2019 Physical Chemistry (Statistical Mechanics)

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Ougizawa Toshiaki 
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Course description and aims

This course focuses on the basics of statistical thermodynamics including entropy, Boltzmann distribution, partition function and the thermodynamics function that then is led. First, explanation is provided on what statistical thermodynamics is and its importance.
In the study of materials, thermodynamics is essential. It is important to understand by combining macro-thermodynamics with micro-thermodynamics, which is the statistical thermodynamics. It is desirable to understand the basic concepts of entropy, enthalpy, and the free energy function influencing thermodynamics from a statistical perspective.

Student learning outcomes

By the end of this course, students will be able to understand:
1) The basics of entropy, Boltzmann distribution, partition function, and thermodynamic functions
2) The relation between the mathematical concept with statistics and thermodynamics
3) Important points of statistical thermodynamics in the study of materials


Entropy, Stirling's approximation, Boltzmann distribution, Boltzmann formula, Molecular partition function, Canonical ensemble, Internal energy, Free energy function, Equation of state

Competencies that will be developed

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

Based on a textbook, I push forward a lecture with questions. In addition, at the beginning of each class, solutions of the quiz (small test) in the previous class are reviewed. Towards the end of class, students are given a quiz related to the lecture given that day to solve.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction: What is the statistical thermodynamics? Relation between thermodynamics and statistics
Class 2 Review of entropy Basics of entropy (Review of classical thermodynamics)
Class 3 Boltzmann distribution and molecular patrition function Derivation of Boltzmann distribution and its relation with molecular partition function
Class 4 Molecular partition function and population (occupancy) Way of the distribution of the molecules to energy levels
Class 5 Canonical ensemble and Canonical partition function Concept of ensemble and way of thinking of statistical mechanics model
Class 6 Partition function and thermodynamic functions Derivation of thermodynamic functions from partition function
Class 7 Equation of state Derivation of equation of state from partiticon function
Class 8 Applications of statistical thermodynamics Applications of partition function to material studies


Atkins' PHYSICAL CHEMISTRY, 10th Edition; Chapter 15(Statistical thermodynamics); Oxford University press (2014)

Reference books, course materials, etc.

None required.

Assessment criteria and methods

Evaluation is carried out by quizzes of every time and a term-end examination.

Related courses

  • MAT.A204 : Thermodynamics of Materials
  • MAT.P204 : Physical Chemistry (Thermodynamics)

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

No prerequisites are necessary, but enrollment in the thermodynamics of physical chemistry is desirable.T
Taking this class with Statistical Mechanics (M)(MAT.M202) and Statistical Mechanics (C)(MAT.C203) redundantly is prohibited.

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