Thermal and Statistical Mechanics

Course title

S2094000

Course description

Thermodynamical and statistical physics is one of the most important study in engineering. If you want to participate in industry as an engineer, you must learn and understand its basic philosophy, technical terms, and how the idea is applied to real substances. It involves in heat efficiency, environment, and material sciences, which are well-known applications of this study. Recently, it extends its application to various new field such as information science, economy, social science, and biology. Therefore, a need for this study is increasing very much.

The first part of this lecture deals with the thermodynamics. It studies thermal phenomena from the macroscopic point of view. We learn two novel laws of thermodynamics in this part. The internal energy, entropy, and free energy are typical keywords here. The second part is the statistical physics. It studies thermal phenomena from the microscopic point of view. We connect a realization of a thermal state with the probability. Entropy is defined by a logarithms of a realization number. We learn how the microscopic state and its energy contribute to the thermal state. The partition function is the most important keyword here. Various physical quantities are deduced from the partition function.

Purpose of class

To understand The First Law of Thermodynamics and The Second Law of Thermodynamics.
To solve real problems about heat using these laws, particularly heat efficiency of a heat engine.
To understand the principle of Boltzmann statistics: a realization of thermal state has the maximum of its probability.
To solve real problems about the statistical physics: calculations of a partition function, free energy, internal energy, heat capacity.

Goals and objectives

	Goals and objectives	Course Outcomes
1.	One can explain what is a basic law of thermodynamics, what is temperature, what is entropy, and what is a free energy.
2.	One can calculate a work in quasi-static process and a heat capacity of an ideal gas.
3.	One can explain Carnot cycle, and can explain its efficiency. One can also apply it to various heat engine.
4.	One can explain the principles of statistical physics.
5.	One can calculate various physical quantities on two-level systems, on ideal gas, an on harmonic oscillator.

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Report and short test	Total.
1.	10%	10%
2.	10%	10%
3.	30%	30%
4.	15%	15%
5.	35%	35%
Total.	100%	-

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	The first law of thermodynamics I What is a temperature? What is a heat?	Equation for an ideal gas The first law of thermodynamics (Textbook p. 7-31)	190分
2.	The first law of thermodynamics II A work in quasi-static process What is a heat capacity?	Differentiations and integrations of logarithmic functions Partial differentiations (Textbook p.32-38)	190分
3.	The first law of thermodynamics III 　A heat capacity of ideal gas 　An adiabatic process	Ideal gas (Textbook p.38-42)	190分
4.	The second law of thermodynamics I Carnot cycle and entropy	Carnot cycle (Textbook p.46-50)	190分
5.	The second law of thermodynamics II Reversible and irreversible Flow chart of energy and entropy Heat efficiency of various engines	Heat engine and heat pomp (Textbook p.51-52)	190分
6.	The second law of thermodynamics III Irreversibility and entropy A microscopic description for entropy	Entropy change and its increase (Textbook p.63-67)	190分
7.	Thermodynamic functions A free energy A thermodynamic equality A phase and an equilibrium	Free energy Chemical potential (Textbook p.74-76, 82-83)	190分
8.	Classical statistical physics Microcanonical ensembles and canonical ensembles Formulation for statistical physics Boltzmann's principles	Canonical ensemble (Textbook p.108-113)	190分
9.	Application of canonical statistical physics I 　A two-level system	Two-level system (Textbook p.141-143, 148-149)	190分
10.	Application of canonical statistical physics II 　An ideal gas	Gauss integration (Textbook p.115-116)	190分
11.	Application of canonical statistical physics III 　An ideal gas as Gibbs pardox DNA and zipper model	Gibbs paradox (Textbook p.134-136)	190分
12.	Application of canonical statistical physics IV 　A classical harmonic oscillator	Harmonic oscillator (Textbook p.148)	190分
13.	Application of canonical statistical physics V A quantum harmonic oscillator (Einstein model)	Harmonic oscillator (Textbook p.149)	190分
14.	Summary and discussion Some extra topics What is thermodynamic and statistical physics?	All of this lecture	190分
Total.	-	-	2660分

Evaluation method and criteria

Report and short test point (100%)

A report point exceeds 60%

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in the class

Textbooks and reference materials

Textbook
・「ゼロからの熱力学と統計力学」　和達三樹、十河清、出口哲生著　岩波書店

Reference book
"Thermal physics" 2nd. Ed. C. Kittel

Prerequisites

Must be very familiar with differentiation and integration of various functions (log, exp, sin, cos and their combinations)
Must be very familiar with the energy and potentials in classical mechanics.
Must be familiar with the total differentiation and the partial differentiation.
Must have received credit for Mechanics or Introduction to physics.

Office hours and How to contact professors for questions

30 minutes after the lecture in the classroom.
Please contact by e-mail in case of emergency.
On-line students also contact by e-mail and arrange the zoom meeting.

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge

Active-learning course

About half of the classes are interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	N/A

Education related SDGs:the Sustainable Development Goals

9.INDUSTRY, INNOVATION AND INFRASTRUCTURE

Last modified : Sat Jun 29 04:46:36 JST 2024