# Statistical Thermodynamics

This specialized course delves into the fundamental principles of Statistical Thermodynamics, catering to advanced undergraduate and graduate students in mechanical or aerospace engineering. It equips learners with the knowledge to bridge the gap between macroscopic and microscopic thermodynamics, exploring the behavior of ideal gases, dense gases, liquids, and solids.

Through a postulatory approach, students will gain a deep understanding of temperature, thermodynamic pressure, and chemical potential, while also delving into quantum mechanics and its impact on atomic and molecular structural behavior. The course also covers the analysis of non-equilibrium phenomena, incorporating computational skills to estimate material behavior.

• Explore the connection between atomic/molecular structure and macroscopic properties
• Gain insights into modern quantum chemistry numerical solution methods
• Analyze the behavior of ideal gases and their industrial applications
• Evaluate the impact of intermolecular forces on the transition of gases to liquids
• Recognize the role of spectroscopic methods in determining the thermodynamic state of a system

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##### Course Modules

Statistical Thermodynamics modules cover fundamental concepts, quantum mechanics, ideal gases, dense gases/liquids/solids, and non-equilibrium applications. Gain insights into macroscopic and microscopic thermodynamics and computational skills.

#### Fundamentals of Macroscopic and Microscopic Thermodynamics

Explore the concept of temperature, thermodynamic pressure, and chemical potential from a postulatory perspective, elucidating the Fundamental Relation’s role in establishing connections between atomic/molecular structure and macroscopic properties.

#### Quantum Mechanics

Delve into the relationship between the Schrödinger wave equation and atomic/molecular structural behavior, and understand modern quantum chemistry numerical solution methods for solving the wave equation. Analyze the role of quantum mechanics in explaining atomic and molecular structural behavior.

#### Ideal Gases

Analyze the behavior of monatomic, diatomic, and polyatomic ideal gases under various conditions, distinguishing between pure ideal gases and ideal gas mixtures, and identifying the key components of partition functions used to describe translational, rotational, vibrational, and electronic motion.

#### Dense Gases, Liquids and Solids

Analyze the impact of intermolecular forces on the transition of gases to liquids as density increases, evaluate the stability of a thermodynamic system as it transitions from gas to liquid state, and assess the role of the radial distribution function (RDF) in determining thermodynamic properties of liquids. Describe the behavior of crystalline solids using simple statistical thermodynamics.

#### Non-Equilibrium Applications of Statistical Thermodynamics

Recognize the role of spectroscopic methods in determining the thermodynamic state of a system, utilize the Boltzmann Equation and the Chapman-Enskog solution to determine transport properties in dense gases and liquids, and analyze the impact of reaction rates and rate constants on fluid/thermal applications such as combustion.

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