## An Introduction to the Properties of Fluids and Solids

Robert Heideman, Ayodeji A. Jeje, and Farhang Mohtadi

$26.95 CAD / $26.95 USD (S)

440 pages, formulae

6 x 9 inches

978-0-91981-306-9 (Paperback)

October 1984

## About the Book

**Written especially for first-year university students studying engineering, this text provides a sound first treatment of many properties of fluids and solids of interest across disciplines.**

*An Introduction to the Properties of Fluids and Solids* deals with some basic thermodynamic and transport properties of fluids and solids that are of interest in engineering applications

Various notions about the basic structure of matter, fundamental concepts of our physical world and the conditions of equilibrium between different phases of matter are discussed in the first part of the book. The macroscopic properties of fluids and solids are explained in the latter part

Written for first-year university students in engineering, simple derivations and clear explanations have been preferred to detailed theoretical treatment. Illustrative problems, spaced throughout the text, demonstrate the application of various concepts and facilitate a better understanding of the theory.

*An Introduction to the Properties of Fluids and Solids* provides a sound first treatment of many properties of fluids and solids of interest in all the engineering disciplines.

### About the Authors

**Robert A. Heidemann** is associated with the Department of Chemical and Petroleum Engineering at the University of Calgary.

**Ayodeji A. Jeje **is associated with the Department of Chemical and Petroleum Engineering at the University of Calgary.

**Farhang Mohtadi** is associated with the Department of Chemical and Petroleum Engineering at the University of Calgary.

##
## Table of Contents

#####

**1. Introduction**

1.1 The States of Matter

1.2 Atoms and Molecules

1.3 The Properties of Matter

**2. Basic Concepts and Principles**

2.1 Scales of Magnitude in Space and Time

2.2. Fundamental and Derived outcomes

2.3 The Conservation Principles

2.4 The Concepts of Temperature

2.5 Interconvertibility of Energy

**3. Notations about the Nature of Matter **

3.1 Early Notations about the Structure of Matter

*3.1.1 Dalton’s Postulates *

3.1.2 Avogadro’s Hypothesis

3.2 Contemporary Picture of the Atom

*3.2.1 The Nucleus *

3.2.2 The Electron

3.2.2 TheElementary Particles

3.3 Proof of the Particulate Nature of Matter

*3.3.1 Brownian Motion *

3.3.2 Field Emission Microscopy

3.3.3 Radioactivity

3.4 The Classification of Elements

*3.4.1 The Periodic Table *

3.4.2 Chemical Reactivity

3.5 The Size of Atoms and Molecules

3.5 The Nature of Bonds Between Atoms and Molecules

3.7 Potential Energy Functions

3.8 Structure of Solids

*3.8.1 Crystals and non-Crystals *

3.8.2 Bravais Lattices

3.8.3 Atomic Densities and Dimensions

3.9 The States of Matter and Their Transformations

**Equilibrium Between Phases of Matter**

4.1 States of Equilibrium

4.2 Phases and Composition

4.3 The Phase Rule

*4.3.1 The Number of Phases, P *

4.3.2 The Number of Independent Components, C

4.3.3 The Degrees of Freedom, F

4.3.4 Phase Rule Examples

4.4 Phase Equilibria in Single Component Systems

*4.4.1 Single Phase Systems *

4.4.2 Two Phase Systems

4.4.3 Three Phase Systems

4.4.4 Systems with more than Three Phases

4.4.5 The Pressure–Temperature Diagram for a Pure Substance

4.4.6 The Pressure–Volume Diagram for a Pure Substance

4.4.7 The Critical Point

4.4.8 The Lever Rule

4.4.9 The P–V–T Surface

4.5 Systems with Two Independent Components

*4.5.1 Binary Phase Diagrams *

4.6 Vapor–Liquid Systems

*4.6.1 Two Completely Miscible Liquids *

4.6.2 Two Completely Miscible Liquids with Azeotropic Point

4.6.3 Two Partially Miscible Liquids

4.7 Liquid–Solid Systems

*4.7.1 Completely Miscible Solids *

4.7.2 Immiscible Solids

4.7.3 Partially Miscible Solids

4.7.4 Invariant Reactions

4.7.5 Compound Phases

4.8 Phase Diagrams for Some Systems of Special Engineering Interest

*4.8.1 The Iron–Carbon System *

4.8.2 Steeles and Cast–Irons

4.8.3 Non–Equilibrium Steeles

4.8.4 Copper–Zinc Mixtures

4.8.5 Methan–n–Heptane Mixtures

**5. Ideal Gasses **

5.1 P–V–T Behavior of the Ideal Gas

5.2 The Equation of the State of an Ideal Gas

*5.2.1 The Universal Gas Constant *

5.3 Ideal Gas Mixtures

5.4 Elementary Kinetic Theory of Gasses

5.5 Deductions from the Kinetic Theory

*5.5.1 Boyle’s Law *

5.5.2 Avogadro’s Law

5.5.3 Temperature and Motion of Molecules

5.5.4 Distribution of Molecular Velocities in Gasses

5.5.5 The Relationship between the Gas Constant and Heat Capacities

5.5.6 Mean Free Path and Collision of Molecules

5.6 Transport Properties of Gasses

*5.6.1 Transfer of Momentum; Viscosity *

5.6.2 Conduction of Heat; Thermal Conductivity

5.6.3 Molecular Diffusion; Diffusivity

**6. Real Gasses **

6.1 Deviation from Ideal Gas Behavior

6.2 P–V–T Behavior of Real Gases

6.3 The van der Walls Equation of State

6.4 Applicability of the van der Waals Equation

6.5 The van der Waals Equation and the Critical Point

6.6. Other Equations of State

6.7 Compressibility Factor and Corresponding States

6.8 Real Gas Mixtures

*6.8.1 The Pseudocritical Point Method *

6.8.2 Application of Dalton’s and Amagat’s Laws

6.8.3 Mixing Rules Method

**7. Liquids **

7.1 The Liquid State

*7.1.1 Models of the Liquid State *

7.1.2 The Glassy State and Liquid Crystals

7.2 Volumetric Behaviour of Liquids

*7.2.1 Thermal Expransion of Liquids *

7.2.2 Compressibility; Tait’s Equation

7.2.3 The van der Waals Equation

7.2.4 The Corresponding States

7.3 Energy Effects in Liquids

*7.3.1 Heat Capacity *

7.3.2 Latent Heat of Vaporization

7.3.3 The Clausis&Clapeyron Equation

7.3.4 Correlating Vapor Pressure Data

7.3.5 Equilibrium Pressure Above Liquid Mixtures

7.4 Cohesion and Surface Tension

*7.4.1 Surface Tension; Pressure Inside Drops and Bubbles *

7.4.2 The Contact Angle

7.4.3 Capillary Rise

7.4.4 Interfacial Tension

7.4.5 Variations in Surface Tension

7.5 Colligative Properties of Liquid Solutions

*7.5.1 Elevation of Boiling Point *

7.5.2 Depression of Freezing Point

7.5.3 Osmotic Pressure

7.6 Transport Properties of Liquids

*7.6.1 Viscosity of Liquids *

7.6.2 Thermal Conductivity of Liquids

7.6.3 Molecular Diffusion in Liquids

**8. The Motion of Fluids **

8.1 The Basic Concepts

*8.1.1 Stress and Strain in Fluids *

8.1.2 Ideal Fluids

8.1.3 Newtonian Fluids

8.1.4 The Effects of Temperature and Pressure on Viscosity

8.1.5 Non–Newtonian Fluids

8.1.6 The Measurement of Viscosity

8.2 Potential Flow

*8.2.1 Bernoulli’s Equation *

8.3 Flow of Viscous Fluids

*8.3.1 The Boundary Layer *

8.4 Laminar Flow in Pipes; The Hagen–Poiseuille Equation

*8.4.1 Velocity Distribution in a Pipe*

8.4.2 Power Consumption

8.4.3 Working Equations for Laminar Flow

8.5 Turbulent Flow in Piper

*8.5.1 The Friction Factor *

8.5.2 Power Consumption

8.5.3 Pressure Drop in Fittings, Bends and Valves

8.6 Drag on Submerged Bodies

*8.6.1 Flow on a Flat Plate *

8.6.2 Flow on a Curved Surface

8.6.3 Drag on a Two–dimensional Surface

**9. The Structure and Transport of Properties of Solids **

9.1 Macrostructure of Solids

*9.1.1 Crystalline Solutions *

9.1.2 Amorphous Solids

9.1.3 Polymeric Solids

9.2 Thermal Properties in Heat Conduction

*9.1.1 Heat Capacity *

9.1.2 Thermal Expansion

9.2.3 Thermal Conductivity

9.2.4 The Rate of Heat Conduction

9.3 Diffusion in Solids

*9.3.1 Mechanisms of Diffusion in Solids *

9.3.2 The Phenomenological Theory of Diffusion

9.3.3 Diffusion of Neutrons

9.3.4 Diffusion of Porous and Non–porous Solids

9.3.5 Solid Diffusivity Data

9.4 The Transport of Electrical Charge in Solids

*9.4.1 Basic Conception and Terminologies *

9.4.2 Electric Conduction in Metals

9.4.3 Superconductivity

9.4.4 Semiconductors

**10. Stress–Strain Relationships for Solids **

10.1 Stress and Strain in Solids

*10.1.1 Normal and Shear Stresses *

10.1.2 Normal and Shear Strains

10.2.3 Typical Stress–Strain Behaviors

10.2 Elastic Deformation of Solids

*10.2.1 Young Modulus for Linear Deformation *

10.2.2 Poisson’s Ratio

10.2.3 The Bulk Modulus for Volume Change

10.2.4 Modulus of Rigidity for Shear Deformation

10.2.5 Effect of Anisotropy on Elasticity

10.2.6 Effects of Temperature on Elasticity

10.3 Plastic Deformation

*10.3.1 Maximum Strength of Perfect Crystals *

10.3.2 Dislocations and Slip

10.4 Linear Visco–Elastic Models

*10.4.1 The Maxwell Models *

10.4.2 The Temperature Effects on Visco–Elastic Models

10.5 Creep

*10.5.1 Correlating Minimum Creep Rate *

10.6 Brittle Failure

*10.6.1 Effect of Cracks on Strength *

10.6.2 Brittle–Ductile Transition

Appendix 1 – Constants and Units

Appendix B – Properties of Elements and Pure Substances

Appendix C – Volumetric Properties

Subject Index

## Table of Contents

**1. Introduction**

1.1 The States of Matter

1.2 Atoms and Molecules

1.3 The Properties of Matter

**2. Basic Concepts and Principles**

2.1 Scales of Magnitude in Space and Time

2.2. Fundamental and Derived outcomes

2.3 The Conservation Principles

2.4 The Concepts of Temperature

2.5 Interconvertibility of Energy

**3. Notations about the Nature of Matter **

3.1 Early Notations about the Structure of Matter

*3.1.1 Dalton’s Postulates 3.1.2 Avogadro’s Hypothesis *

3.2 Contemporary Picture of the Atom

*3.2.1 The Nucleus*

3.2.2 The Electron

3.2.2 TheElementary Particles

3.3 Proof of the Particulate Nature of Matter

3.2.2 The Electron

3.2.2 TheElementary Particles

*3.3.1 Brownian Motion*

3.3.2 Field Emission Microscopy

3.3.3 Radioactivity

3.3.2 Field Emission Microscopy

3.3.3 Radioactivity

3.4 The Classification of Elements

*3.4.1 The Periodic Table*

3.4.2 Chemical Reactivity

3.5 The Size of Atoms and Molecules

3.4.2 Chemical Reactivity

3.5 The Size of Atoms and Molecules

3.5 The Nature of Bonds Between Atoms and Molecules

3.7 Potential Energy Functions

3.8 Structure of Solids

*3.8.1 Crystals and non-Crystals*

3.8.2 Bravais Lattices

3.8.3 Atomic Densities and Dimensions

3.9 The States of Matter and Their Transformations

3.8.2 Bravais Lattices

3.8.3 Atomic Densities and Dimensions

**Equilibrium Between Phases of Matter**

4.1 States of Equilibrium

4.2 Phases and Composition

4.3 The Phase Rule *4.3.1 The Number of Phases, P 4.3.2 The Number of Independent Components, C 4.3.3 The Degrees of Freedom, F 4.3.4 Phase Rule Examples *

4.4 Phase Equilibria in Single Component Systems

*4.4.1 Single Phase Systems*

4.4.2 Two Phase Systems

4.4.3 Three Phase Systems

4.4.4 Systems with more than Three Phases

4.4.5 The Pressure–Temperature Diagram for a Pure Substance

4.4.6 The Pressure–Volume Diagram for a Pure Substance

4.4.7 The Critical Point

4.4.8 The Lever Rule

4.4.9 The P–V–T Surface

4.4.2 Two Phase Systems

4.4.3 Three Phase Systems

4.4.4 Systems with more than Three Phases

4.4.5 The Pressure–Temperature Diagram for a Pure Substance

4.4.6 The Pressure–Volume Diagram for a Pure Substance

4.4.7 The Critical Point

4.4.8 The Lever Rule

4.4.9 The P–V–T Surface

4.5 Systems with Two Independent Components

*4.5.1 Binary Phase Diagrams*

4.6 Vapor–Liquid Systems

*4.6.1 Two Completely Miscible Liquids*

4.6.2 Two Completely Miscible Liquids with Azeotropic Point

4.6.3 Two Partially Miscible Liquids

4.6.2 Two Completely Miscible Liquids with Azeotropic Point

4.6.3 Two Partially Miscible Liquids

4.7 Liquid–Solid Systems

*4.7.1 Completely Miscible Solids*

4.7.2 Immiscible Solids

4.7.3 Partially Miscible Solids

4.7.4 Invariant Reactions

4.7.5 Compound Phases

4.7.2 Immiscible Solids

4.7.3 Partially Miscible Solids

4.7.4 Invariant Reactions

4.7.5 Compound Phases

4.8 Phase Diagrams for Some Systems of Special Engineering Interest

*4.8.1 The Iron–Carbon System*

4.8.2 Steeles and Cast–Irons

4.8.3 Non–Equilibrium Steeles

4.8.4 Copper–Zinc Mixtures

4.8.5 Methan–n–Heptane Mixtures

4.8.2 Steeles and Cast–Irons

4.8.3 Non–Equilibrium Steeles

4.8.4 Copper–Zinc Mixtures

4.8.5 Methan–n–Heptane Mixtures

**5. Ideal Gasses **

5.1 P–V–T Behavior of the Ideal Gas

5.2 The Equation of the State of an Ideal Gas *5.2.1 The Universal Gas Constant *

5.3 Ideal Gas Mixtures

5.4 Elementary Kinetic Theory of Gasses

5.5 Deductions from the Kinetic Theory *5.5.1 Boyle’s Law 5.5.2 Avogadro’s Law 5.5.3 Temperature and Motion of Molecules 5.5.4 Distribution of Molecular Velocities in Gasses 5.5.5 The Relationship between the Gas Constant and Heat Capacities 5.5.6 Mean Free Path and Collision of Molecules *

5.6 Transport Properties of Gasses

*5.6.1 Transfer of Momentum; Viscosity*

5.6.2 Conduction of Heat; Thermal Conductivity

5.6.2 Conduction of Heat; Thermal Conductivity

5.6.3 Molecular Diffusion; Diffusivity

**6. Real Gasses **

6.1 Deviation from Ideal Gas Behavior

6.2 P–V–T Behavior of Real Gases

6.3 The van der Walls Equation of State

6.4 Applicability of the van der Waals Equation

6.5 The van der Waals Equation and the Critical Point

6.6. Other Equations of State

6.7 Compressibility Factor and Corresponding States

6.8 Real Gas Mixtures *6.8.1 The Pseudocritical Point Method 6.8.2 Application of Dalton’s and Amagat’s Laws *

6.8.3 Mixing Rules Method

**7. Liquids **

7.1 The Liquid State

*7.1.1 Models of the Liquid State
7.1.2 The Glassy State and Liquid Crystals *

7.2 Volumetric Behaviour of Liquids

*7.2.1 Thermal Expransion of Liquids*

7.2.2 Compressibility; Tait’s Equation

7.2.3 The van der Waals Equation

7.2.4 The Corresponding States

7.2.2 Compressibility; Tait’s Equation

7.2.3 The van der Waals Equation

7.2.4 The Corresponding States

7.3 Energy Effects in Liquids

*7.3.1 Heat Capacity*

7.3.2 Latent Heat of Vaporization

7.3.3 The Clausis&Clapeyron Equation

7.3.4 Correlating Vapor Pressure Data

7.3.5 Equilibrium Pressure Above Liquid Mixtures

7.3.2 Latent Heat of Vaporization

7.3.3 The Clausis&Clapeyron Equation

7.3.4 Correlating Vapor Pressure Data

7.3.5 Equilibrium Pressure Above Liquid Mixtures

7.4 Cohesion and Surface Tension

*7.4.1 Surface Tension; Pressure Inside Drops and Bubbles*

7.4.2 The Contact Angle

7.4.3 Capillary Rise

7.4.4 Interfacial Tension

7.4.5 Variations in Surface Tension

7.4.2 The Contact Angle

7.4.3 Capillary Rise

7.4.4 Interfacial Tension

7.4.5 Variations in Surface Tension

7.5 Colligative Properties of Liquid Solutions

*7.5.1 Elevation of Boiling Point*

7.5.2 Depression of Freezing Point

7.5.3 Osmotic Pressure

7.5.2 Depression of Freezing Point

7.5.3 Osmotic Pressure

7.6 Transport Properties of Liquids

*7.6.1 Viscosity of Liquids*

7.6.2 Thermal Conductivity of Liquids

7.6.3 Molecular Diffusion in Liquids

7.6.2 Thermal Conductivity of Liquids

7.6.3 Molecular Diffusion in Liquids

**8. The Motion of Fluids **

8.1 The Basic Concepts

*8.1.1 Stress and Strain in Fluids 8.1.2 Ideal Fluids 8.1.3 Newtonian Fluids 8.1.4 The Effects of Temperature and Pressure on Viscosity 8.1.5 Non–Newtonian Fluids 8.1.6 The Measurement of Viscosity *

8.2 Potential Flow

*8.2.1 Bernoulli’s Equation*

8.3 Flow of Viscous Fluids

*8.3.1 The Boundary Layer*

8.4 Laminar Flow in Pipes; The Hagen–Poiseuille Equation

*8.4.1 Velocity Distribution in a Pipe*

8.4.2 Power Consumption

8.4.3 Working Equations for Laminar Flow

8.4.2 Power Consumption

8.4.3 Working Equations for Laminar Flow

8.5 Turbulent Flow in Piper

*8.5.1 The Friction Factor*

8.5.2 Power Consumption

8.5.3 Pressure Drop in Fittings, Bends and Valves

8.5.2 Power Consumption

8.5.3 Pressure Drop in Fittings, Bends and Valves

8.6 Drag on Submerged Bodies

*8.6.1 Flow on a Flat Plate*

8.6.2 Flow on a Curved Surface

8.6.3 Drag on a Two–dimensional Surface

8.6.2 Flow on a Curved Surface

8.6.3 Drag on a Two–dimensional Surface

**9. The Structure and Transport of Properties of Solids **

9.1 Macrostructure of Solids

*9.1.1 Crystalline Solutions 9.1.2 Amorphous Solids 9.1.3 Polymeric Solids *

9.2 Thermal Properties in Heat Conduction

*9.1.1 Heat Capacity*

9.1.2 Thermal Expansion

9.2.3 Thermal Conductivity

9.2.4 The Rate of Heat Conduction

9.1.2 Thermal Expansion

9.2.3 Thermal Conductivity

9.2.4 The Rate of Heat Conduction

9.3 Diffusion in Solids

*9.3.1 Mechanisms of Diffusion in Solids*

9.3.2 The Phenomenological Theory of Diffusion

9.3.3 Diffusion of Neutrons

9.3.4 Diffusion of Porous and Non–porous Solids

9.3.5 Solid Diffusivity Data

9.3.2 The Phenomenological Theory of Diffusion

9.3.3 Diffusion of Neutrons

9.3.4 Diffusion of Porous and Non–porous Solids

9.3.5 Solid Diffusivity Data

9.4 The Transport of Electrical Charge in Solids

*9.4.1 Basic Conception and Terminologies*

9.4.2 Electric Conduction in Metals

9.4.3 Superconductivity

9.4.4 Semiconductors

9.4.2 Electric Conduction in Metals

9.4.3 Superconductivity

9.4.4 Semiconductors

**10. Stress–Strain Relationships for Solids **

10.1 Stress and Strain in Solids

*10.1.1 Normal and Shear Stresses 10.1.2 Normal and Shear Strains 10.2.3 Typical Stress–Strain Behaviors *

10.2 Elastic Deformation of Solids

*10.2.1 Young Modulus for Linear Deformation*

10.2.2 Poisson’s Ratio

10.2.3 The Bulk Modulus for Volume Change

10.2.4 Modulus of Rigidity for Shear Deformation

10.2.5 Effect of Anisotropy on Elasticity

10.2.6 Effects of Temperature on Elasticity

10.2.2 Poisson’s Ratio

10.2.3 The Bulk Modulus for Volume Change

10.2.4 Modulus of Rigidity for Shear Deformation

10.2.5 Effect of Anisotropy on Elasticity

10.2.6 Effects of Temperature on Elasticity

10.3 Plastic Deformation

*10.3.1 Maximum Strength of Perfect Crystals*

10.3.2 Dislocations and Slip

10.3.2 Dislocations and Slip

10.4 Linear Visco–Elastic Models

*10.4.1 The Maxwell Models*

10.4.2 The Temperature Effects on Visco–Elastic Models

10.4.2 The Temperature Effects on Visco–Elastic Models

10.5 Creep

*10.5.1 Correlating Minimum Creep Rate*

10.6 Brittle Failure

*10.6.1 Effect of Cracks on Strength*

10.6.2 Brittle–Ductile Transition

10.6.2 Brittle–Ductile Transition

Appendix 1 – Constants and Units

Appendix B – Properties of Elements and Pure Substances

Appendix C – Volumetric Properties

Subject Index