Free online courseStatistical Thermodynamics
Duration of the online course: 3 hours and 52 minutes
New course
Explore statistical thermodynamics online, mastering core concepts and practical applications. Ideal for anyone looking to deepen their physics knowledge.
In this free course, learn about
- Foundations of Statistical Thermodynamics
- Stirling Approximation and Large Systems
- Entropy and Microstates in Particle Distributions
- Combinatorics of Molecules in Compartments
- Stirling Approximation in Entropy and Gas Processes
- Energy Levels, Degeneracy, and Quantum States
- Quantum Numbers and Macroscopic Gases
Course Description
Delve into the fascinating world of statistical thermodynamics with this comprehensive online course designed to equip learners with a thorough understanding of core concepts. Explore foundational terms and concepts that form the backbone of statistical thermodynamics, ensuring you grasp the purpose and objectives that guide this intricate field.
Engage with detailed explorations on crucial topics like the average occupation number and the calculation of microstates. The course guides you through Stirling's approximation, offering both further explanations and a concise summary. Examine the detailed analyses of the number of microstates across various scenarios, from small systems with N=10 to large ones with N=1000.
Gain insight into how microstates operate within multi-energy state systems, and learn about the definition and calculation of entropy. Explore the dynamics of molecules in confined spaces with varying divisions—from halves to multiple equal sections—providing a detailed view of microstates in action.
The lessons address key questions about entropy and Sterling's Approximation, cover the dynamic shifts in entropy for moving molecules, and tackle improbability versus impossibility. Additional topics include probability comparison to macrostates, methods for counting with distinguishable molecules, and unique energy level examples.
Discover what it means for a state to be degenerate, delve into the potential wells, and learn techniques for determining quantum numbers. Each segment is crafted to build your understanding step by step, ensuring you emerge with a robust knowledge of statistical thermodynamics.
Course content
- Video class: Physics 32.5 Statistical Thermodynamics (1 of 39) Basic Term and Concepts 06m
- Exercise: Counting microstates for a two-state assembly
- Video class: Physics 32.5 Statistical Thermodynamics (2 of 39) Purpose and Objective Statistical Thermodynamics 05m
- Exercise: Why is statistical thermodynamics essential for analyzing macroscopic assemblies?
- Video class: Physics 32.5 Statistical Thermodynamics (3 of 39) Understanding Statistical Thermodynamics 1 04m
- Exercise: For four fair coin tosses, what is the thermodynamic probability W_k (multiplicity) for the macrostate with two heads and two tails?
- Video class: Physics 32.5 Statistical Thermodynamics (4 of 39) Understanding Statistical Thermodynamics 2 05m
- Exercise: Which macrostate has the highest number of microstates for four coins with two energy levels?
- Video class: Physics 32.5 Statistical Thermodynamics (5 of 39) The Average Occupation Number 03m
- Exercise: Average occupation number of heads in a four-coin system
- Video class: Physics 32.5 Statistical Thermodynamics (6 of 39) Calculate the Number of Microstates 06m
- Exercise: How many microstates exist for the macrostate with 10 coin tosses yielding 5 heads and 5 tails?
- Video class: Physics 32.5 Statistical Thermodynamics (7 of 39) Stirling's Approximation Explained 09m
- Exercise: Using the large n factorial approximation, what is log10 of 100 factorial approximately equal to
- Video class: Physics 32.5 Statistical Thermodynamics (8 of 39) Stirling's Approximation: Summery 05m
- Exercise: Estimate the order of magnitude of 100! using Stirling approximation and base-10 conversion
- Video class: Physics 32.5 Statistical Thermodynamics (9 of 39) Number of Microstates Analyzed N=10 07m
- Exercise: Two state system with 10 objects maximum microstates
- Video class: Physics 32.5 Statistical Thermodynamics (10 of 39) Number of Microstates Analyzed N=50 07m
- Exercise: Relative microstate height 10 percent from the maximum for N = 50 two state system
- Video class: Physics 32.5 Statistical Thermodynamics (11 of 39) Number of Microstates Analyzed N=100 09m
- Exercise: In a two-state system with N = 100 objects, which distribution maximizes the number of microstates W?
- Video class: Physics 32.5 Statistical Thermodynamics (12 of 39) Number of Microstates Analyzed N=1000 10m
- Exercise: Multiplicity peak in a two-state system with N=1000
- Video class: Physics 32.5 Statistical Thermodynamics (13 of 39) Number of Microstates in a Multi-State System 07m
- Exercise: Counting microstates in a multi state system
- Video class: Physics 32.5 Statistical Thermodynamics (14 of 39) Number of Microstates in a Multi-Energy State Sys 05m
- Exercise: In a system with 3 distinguishable particles and four energy levels 0, e, 2e, 3e constrained to total energy U equal 3e, how many microstates are possible
- Video class: Physics 32.5 Statistical Thermodynamics (15 of 39) Definition of Entropy of a Microstate 05m
- Exercise: Which macrostate of four fair coins has the highest entropy?
- Video class: Physics 32.5 Statistical Thermodynamics (16 of 39) Definition of Entropy of a Microstate: Example 04m
- Exercise: For 6 molecules in a two-compartment box of equal size, what is the entropy change ΔS when going from all 6 in one compartment to the most probable state with 3 in each?
- Video class: Physics 32.5 Statistical Thermodynamics (17 of 39) Microstates 07m
- Exercise: Which statement best describes the thermodynamic probability W for a macrostate in 100 distinguishable coin tosses?
- Video class: Physics 32.5 Statistical Thermodynamics (18 of 39) 6 Molecules in a Box (Divided in Half) 08m
- Exercise: For six distinguishable molecules in a box divided into two halves, which macrostate has the highest entropy?
- Video class: Physics 32.5 Statistical Thermodynamics (19 of 39) 6 Molecules in a Box: Microstates in Detail 04m
- Exercise: A box is divided into two compartments by a partition. When the partition is removed and an ideal gas expands freely into the full volume, what happens to the internal energy and entropy of the gas
- Video class: Physics 32.5 Statistical Thermodynamics (20 of 39) 6 Molecules in a Box: Divided in 3 Equal Sections 05m
- Exercise: Entropy from number of microstates
- Video class: Playlist Organizer 01m
- Exercise: Which ensemble is appropriate for a system that can exchange both energy and particles with a reservoir
- Video class: Physics 32.5 Statistical Thermodynamics (21 of 39) 6 Molecules in a Box: Divided in 3 Equal Sections 04m
- Exercise: How many microstates exist for 6 distinguishable molecules in a box divided into 3 equal sections, counting all possible configurations?
- Video class: Physics 32.5 Statistical Thermodynamics (22 of 39) 6 Molecules in a Box: Divided in 3 Equal Sections 05m
- Exercise: How many total microstates exist for 6 distinguishable molecules distributed among 3 equal partitions?
- Video class: Physics 32.5 Statistical Thermodynamics (23 of 39) 6 Molecules in a Box: Divided in 6 Equal Sections 05m
- Exercise: Total microstates for 6 distinguishable molecules in 6 partitions
- Video class: Physics 32.5 Statistical Thermodynamics (24 of 39) N Molecules in a Box: Divided in N Equal Sections 04m
- Exercise: Microstates for n molecules in n partitions (one per partition)
- Video class: Physics 32.5 Statistical Thermodynamics (25 of 39) What is Sterling's Approximation? S = k ln n! 04m
- Exercise: Using Stirling's approximation, which value is closest to ln(100!)?
- Video class: Physics 32.5 Statistical Thermodynamics (26 of 39) What is Entropy of 1 mol of Gas Distributed? 04m
- Exercise: In applying Stirling approximation to compute S = k ln W for one mole with W = N!, which term can be neglected in ln(N!) for N ≈ Avogadro number?
- Video class: Physics 32.5 Statistical Thermodynamics (27 of 39) Entropy Change for Moving N Molecules 04m
- Exercise: For an isothermal compression of an ideal gas where N molecules move from volume V1 to smaller volume V2, which expression gives the entropy change Delta S
- Video class: Physics 32.5 Statistical Thermodynamics (28 of 39) Improbability vs Impossibility 05m
- Exercise: For 10 ideal gas molecules in volume V1, what is the probability that at an instant all are found in the subvolume V1 divided by 2
- Video class: Physics 32.5 Statistical Thermodynamics (29 of 39) Probability Compared to Macrostates 06m
- Exercise: Probability that six molecules are all in one half of a box
- Video class: Physics 32.5 Statistical Thermodynamics(30 of 39) 6 Distinguishable Molecules in a Box with 2 Halves 06m
- Exercise: Total microstates for six distinguishable molecules in a two-compartment box
- Video class: Physics 32.5 Statistical Thermodynamics (31 of 39) General Counting Method for w 07m
- Exercise: Microstates for distributing N distinguishable particles among n energy levels
- Video class: Physics 32.5 Statistical Thermodynamics (32 of 39) Energy Level Example 1 05m
- Exercise: For three distinguishable particles in levels n0 n1 n2 n3 with total energy 3 quanta, how many microstates correspond to the macrostate with one particle in n0, one in n1, and one in n2
- Video class: Physics 32.5 Statistical Thermodynamics (33 of 39) Energy Level Example 2 07m
- Exercise: Total microstates for three distinguishable particles with total energy 4 quanta across levels 0, 1, 2, 3
- Video class: Physics 32.5 Statistical Thermodynamics (34 of 39) Energy Level Example 3 08m
- Exercise: Total microstates for six distinguishable particles with total energy 4 quanta across five energy levels
- Video class: Physics 32.5 Statistical Thermodynamics (35 of 39) What is a Degenerate Quantum State? 04m
- Exercise: Degree of degeneracy for p orbitals at the same energy
- Video class: Physics 32.5 Statistical Thermodynamics (36 of 39) The One-Dimensional Potential Well 04m
- Video class: Physics 32.5 Statistical Thermodynamics (37 of 39) The Three-Dimensional Potential Well 03m
- Exercise: How do energy levels scale with volume in a cubic 3D infinite potential well
- Video class: Physics 32.5 Statistical Thermodynamics (38 of 39) Find the Quantum Number of Volume L^3 of He Ex1 04m
- Exercise: For helium at 298 K in a 0.10 m cubic box, estimate the 1D quantum number n using de Broglie wavelength with v_rms and n = L divided by half wavelength.
- Video class: Physics 32.5 Statistical Thermodynamics (39 of 39) Find the Quantum Number of Volume L^3 of He Met 2 02m
- Exercise: Estimate the effective quantum number n for a helium atom confined in a cubic box of side 0.10 m at 298 K using E = 3/2 k T and E = n^2 π^2 ħ^2 / (2 m V^{2/3})
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