2016 Thermodynamics for Phase Equilibria

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Academic unit or major
Graduate major in Materials Science and Engineering
Kajihara Masanori  Sone Masato 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(J234)  Thr3-4(J234)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

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.

Student learning outcomes

・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.


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

Competencies that will be developed

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/Required learning

  Course schedule Required learning
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 the 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 Jacobi method Explain application of Jacobian into thermodynamics
Class 9 The extremum princip for various fundamental equations Explain concept of extremum principle for various fundamental equations
Class 10 Equilibrium state and reversible process Explain equilibrium state and reversible process in thermodynamics
Class 11 Phase equilibiria for multicomponent system Explain concept of phase equilibria for multicomponent system
Class 12 Gibbs phase rule Explain concept of Gibbs phase rule and the application
Class 13 Thermodynamic caliculation of Equilibrium diagram Explain the detail in thermodynamic calculation of equilibrium phase diagram
Class 14 Regular solution Explain concept of regular solution
Class 15 Driving force in precipitation reaction Explain driving force in precipitation reaction



Reference books, course materials, etc.


Assessment criteria and methods

Evaluation by examinations.

Related courses

  • MAT.A204 : Thermodynamics of Materials

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None required

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

M.Kajihara (kajihara[at]materia.titech.ac.jp)
M.Sone (sone.m.aa[at]m.titech.ac.jp)

Office hours

Contact by email


None required

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