time slot, 1 of the questions may be due the next day
Computational Exercises (3) 5%  Coordinated by Dr. Mike Massa
Final Exam 30% Thurs. Dec 17, 2020, 8:30 am to 10:30 am, online

Computational Tutorials will be tentatively held Thursdays 10:30-11:30 with Dr. Mike Massa.  The first tutorial will be Thursday, Sept. 17.
Assignments are due in the Courselink drop box at 11:59pm on the stated due date; late assignments will receive a grade of zero since answers will be posted the day after assignments are due.  Note: For Assignment  #1, to accommodate any technical difficulties, I will allow assignments to be submitted up to one day late with a 10% late penalty (which I will probably waive if you send me a very polite email stating the reason for the late assignment submission).

Course Outline

This course will introduce you to the basic ideas of thermal physics, including tem- perature, 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. 

  1. Equilibrium, state variables, and equations of state (5-7 lectures)  [1.1, 1.2]
    •    The microscopic world and the macroscopic world, temperature, thermal equilibrium, ideal gas equation of state, thermal expansion, Pressure
    •    Math Review: Differentials, partial derivatives, and the mathematics of functions of multiple variables
    •    Interacting gas: the van der Waals equation of state, P-V diagram, isotherm,  isothermal compression, instability, phase transition (pp. 180 - 181)
  2. Conservation of energy: work and heat (5-7 lectures) [1.4 - 1.6]
    •    Mechanical work; quasi-static, isothermal expansion of an ideal gas, Work is path-dependent, energy is a state function. What is heat?
    First law: energy conservation.
    •    Quasi-static, adiabatic expansion of an ideal gas, Adiabatic atmosphere example. Internal energy, heat and temperature
    •    Heat capacity at constant V or constant P, heat transfer example
  3. Microstates and multiplicity: the statistical origin of entropy  (8-10 lectures) [2.1 - 2.5]
    •    The big questions of thermodynamics, two-state system, Microvariables and microstates of the two-state system, counting microstates, constraints and the multiplicity function
    •    Macrovariables and macrostates of the two-state system, Einstein solid and their Multiplicity.
    •    Interacting systems: two Einstein solids (microscopic and macroscopic) in thermal contact, Large systems and the behaviour of the multiplicity function
    •    Multiplicity of a monatomic ideal gas, indistinguishability, energy hyper-surface
    •    Two interacting ideal gases, behaviour of multiplicity, entropy (finally!)
  4. Entropy, second law, thermodynamic equilibrium, applications (10-12 lectures) [2.6, 3.1, 3.2, 3.4 - 3.6, 1.3, 1.6, 4.1]
    •    Second Law: Increase of entropy following release of internal constraints
    •    Entropy changes in ideal gas: isothermal expansion, adiabatic expansion, free expansion, mixing and low temperature heat capacity
    •    Mechanical equilibrium, entropy and pressure, thermodynamic identity, relation between entropy and constant-pressure heat capacity
    •    Diffusive equilibrium, chemical potential
    •    The isothermal atmosphere revisited, surface adsorption, Internal degrees of freedom, equipartition of energy, heat capacity data
    •    Heat engines and the Carnot cycle
    •    Entropy of the van der Waals fluid (pp. 180 - 186)
  5. Phase transitions and Gibbs free energy (3-5 lectures) [5.1 - 5.3]
    •    Phase transitions, constant T, P, N, Gibbs free energy of van der Waals fluid, minimum free energy and equilibrium (pp. 170-171, 182-184)
    •    Second law for constant T, P, N, thermodynamic identity, chemical potential
    •    Phase transition in the van der Waals fluid, metastability and instability, jump in V and S at the liquid-gas transition, Slope of the phase boundary: the Clausius-Clapeyon relation 

Learning Outcomes

  1. 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. 
  2. 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.
  3. 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.
  4. 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.
  5. 4. 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.

Course Statements

Working with others

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.

University Statements


Please note that the ongoing COVID-19 pandemic may necessitate a revision of the format of course offerings and academic schedules. Any such changes will be announced via CourseLink and/or class email. All University-wide decisions will be posted on the COVID-19 website and circulated by email.  


The University will not normally require verification of illness (doctor's notes) for fall 2020 or winter 2021 semester courses.  However, requests for Academic Consideration may still require medical documentation as appropriate.

E-mail Communication

As per university regulations, all students are required to check their 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. The grounds for Academic Consideration are detailed in the Undergraduate and Graduate Calendars.

Drop Date

Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars.

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.


The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student.
When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway.
Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability.
Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.

Academic Integrity

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 encourages academic integrity. 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

The University of Guelph’s primary mode of course delivery has shifted from face-to-face instruction to remote and online learning due to the ongoing COVID-19 pandemic. As a result, some learning activities (e.g., synchronous lectures or student presentations) may be recorded by faculty, instructors and TAs and posted to CourseLink for grading and dissemination; students may be recorded during these sessions. 
The following statements may be added to the course outline and it is recommended these are discussed in any synchronous courses during the first week of classes.  

By enrolling in a course, unless explicitly stated and brought forward to their instructor, it is assumed that students agree to the possibility of being recorded during lecture, seminar or other “live” course activities, whether delivery is in-class or online/remote.
If a student prefers not to be distinguishable during a recording, they may:

  1. turn off their camera
  2. mute their microphone 
  3. edit their name (e.g., initials only) upon entry to each session
  4. use the chat function to pose questions.  

Students who express to their instructor that they, or a reference to their name or person, do not wish to be recorded may discuss possible alternatives or accommodations with their instructor.

Online Behaviour

Inappropriate online behaviour will not be tolerated.
Examples of inappropriate online behaviour include:

  • Posting inflammatory messages about your instructor or fellow students
  • Using obscene or offensive language online
  • Copying or presenting someone else's work as your own
  • Adapting information from the Internet without using proper citations or references
  • Buying or selling term papers or assignments
  • Posting or selling course materials to course notes websites
  • Having someone else complete your quiz or completing a quiz for/with another student
  • Stating false claims about lost quiz answers or other assignment submissions
  • Threatening or harassing a student or instructor online
  • Discriminating against fellow students, instructors and/or TAs
  • Using the course website to promote profit-driven products or services
  • Attempting to compromise the security or functionality of the learning management system
  • Sharing your user name and password
  • Recording lectures without the permission of the instructor


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

Undergraduate Calendar