2021 Faculty Courses School of Materials and Chemical Technology Department of Materials Science and Engineering Graduate major in Materials Science and Engineering

Thermodynamics for Phase Equilibria

Academic unit or major: Graduate major in Materials Science and Engineering
Instructor(s): Masato Sone / Masaki Tahara
Class Format: Lecture
Media-enhanced courses: -
Day of week/Period (Classrooms): 3-4 Mon / 3-4 Thu
Class: -
Course Code: MAT.M409
Number of credits: 200
Course offered: 2021
Offered quarter: 1Q
Syllabus updated: Jul 10, 2025
Language: English

Syllabus

Course overview and goals

Thermodynamics is one of the most important fundamental sciences. In this lecture, the fundamental aspects in thermodynamics of materials science are explained on the focus of metallic alloys which are relatively easy in analytical treatments. Through precise reviewing the fundamental thermodynamic principles "first and second laws of thermodynamics", students understand stability conditions of thermodynamic systems such as "the energy minimum principle" and "the entropy maximum principle". The equilibrium state of materials can be described by the fundamental equation. On this concept, thermodynamic calculation of equilibrium phase diagram is introduced.

Course description and aims

・Students acquire basic knowledge of the basic laws and principles in thermodynamics.
・Students understand relationships between the independent and conjugate variables of the fundamental equation.
・Students understand equilibrium states for given combination of the independent variables.

Keywords

Internal energy, entropy, first law, second law, fundamental equation, Equilibrium, Legendre transformation, Maxwell relations, Jacobian, Gibbs phase rule, regular solution

Competencies

Specialist skills
Intercultural skills
Communication skills
Critical thinking skills
Practical and/or problem-solving skills

Class flow

On handouts, every topics of the classes are explained.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	First and second laws of thermodynamics	Explain concept of first and second laws of thermodynamics
Class 2	The internal energy and the entropy	Explain concept of internal energy and entropy
Class 3	The fundamental equation and the conjugate variable	Explain the fundamental equation in thermodynamics and the independent and conjugate variables
Class 4	The fundamental equation of multicomponent system	Explain the fundamental equation of multicomponent system in thermodynamics
Class 5	Evaluation of equilibrium state	Explain concept of equilibrium state
Class 6	Legendre transformation	Explain concept of Legendre transformation
Class 7	The Maxwell relations	Explain concept of the Maxwell relations
Class 8	The extremum princip for various fundamental equations	Explain concept of extremum principle for various fundamental equations
Class 9	Equilibrium state and reversible process	Explain equilibrium state and reversible process in thermodynamics
Class 10	Phase equilibiria for multicomponent system	Explain concept of phase equilibria for multicomponent system
Class 11	Gibbs phase rule	Explain concept of Gibbs phase rule and the application
Class 12	Thermodynamic caliculation of equilibrium phase diagram	Explain detail in thermodynamic calculation of equilibrium phase diagram
Class 13	Regular solution	Explain concept of regular solution
Class 14	Driving force in precipitation reaction	Explain driving force in precipitation reaction

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

TBD

Reference books, course materials, etc.

Handouts

Evaluation methods and criteria

Evaluation by examinations.

Related courses

MAT.A204 ： Thermodynamics of Materials

Prerequisites

None required

Other

None required