### Thermodynamics and Statistical Physics

Course Code:B22002Y-02

Course Name: Thermodynamics and Statistical Physics

Credits: 4.0

Level: Undergraduate

Pre-requisite: Thermal Physics, Calculus, Method of Mathematical Physics

Lecture Time: 40 sessions, 2 hours/session

Course Description

Thermodynamics and Statistical Physics is a professional basic coursefor physics majors. It is a theoretical course to study the thermal phenomena and the laws of thermal motion of macroscopic systems composed of a large number of microscopic particles. Thermodynamics is based on basic laws obtained from a large number of experimental results, and research on the macroscopic properties of the object and the thermal phenomena by strict logical reasoning and mathematical operation, so its results are universal and reliable, but can’t derive specific characteristics of concrete material. Statistical physics starts from the microscopic structure of material, to consider the thermal motion of microscopic particles, and by the statistical average method to study the thermal properties of macroscopic objects and the laws related to the thermal phenomena. It can reveal the characteristic of concrete material, but the reliability depends on the assumption of microstructure. The tasks of the two research ways are the same, and they are complementary to each other, although the research methods are different. Through the study of this course, students should master the basic concepts, basic principles and basic methods of thermodynamics and statistical physics. Thermodynamics and statistical physics is the most widely used course, and we hope students achieve the goal of applying what they have learned.

Topics and Schedule

Chapter 1. Basic Laws of Thermodynamics (6 hrs)

Main Content: Equation of state; thermometer principle; the first law of thermodynamics; the second law of thermodynamics; the third law of thermodynamics.

Requirement: If given equation of state, students can skillfully obtain the constant pressure expansion coefficient, the constant volume pressure coefficient, and the isothermal compression coefficient, or determine the equation of state with any two of the three efficient known; Students are required to skillfully calculate heat and work of some process, master the calculation of the three TdS equations and entropy change of reversible process, and understand the expression and significance of the third law.

Chapter 2. Thermodynamic Functions and Relations (6 hrs)

Main Content: Enthalpy, free energy and Gibbs function; Characteristic function and Maxwell relation; the thermodynamics of the homogeneous material; the thermodynamics of the thermal radiation.

Requirement: Understand and master the intention of introducing enthalpy, free energy and Gibbs's function and remember the two state variables in each of the four characteristic functions; Skillfully use the Maxwell relation to prove the thermodynamic equation of reversible process; Understand the thermodynamics of magnetic media, dielectrics and radiation fields.

Chapter 3. Phase Equilibrium and Phase Transformation (4 hrs)

Main Content:  Phase rule; Clapeyron equation; Equilibrium and transition of the two phases, gas-liquid; classification of phase transition.

Requirement: Master the derivation of the Clapeyron equation; Skillfully analyze the gas-liquid phase equilibrium and transition process; Master Van der Waals isothermal curve and Maxwell equal area rule; Understand classification of phase transitions and critical phenomena.

Chapter 4. Statistical Thermodynamics (4 hrs)

Main Content: Thermodynamic probability; Boltzmann formula; quantum mechanical description of microscopic state.

Requirement: Master thermodynamic probability and Boltzmann formula; Skillfully calculate classical and quantum states number; Understand the thermodynamic fluctuations and the significance of microscopic reversible and macroscopic irreversible property of thermodynamic system; This part is the bridge between thermodynamics and statistical physics.

Chapter 5. Boltzmann Statistics (10 hrs)

Main Content: Boltzmann distribution of single particle equilibrium state; partition function method; equipartition theorem; application of Boltzmann statistics.

Requirement: Be proficient in calculation of phase volume and states density; fully understand the concept of phase lattice; understand the derivation process of Boltzmann distribution; Skillfully calculate the partition function and determine the various thermodynamic functions of the system according to the partition function; Master derivation of equipartition theorem; Master Quantum constant volume heat capacity of double atom molecule ideal gas.

Chapter 6. Ensemble Theory (8 hrs)

Main Content: Three ensembles and their relations; the distribution function of the canonical ensemble; the grand canonical ensemble distribution function.

Requirement: Understand the derivation of the distribution function of the canonical ensemble, and master canonical partition function and the calculation of its thermodynamic function; Understand grand partition function; Master the relationship between three kinds of ensemble, and correctly understand Gibbs correction factor and the Gibbs paradox.

Chapter 7. Quantum statistics (8 hrs)

Main Content: Bosons and fermions; Fermi-Dirac distribution and Bose-Einstein distribution; free electron gas; Bose-Einstein condensation.

Requirement: Master the derivation of Fermi-Dirac distribution and Bose-Einstein distribution; Master the conditions for the transition from quantum statistics to classical statistics; Remember the definition of the Fermi energy; Master the calculation of the average energy of an electron and zero point pressure in the situation of zero temperature limit, and apply it to the metal model; Understand the Bose-Einstein condensation mechanism.

Chapter 8. Primary course of non-equilibrium statistical physics (4 hrs)

Main Content: Boltzmann equation; H theorem; Brown motion; molecular motor.

Requirement: Understand the derivation of Boltzmann equation; Master the relationship between H function and entropy; Know the basis of macroscopic Non-reversible process; Master the Brown movement model.

Chapter 9. Introduction to the frontiers of statistical physics (4 hrs)

Requirement: This part comes as an extension outside of the scope of examinations, but it will significantly help students carry out academic research.

Chapter 10. Random Arrangement (4 hrs)

This part will be arranged for midterm test and final review.

Grading

Daily Performance (homework, academic report and discussion) 40%
Midterm Examination  20%  Closed-book written examination
Final Examination     40%  Closed-book written examination

Textbook

Zhi-Cheng Wang, Thermodynamics, Statistical Physics, Fifth Edition, Higher Education Press, 2013

References

[1] Zhi-Cheng Wang, Thermodynamics, Statistical Physics, Fifth Edition, Higher Education Press, 2013;
[2] Jing-Dong Bao, Concise Course of Thermodynamics and Statistical Physics, Higher Education Press, 2011;
[3] David Chandler, Guo-Xing Ju (Translator), Introduction to modern statistical mechanics, Higher Education Press, 2013;
[4] Zong-Han Lin, Thermodynamics and Statistical Physics, Peking University press, 2007

[5] Hui-Chuan Shen, Statistical Mechanics, University of Science & Technology of China Press, 2011;

[6] Zi-Fang Zhou, Lie- Zhao Cao, Thermal, Thermodynamics and Statistical physics, Science Publishing Company, 2014.