Lecture 23: Direct and Cross Effects; General Principles of Entropy Production; The Fourth Law
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: Entropy production as sum of force-flux products. Linear force-flux laws for direct effects (Fourier, Fick, Ohm, Navier). Cross effects. Curie symmetry principle. Steepest entropy ascent and Fourth Law. Minimum global entropy production at steady state.
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_lec23_pdf/
Key moments:
00:00:00 - Introduction
00:00:22 - Review: Diffusive and Convective Fluxes
00:05:46 - Review: “Heat&Diffusion” Mode of Interaction
00:09:57 - General Balance Equation for an Extensive Property
00:13:41 - Extrinsic Relations for Entropy Production Density
00:34:27 - Force-Flux Shorthand Notation
00:36:34 - Material Resistance to Fluxes and Forces
00:42:26 - Direct Laws (Neglecting Cross Effects)
00:46:35 - Onsager Cross Effects and Curie Symmetry Principle
00:55:53 - Orthogonality Relations in the Linear Regime
00:59:30 - Orthogonality Relations in the Nonlinear Regime
01:02:13 - Material Resistance to Flux and Forces
01:09:03 - Steepest Entropy Ascent
01:10:10 - Graphical Illustration of Steepest Entropy Ascent
01:14:39 - Fourth Law of Thermodynamics
01:17:25 - Force-Flux Relations from Steepest Entropy Ascent
01:20:48 - The Fourth Law: Existence of a Dis
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Chapters (17)
Introduction
0:22
Review: Diffusive and Convective Fluxes
5:46
Review: “Heat&Diffusion” Mode of Interaction
9:57
General Balance Equation for an Extensive Property
13:41
Extrinsic Relations for Entropy Production Density
34:27
Force-Flux Shorthand Notation
36:34
Material Resistance to Fluxes and Forces
42:26
Direct Laws (Neglecting Cross Effects)
46:35
Onsager Cross Effects and Curie Symmetry Principle
55:53
Orthogonality Relations in the Linear Regime
59:30
Orthogonality Relations in the Nonlinear Regime
1:02:13
Material Resistance to Flux and Forces
1:09:03
Steepest Entropy Ascent
1:10:10
Graphical Illustration of Steepest Entropy Ascent
1:14:39
Fourth Law of Thermodynamics
1:17:25
Force-Flux Relations from Steepest Entropy Ascent
1:20:48
The Fourth Law: Existence of a Dis
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