Lecture 13: The Gibbs Paradox; Shannon Information Entropy; Single Quantum Particle in a Box
MIT 2.43 Advanced Thermodynamics, Spring 2024
Instructor: Gian Paolo Beretta
View the complete course: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/
Complete course table of contents with hyperlinks to slides and video timestamps: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_toc_slides_pdf/
Complete course analytical index with hyperlinks to slides and video timestamps: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_index_slides_pdf/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP6309d0oJDiVo1CvxUQXJ2il
This lecture covers: Extracting the adiabatic availability of mixing. Semipermeable membranes. Gibbs paradox. Shannon information entropy. Quantum model for the stable equilibrium states of a single particle in a box. Ideal gas equation of state for a single particle in a box.
Instructor suggests to set viewing speed at 1.5 for faster learning.
Slides for this lecture: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_lec13_pdf/
Key moments:
00:00:00 - Introduction
00:00:22 - Review: Stable-Equilibrium Properties of Mixtures
00:00:41 - Review: Properties of Isothermobaric Mixing
00:01:09 - Review: Lennard-Jones Potential
00:02:33 - Review: Ideal Gibbs-Dalton Behavior
00:04:29 - Review: Ideal Gibbs-Dalton Mixtures of Ideal Gases
00:05:27 - Review: Mixing of Ideal Gases; Entropy of Mixing
00:06:33 - Review: Adiabatic Availability of Mixing
00:09:26 - Semipermeable Membranes
00:11:53 - Gibbs Paradox (Resolved)
00:22:17 - Information Theory Interpretation: Shannon Entropy
00:38:17 - Quantum Model of a Structureless Particle in a Box
01:03:34 - Energy and Entropy from Quantum Probabilities
01:10:12 - Steepest Entropy Ascent Evolution of Probabilities
01:13:48 - Ideal Gas Equation of State for a Single Particle
01:35:36 - Introducing Ideal Solution Behavior
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Chapters (16)
Introduction
0:22
Review: Stable-Equilibrium Properties of Mixtures
0:41
Review: Properties of Isothermobaric Mixing
1:09
Review: Lennard-Jones Potential
2:33
Review: Ideal Gibbs-Dalton Behavior
4:29
Review: Ideal Gibbs-Dalton Mixtures of Ideal Gases
5:27
Review: Mixing of Ideal Gases; Entropy of Mixing
6:33
Review: Adiabatic Availability of Mixing
9:26
Semipermeable Membranes
11:53
Gibbs Paradox (Resolved)
22:17
Information Theory Interpretation: Shannon Entropy
38:17
Quantum Model of a Structureless Particle in a Box
1:03:34
Energy and Entropy from Quantum Probabilities
1:10:12
Steepest Entropy Ascent Evolution of Probabilities
1:13:48
Ideal Gas Equation of State for a Single Particle
1:35:36
Introducing Ideal Solution Behavior
🎓
Tutor Explanation
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