Lecture 9: Minimum Work of Partitioning Small Systems; The Gibbs Phase Rule; The Van der Waals Model
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: Minimum work of partitioning small systems. Review of equilibrium properties of pure substances. Gibbs phase rule. Clausius-Clapeyron relation. Representation on p-T, u-v-s, h-s, p-v diagrams. The van der Waals model of metastable liquid and vapor states.
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_lec09_pdf/
Key moments:
00:00:00 - Introduction
00:00:09 - Results So Far Hold for Large and Small Systems
00:00:53 - Review: Microscopic and Mesoscopic vs Macroscopic
00:02:18 - Review: Rarefaction Effects Near Walls
00:04:06 - Review: Neglecting Effects of Partitions
00:04:24 - Review: Simple-System Model Limiting Assumptions
00:04:58 - Review: Simple-System Model Implies Euler Relation
00:07:19 - Review: Main Consequence of Euler Relation
00:08:20 - Small Systems: Specific Properties Dependences
00:11:50 - Small Systems: Minimum Work of Partitioning
00:18:21 - Basic Simple-System Models for Pure Substances
00:19:02 - Extensive Properties (Definition)
00:21:45 - Specific Properties (Definition)
00:24:20 - Intensive Properties and Intensive State
00:26:48 - Homogeneous vs Heterogeneous States; Phases
00:32:29 - Gibbs Phase Rule (Proof)
00:39:25 - Gibbs Phase Rule (for a Pure Substance)
00:47:27 - Fundamental Relation for a Pure Substance
00:49:23 - Ideal Incompressible Solid or Fluid Model
00:53:35 - Ideal Gas Model
01:04:28 - Two-Phase States of a Pure Substance
01:09:28 - Properties Liquid-Vapor States of a Pure Substance
01:14:10 - Graphical Representation of Fundamental Relation
01:17:35 - The u-s-v Fundamental Surface (Water)
01:19:04 - The Mollier h-s Diagram (Water)
01:19:50 - The $p$-$v$ Diagram (Water)
01:20:47 - The $p$-$v$ Diagram (Van der Waals Model)
01:30:15 - Exergies and Efficiencies in Energy Conversion
01:30:38 - Exergy and Second-Law Efficiency in Cogeneration
01:31:04 - Exergy of Bulk Flow Interactions
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: Minimum work of partitioning small systems. Review of equilibrium properties of pure substances. Gibbs phase rule. Clausius-Clapeyron relation. Representation on p-T, u-v-s, h-s, p-v diagrams. The van der Waals model of metastable liquid and vapor states.
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_lec09_pdf/
Key moments:
00:00:00 - Introduction
00:00:09 - Results So Far Hold for Large and Small Systems
00:00:53 - Review: Microscopic and Mesoscopic vs Macroscopic
00:02:18 - Review: Rarefaction Effects Near Walls
00:04:06 - Review: Neglecting Effects of Partitions
00:04:24 - Review: Simple-System Model Limiting Assumptions
00:04:58 - Review: Simple-System Model Implies Euler Relation
00:07:19 - Review: Main Consequence of Euler Relation
00:08:20 - Small Systems: Specific Properties Dependences
00:11:50 - Small Systems: Minimum Work of Partitioning
00:18:21 - Basic Simple-System Models for Pure Substances
00:19:02 - Extensive Properties (Definition)
00:21:45 - Specific Properties (Definition)
00:24:20 - Intensive Properties and Intensive State
00:26:48 - Homogeneous vs Heterogeneous States; Phases
00:32:29 - Gibbs Phase Rule (Proof)
00:39:25 - Gibbs Phase Rule (for a Pure Substance)
00:47:27 - Fundamental Relation for a Pure Substance
00:49:23 - Ideal Incompressible Solid or Fluid Model
00:53:35 - Ideal Gas Model
01:04:28 - Two-Phase States of a Pure Substance
01:09:28 - Properties Liquid-Vapor States of a Pure Substance
01:14:10 - Graphical Representation of Fundamental Relation
01:17:35 - The u-s-v Fundamental Surface (Water)
01:19:04 - The Mollier h-s Diagram (Water)
01:19:50 - The $p$-$v$ Diagram (Water)
01:20:47 - The $p$-$v$ Diagram (Van der Waals Model)
01:30:15 - Exergies and Efficiencies in Energy Conversion
01:30:38 - Exergy and Second-Law Efficiency in Cogeneration
01:31:04 - Exergy of Bulk Flow Interactions
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.
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