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Physical Chemistry-Statistical Thermodynamics Preliminary
Physical Chemistry - Preliminary mind map of statistical thermodynamics, such as particles, molecules, atoms, ions, etc. gathered in gases, liquids, and solids are collectively called particles, or particles for short.
Edited at 2023-06-10 14:44:03- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- Project Management Process Template
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
Physical Chemistry-Statistical Thermodynamics Preliminary
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- Project Management Process Template
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
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Statistical Thermodynamics Preliminary
Basic concepts of statistical thermodynamics
Classification of Statistical Thermodynamic Systems
particle
Molecules, atoms, ions, etc. gathered in gases, liquids, and solids are collectively called particles, or particles for short.
microscopic particles
Molecules, atoms, protons, electrons, photons, etc.
Classification of classical and quantum descriptions of particles
Classic statistics
Based on classical mechanics - Boltzmann statistics
Quantum statistics
Quantum mechanics as the basis--Bose-Einstein statistics and Fermi-Dirac statistics
Classification according to particle motion
Localized subsystem (discernible particle system): solid
The position of the particles is fixed
motion localization
Particles at different positions can be numbered to distinguish them.
Delocalized subsystem (identical particle system): gas, liquid
The position of the particles is not fixed
Movement is chaotic
The position of the particle cannot be determined→indistinguishable
Classification according to the interaction between particles (This chapter only discusses independent subsystems)
Independent subsystem (nearly independent subsystem): ideal gas
A system in which interactions between particles are negligible
basic equations
Dependent subsystems: real gases, liquids, etc.
A system in which particle interactions cannot be ignored
Fundamentals of Quantum Mechanics
Quantum mechanical description of microscopic particle motion
particle
wave function
energy
degeneracy
The phenomenon that different quantum states have the same energy, that is, correspond to the same energy level, is called degeneracy
The number of independent quantum states corresponding to the same energy level is called the degeneracy of the energy level, also known as the statistical weight.
An energy level with a degeneracy of 1 is also called a non-degenerate energy level.
system
a set of distributions
Three-dimensional translational mover
The lowest energy is 3A (nearly 0)
The energy level interval is too small and can be regarded as a continuous change.
Diatomic molecular rigid rotor
One-dimensional harmonic oscillator
Energy level distribution
satisfy
state distribution
satisfy
Qualitative conclusion
N, then W
Occupies the energy level, then W
g, then W
Calculation of microstate numbers of energy level distribution of localized subsystems
1) N discernible particles are distributed at N different energy levels, that is, gi=1, ni=1
2)gi=1,ni¹1
3)gi¹1,ni¹1
Calculation of microstate numbers of energy level distribution of delocalized subsystems
1) Any energy level is non-degenerate, that is, gi=1
2) The energy level is degenerate, that is, gi¹1
Most probable distribution and Boltzmann distribution
1. The principle of equal probability - the basic assumption of statistical thermodynamics
2. The most probable distribution
3. Boltzmann distribution and partition function
(inherent conclusion)
q is the partition function of the particle
Boltzmann distribution
Calculation of particle partition function
Factorial Properties of Partition Functions
Selection of energy base point (zero point) and partition function
Calculation of translational partition function
The derivation process
example
Calculation of rotational partition function
Rotation characteristic temperature Qr
Symmetry number s
The derivation process
(Because it is approximately continuous, the sum can be converted into an integral)
Calculation of electron motion and nuclear motion partition functions
Ensemble (system of dependent particles)
Limitations of Boltzmann statistics
(1) Only applicable to nearly independent particle systems
(2) Only applicable to isolated particle systems
Ensemble definition
A large collection of independent specimen systems
Specimen system: a microscopic state of the macroscopic system under study
Classification
Microcanonical ensemble: [U, V, N], isolated system
Canonical ensemble: [T, V, N], closed system
Giant canonical ensemble: [T, V, m], open system