advanced thermodynamics engineering - thermodynamics.abdphysics.org

Nomenclature**

Introduction

Importance, Significance and Limitations
Limitations of Thermodynamics
- System and Boundary
- Simple System
- Constraints and Restraints
- Composite System
- Phase
- Homogeneous
- Pure Substance
- Amount of Matter and Avogadro Number
- Mixture
- Property
- State
- Equation of State
- Standard Temperature and Pressure
- Partial Pressure
- Process
- Vapor–Liquid Phase Equilibrium
Mathematical Background
- Explicit and Implicit Functions and Total Differentiation
- Exact (Perfect) and Inexact (Imperfect) Differentials
  - Mathematical Criteria for an Exact Differential
- Conversion from Inexact to Exact Form
- Relevance to Thermodynamics
  - Work and Heat
  - Integral over a Closed Path (Thermodynamic Cycle)
- Homogeneous Functions
  - Relevance of Homogeneous Functions to Thermodynamics
- Taylor Series
- LaGrange Multipliers
- Composite Function
- Stokes and Gauss Theorems
  - Stokes Theorem
  - Gauss–Ostrogradskii Divergence Theorem
  - The Leibnitz Formula
Overview of Microscopic Thermodynamics
- Matter
- Intermolecular Forces and Potential Energy
- Internal Energy, Temperature, Collision Number and Mean Free Path
  - Internal Energy and Temperature
  - Collision Number and Mean Free Path
- Pressure
  - Relation between Pressure and Temperature
- Gas, Liquid, and Solid
- Work
- Heat
- Chemical Potential
  - Multicomponent into Multicomponent
  - Single Component into Multicomponent
- Boiling/Phase Equilibrium
  - Single Component Fluid
  - Multiple Components
Entropy
Properties in Mixtures – Partial Molal Property
Summary
Appendix
- Air Composition
- Proof of the Euler Equation
- Brief Overview of Vector Calculus
  - Scalar or Dot Product
  - Vector or Cross Product
  - Gradient of a Scalar
  - Curl of a Vector

First Law of Thermodynamics

Introduction
- Zeroth Law
- First Law for a Closed System
  - Mass Conservation
  - Energy Conservation
  - Systems with Internal Motion
  - Cyclical Work and Poincare Theorem
  - Quasiequilibrium Work
  - Nonquasi equilibrium Work
- First Law in Enthalpy Form
  - Conservation of Mass
  - Conservation of Energy
  - Multiple Inlets and Exits
  - Nonreacting Multicomponent System
- Illustrations
  - Heating of a Residence in Winter
  - Thermodynamics of the Human Body
  - Charging of Gas into a Cylinder
  - Discharging Gas from Cylinders
  - Systems Involving Boundary Work
  - Charging of a Composite System
Integral and Differential Forms of Conservation Equations
- Mass Conservation
  - . Integral Form
  - Differential Form
- Energy Conservation
  - Integral Form
  - Differential Form
  - Deformable Boundary
Summary
Appendix
- Conservation Relations for a Deformable Control Volume

Second Law and Entropy

Introduction
- Thermal and Mechanical Energy Reservoirs
  - Heat Engine
  - Heat Pump and Refrigeration Cycle
Statements of the Second Law
- Informal Statements
  - Kelvin (1824-1907) – Planck (1858-1947) Statement
  - Clausius (1822-1888) Statement
Consequences of the Second Law
- Reversible and Irreversible Processes
- Cyclical Integral for a Reversible Heat Engine
- Clausius Theorem
- Clausius Inequality
- External and Internal Reversibility
- Entropy
  - Mathematical Definition
  - Characteristics of Entropy
- Relation between ds, δq and T during an Irreversible Process
  - Caratheodary Axiom II
Entropy Balance Equation for a Closed System
- Infinitesimal Form
  - Uniform Temperature within a System
  - Nonuniform Properties within a System
- Integrated Form
- Rate Form
- Cyclical Form
- Irreversibility and Entropy of an Isolated System
- Degradation and Quality of Energy
  - Adiabatic Reversible Processes
Entropy Evaluation
- Ideal Gases
  - Constant Specific Heats
  - Variable Specific Heats
- Incompressible Liquids
- Solids
- Entropy during Phase Change
  - T–s Diagram
- Entropy of a Mixture of Ideal Gases
  - Gibbs–Dalton´s Law
  - Reversible Path Method
Local and Global Equilibrium
Single Component Incompressible Fluids
Third Law
Entropy Balance Equation for an Open System
- General Expression
- Evaluation of Entropy for a Control Volume
- Internally Reversible Work for an Open System
- Irreversible Processes and Efficiencies
- Entropy Balance in Integral and Differential Form
  - Integral Form
  - Differential Form
- Application to Open Systems
  - Steady Flow
  - Solids
Maximum Entropy and Minimum Energy
- Maxima and Minima Principles
  - Entropy Maximum (For Specified U, V, m)
  - Internal Energy Minimum (for specified S, V, m)
  - Enthalpy Minimum (For Specified S, P, m)
  - Helmholtz Free Energy Minimum (For Specified T, V, m)
  - Gibbs Free Energy Minimum (For Specified T, P, m)
- Generalized Derivation for a Single Phase
  - Special Cases
Summary
Appendix
- Proof for Additive Nature of Entropy
- Relative Pressures and Volumes
- LaGrange Multiplier Method for Equilibrium
  - U, V, m System
  - T, P, m System

Availability

Introduction
Optimum Work and Irreversibility in a Closed System
- Internally Reversible Process
- Useful or External Work
- Internally Irreversible Process with no External Irreversibility
  - Irreversibility or Gouy–Stodola Theorem
- Nonuniform Boundary Temperature in a System
Availability Analyses for A Closed System
- Absolute and Relative Availability under Interactions with Ambient
- Irreversibility or Lost Work
  - Comments
Generalized Availability Analysis
- Optimum Work
- Lost Work Rate, Irreversibility Rate, Availability Loss
- Availability Balance Equation in Terms of Actual Work
  - Irreversibility due to Heat Transfer
- Applications of the Availability Balance Equation
- Gibbs Function
- Closed System (Non–Flow Systems)
  - Multiple Reservoirs
  - Interaction with the Ambient Only
  - Mixtures
- Helmholtz Function
Availability Efficiency
- Heat Engines
  - Efficiency
  - Availability or Exergetic (Work Potential) Efficiency
- Heat Pumps and Refrigerators
  - Coefficient of Performance
- Work Producing and Consumption Devices
  - Open Systems:
  - Closed Systems
- Graphical Illustration of Lost, Isentropic, and Optimum Work
- Flow Processes or Heat Exchangers
  - Significance of the Availability or Exergetic Efficiency
  - Relation between ηAvail,f and ηAvail,0 for Work Producing Devices
Chemical Availability
- Closed System
- Open System
  - Ideal Gas Mixtures
  - Vapor or Wet Mixture as the Medium in a Turbine
  - Vapor–Gas Mixtures
  - Psychometry and Cooling Towers
Integral and Differential Forms
- Integral Form
- Differential Form
- Some Applications
Summary

Postulatory (Gibbsian) Thermodynamics

Introduction
Classical Rationale for Postulatory Approach
- Simple Compressible Substance
Legendre Transform
- Simple Legendre Transform
  - Relevance to Thermodynamics
- Generalized Legendre Transform
- Application of Legendre Transform
Generalized Relation for All Work Modes
- Electrical Work
- Elastic Work
- Surface Tension Effects
- Torsional Work
- Work Involving Gravitational Field
- General Considerations
Thermodynamic Postulates for Simple Systems
- Postulate I
- Postulate II
- Postulate III
- Postulate IV
Entropy Fundamental Equation
Energy Fundamental Equation
Intensive and Extensive Properties
Summary

State Relationships for Real Gases and Liquids

Introduction
Equations of State
Real Gases
- Virial Equation of State
  - Exact Virial Equation
  - Approximate Virial Equation
- Van der Waals (VW) Equation of State
  - Clausius–I Equation of State
  - VW Equation
- Redlich-Kwong Equation of State
- Other Two–Parameter Equations of State
- Compressibility Charts (Principle of Corresponding States)
- Boyle Temperature and Boyle Curves
  - Boyle Temperature
  - Boyle Curve
  - The Z = 1 Island
- Deviation Function
- Three Parameter Equations of State
  - Critical Compressibility Factor (Zc) Based Equations
  - Pitzer Factor
  - Evaluation of Pitzer factor,ω
- Other Three Parameter Equations of State
  - One Parameter Approximate Virial Equation
  - Redlich–Kwong–Soave (RKS) Equation
  - Peng–Robinson (PR) Equation
- Generalized Equation of State
- Empirical Equations of State
  - Benedict–Webb–Rubin Equation
  - b. Beatie – Bridgemann (BB) Equation of State
  - c. Modified BWR Equation
  - d. Lee–Kesler Equation of State
  - e. Martin–Hou
- State Equations for Liquids/Solids
  - Generalized State Equation
  - Murnaghan Equation of State
  - Racket Equation for Saturated Liquids
  - Relation for Densities of Saturated Liquids and Vapors
  - Lyderson Charts (for Liquids)
  - Incompressible Approximation
- Summary
- Appendix
  - Cubic equation
    - Case I: γ > 0
    - Case II: γ < 0
  - Another Explanation for the Attractive Force
  - Critical Temperature and Attraction Force Constant

Thermodynamic Properties of Pure Fluids

Introduction
Ideal Gas Properties
James Clark Maxwell (1831–1879) Relations
- First Maxwell Relation
  - Remarks
- Second Maxwell Relation
  - Remarks
- Third Maxwell Relation
  - Remarks
- Fourth Maxwell Relation
  - Remarks
- Summary of Relations
Generalized Relations
- Entropy ds Relation
  - Remarks
- Enthalpy (dh) Relation
  - Remarks

Thermodynamic Properties of Mixtures

Phase Equilibrium for a Mixture

Stability

Chemically Reacting Systems

Reaction Direction and Chemical Equilibrium

Availability Analysis for Reacting Systems

Postulatory (Gibbsian) Thermodynamics

State Relationships for Real Gases and Liquids

Deviation Function

Three Parameter Equations of State

Other Three Parameter Equations of State

Generalized Equation of State

Empirical Equations of State

State Equations for Liquids/Solids

Thermodynamic Properties of Pure Fluids

Thermodynamic Properties of Mixtures

Phase Equilibrium for a Mixture

Stability

Chemically Reacting Systems

Reaction Direction and Chemical Equilibrium

Availability Analysis for Reacting Systems

Problems

Appendix A. Tables

Appendix B. Charts

Appendix C. Formulae