# Thermal Physics (PHYS*2240)

**Code and section:** PHYS*2240*01

**Term:** Fall 2015

**Instructor:** Robert Wickham

## Details

## Course Information

### Instruction

Lecturer | Office | Phone | |
---|---|---|---|

Rob Wickham | MacN 448 | (519) 824-4120 × 53704 | rwickham@uoguelph.ca |

**Office Hours:** Monday, 2:30 pm; Tuesday, 3:00 pm

### Lectures

Day | Time | Location |
---|---|---|

Monday, Wednesday, and Friday | 1:30 pm – 2:20 pm | JTP 212 |

### Course Materials

#### Required text

- 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: www.compadre.org/stp/

### Student Evaluation

Assessment | Weight |
---|---|

Assignments (every two weeks) | 30% |

Midterm Test | 20% |

Final Exam | 50% |

Students may discuss problems 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.

**Midterm test date: **Monday, November 2nd, time/place TBA.

**Exam date:** Saturday, December 12th, 2:30 pm – 4:30 pm, room TBA.

(A medical certificate is required if the exam is missed.)

### Course Outline

This course will introduce students to the basic ideas of thermal physics, including temperature, heat, work, thermal and diffusive equilibrium, and the Boltzmann distribution. The statistical basis for entropy and thermodynamics will be discussed. Applications of thermodynamics to both non-interacting and interacting systems will be presented.

PART I: Antipasti: Energy in Thermal Physics (Chapter 1)

- Week 1: Temperature, pressure, and energy. Overview: the microscopic world and the macroscopic world. Temperature, thermal equilibrium, thermometry. Thermal expansion coefficient. Ideal gas law. A microscopic model for pressure. Equipartition of energy.
- Week 2: Work and heat. An interacting system: van der Waals fluid (pp. 180 - 181). Isothermal compressibility. Work and heat. Isothermal and adiabatic processes. Heat capacity at constant V and at constant P. Enthalpy.
- Week 3: Some kinetics and some mathematics. Rates of processes: heat conduction, viscosity, diffusion. Boltzmann factor, Maxwell-Boltzmann distribution (Sec. 6.4). Gaussian integrals, averages, variance (Appendix B.1).

PART II: Primo Piatto: Entropy and Equilibrium (Chapters 2 and 3)

- Week 4: The microscopic and statistical basis for thermodynamics. Random numbers, probability, and averaging. The big questions. Two-state system, paramagnet, random walker. Einstein solid. Microstates, constraints, and the multiplicity function.
- Week 5: Statistical description of large systems. Thanksgiving. Two Einstein solids in thermal contact. Multiplicity function of large systems.
- Week 6: Entropy. Most probable macrostate, thermal equilibrium, fluctuations. Entropy of an ideal gas, modification for van der Waals fluid. Increase of entropy following release of internal constraints, coiling of a polymer. Entropy of mixing. Reversible and irre- versible processes.
- Week 7: Equilibrium. Temperature, heat flow and entropy. Laws of thermodynamics. Thermal equilibrium. Mechanical equilibrium. Diffusive equilibrium. Chemical potential.

Part III: Secondo: Thermodynamic Formalism and Applications (Chapter 5)

- Week 8: The structure of thermodynamics. Energy representation. Response functions as second derivatives of thermodynamic potentials. Relations for multivariable functions and partial derivatives. Thermodynamic information content. Euler equation. Gibbs-Duhem relation. Triple points.
- Week 9: Other representations of thermodynamics. Thermodynamic potential for constant temperature situations. Why our naive guess fails. Legendre transformation. Helmholtz and Gibbs free energies, enthalpy. More thermodynamic relationships. Extremal principle in other representations.
- Week 10: Results and applications. Maxwell relations. TdS relations. General relations between heat capacities. General relations between heat capacity and isothermal compressibility. Joule-Thomson process, gas liquefaction (pp. 139 – 144).
- Week 11: Phase transitions. Analysis of phase transitions in the P − T phase diagram in terms of the Gibbs potential. Latent heat. Slope of the coexistence curve. Conditions for liquid-gas coexistence in the van der Waals fluid. Equal area construction.

Part IV: Dolce: The Boltzmann Factor (Chapter 6)

- Week 12: Statistical description of the constant temperature situation. Probability a system at constant T is in a particular microstate: Boltzmann factor. Average values. Partition function. Partition function and Helmholtz free energy. Revisit: equipartition, Maxwell-Boltzmann distribution, ideal gas.

## Course Policies

### Course and Instructor 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 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 Tenure and Promotions Committee only considers comments signed by students or by choosing “I agree” in question 14 (online process). 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.

### 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 as soon as possible.

For more information, contact SAS at 519-824-4120 ext. 56208 or email csd@uoguelph.ca or refer to the SAS website.