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Lecture 9: Minimum Work of Partitioning Small Systems; The Gibbs Phase Rule; The Van der Waals Model

Lecture 9: Minimum Work of Partitioning Small Systems; The Gibbs Phase Rule; The Van der Waals Model

Published 2 months ago
Description

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

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