| Course title | |||||
| 応用熱統計力学 [Thermodynamics and Statistical Mechanics] | |||||
| Course category | common courses | Requirement | Credit | 2 | |
| Department | Year | ～ | Semester | 1st | |
| Course type | 1st | Course code | 1060487 | ||
| Instructor(s) | |||||
| 内藤 方夫 [NAITO Michio] | |||||
| Facility affiliation | Graduate School of Engineering | Office | afjgxte/L1151 | Email address | |
| Course description |
| In the undergraduate course, we considered thermal equilibrium conditions among systems in which energy can be freely exchanged under the condition of constant number of particles. In this lecture, we will develop the concept and consider the diffusion equilibrium between systems in which the number of particles can be freely exchanged. As a preparation, we understand entropy and free energy of Helmholtz, and treat solar spectrum and binary alloys as application examples. Altitude change of atmospheric pressure, p-n junctions will be discussed as an application example of diffusion equilibrium. |
| Expected Learning |
| You will gain an understanding of the advances of Thermodynamics and Statistical Mechanics, and will be able to explain the details of the course content summarized below. |
| Course schedule |
|
Lecture 1: Introduction You are responsible to check your fundamental knowledge of thermodynamics. Course instructors will explain the outline of this lecture as follows. Thermal equilibrium → thermal equilibrium condition → temperature → Boltzmann distribution → partition function → Helmholtz free energy Diffusion equilibrium → Diffusion equilibrium condition → Chemical potential → Gibbs distribution → Gibbs sum Lecture 2: Thermal equilibrium and temperature Instructors will review how to count the number of states, and define the entropy and temperature of the system. Lecture 3: Planck's law The Planck distribution is derived from the entropy of free particles. Lecture 4: Black body radiation Instructors will explain solar light spectrum based on Planck's radiation formula and mode density of electromagnetic radiation. Lecture 5: Partition function and Helmholtz free energy Instructors will calculate Helmholtz free energy, and you are expected to understand that it gives equilibrium conditions in a system at a constant temperature. Lecture 6: Entropy of mixing Instructors will calculate the entropy of mixing and the energy of mixing in a binary alloy. Lecture 7: Binary alloys Instructors will calculate Helmholtz free energy in binary alloys, and you are expected to understand the phase equilibrium and phase separation of the alloys. Lecture 8: Ideal gas Instructors will calculate the distribution function of the ideal gas, and derive the internal energy and equation of state therefrom. Lecture 9: Chemical potential Instructors will explain the concept of diffusion equilibrium, and you are expected to understand that diffusion equilibrium conditions are represented by physical quantities called chemical potentials, just as the physical quantity representing thermal equilibrium conditions is temperature. Lecture 10: Atmospheric pressure change due to altitude in the stratosphere As an example of diffusion equilibrium, the altitude change of atmospheric pressure in the ideal gas is derived from the chemical potential of the ideal gas. Lecture 11: Fermi and Bose statistics Gibbs factor and Gibbs sum in diffusion equilibrium, in the same manner as Boltzmann factor and partition function in thermal equilibrium, are calculated and applied to fermi and Bose particles. Lecture 12: Carrier concentration in semiconductor A graph of Fermi-Dirac distribution will be drawn to explain its physical meaning in detail. Calculate the total number of particles by summing the Fermi distribution, and understand the number of carriers in the semiconductor. Lecture 13: p-type and n-type semiconductors Instructors will explain the Fermi-Dirac distribution under conditions where the negative charge and the positive charge cannot be neutralized, and derive the chemical potential that appears in the Fermi-Dirac distribution function. Lecture 14: p-n junction Instructors will explain that a potential difference is necessary for carrier diffusion equilibrium to occur across the contact interface between the p-type and n-type semiconductors. The resulting rectification of the diode will be introduced. Lecture 15: Summary, general exercises The whole set of lectures will be summarized and the level of comprehension will be measured. |
| Prerequisites |
| Review homework will be distributed for each lecture. At the beginning of the next lecture, we shall check the student’s comprehension level by giving a quiz related to the previous lecture. |
| Required Text(s) and Materials |
|
Thermal Physics Charles Kittel and Herbert Kroemer |
| References |
| Assessment/Grading |
|
A review test of the previous lecture will be conducted at the beginning of each lecture. One mid-term and one final exam will be conducted. Total value of quizzes, 60%; mid-term exam, 20%; final-term exam, 20%. |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| Contact via email. Be sure to include your name and student ID number in the text because emails from mobile phones often list the sender as anonymous. |
| Remarks 1 |
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| Lecture Language |
| English |
| Language Subject |
| Last update |
| 6/12/2020 11:45:38 AM |