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 Dissipative Metric
01:24:26 - Bejan's “Constructal Law” of Design and Evolution
01:28:44 - Maximal Local EP Selects the Hydrodynamic Pattern
01:33:26 - Minimum Entropy Production at Steady State
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
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 Dissipative Metric
01:24:26 - Bejan's “Constructal Law” of Design and Evolution
01:28:44 - Maximal Local EP Selects the Hydrodynamic Pattern
01:33:26 - Minimum Entropy Production at Steady State
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
MIT OpenCourseWare
A free and open online publication of educational material from thousands of MIT courses, covering the entire MIT curriculum, ranging from introductory to the most advanced graduate courses. On the OCW website, each course includes a syllabus, instruction...