| Course title | |||||
| 熱統計力学 [Thermodynamics and Statistical Mechanics] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 3～4 | Semester | 1st | |
| Course type | 1st | Course code | 023653 | ||
| Instructor(s) | |||||
| 箕田 弘喜 [MINODA Hiroki] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
|
The approach of this lecture to thermal physics differs from the traditional one. The leading concepts in the lecture are the entropy, the temperature, the Boltzmann factor, the chemical potential, the Gibbs factor, and the distribution function. The entropy measures the number of the quantum states (eigen states) accessible to a system, which called multiplicity function expressed as g, and plays an important role. A closed system might be in any of theses quantum states with equal probability. Given g accessible states, the entropy is defined as s = log g. The entropy thus defined will be a function of the energy U, the number of particles, and the volume: s(U, N, V). When two systems, each of specified energy, are brought into thermal contact, they may transfer energy; their total energy remains constant, but the constraints on their individual energy are lifted. A transfer of energy in one direction or perhaps in the other, may increase the product g1g2 that measures the number of accessible states of the combined systems. The fundamental assumption biases the outcome in favor of that allocation of the total energy that maximizes g1g2: more g1g2 is more likely to occur. Namely the total entropy of the two systems will increase. Eventually the entropy reach a maximum for the given total energy (the second law of thermodynamics). Reservoirs: various systems are considered: isolated systems at first, systems that only permit exchange of only heat with a reservoir next, and finally systems that permit exchange of heat and also particles with a reservoir. In the second the energy fluctuates whereas in the third case both of the energy and the number of particles fluctuate around their average values. Thus permitting the exchange of energy or both energy and particles, the system appears to be more complicated, but in fact, the calculation becomes easier. Energy: various thermodynamic potentials are also defined, such as internal energy, Helmholtz free energy, Gibbs free energy Statistics: there are classical and quantum statistics. In the classical statistics (the Maxwell-Boltzmann distribution), particles can be distinguished. On the other hand, in the quantum statistics (Fermi-Dirac distribution or Bose-Einstein distribution), particles cannot be distinguished |
| Expected Learning |
| This lecture provides the way to describe and understand the thermodynamic states or macrscopic states of matters in terms of statistical mechanics. |
| Course schedule |
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Chapter 0."Introduction to thermal statistical physics" (weak1) Concept of the text book, C. Kittel "Thermal physics" Chapter 1 "States of a model system" (week 2,3) Chapter 2 "Entropy and temperature" (week 4,5) Chapter 3 "Boltzmann distribution and Helmholtz free energy" (week 6~8) Chapter 4 "Thermal radiation and Planck distribution" (week 9~10) midterm exam Chapter 5 "Chemical potential and Gibbs distribution" (week 10,11) Chapter 6 "Ideal gas" (week 12,13) Chapter 7 "Gibbs free energy and chemical reactions" (week 14) Chapter 8 "Heat and work" (week15) final exam |
| Prerequisites |
| Mechanics I, II, Electromagnetics I, II, Introduction to quantum mechanics, Quantum mechanics I, Mathematical Physics I, II |
| Required Text(s) and Materials |
| Charles Kittel, “Thermal Physics” (W. H. Freeman and Company) |
| References |
| Assessment/Grading |
| Midterm exam (40%), final exam (55%) and comprehensive evaluation with the exercise class |
| Message from instructor(s) |
| Course keywords |
| Entropy, Temperature, Boltzmann factor, Partition function, Helmholtz free energy, Planck distribution, Fermi-Dirac distribution, Bose-Einstein distribution, Gibbs factor, Gibbs sun, Gibbs free energy, Heat and work, Carnot cycle |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 6/8/2022 1:54:35 PM |