From Deep Sea to Laboratory 3

The scientific expedition of H.M.S. Challenger in the 1870s marks the starting point of physical oceanography. This ship traveled the seas of the globe pursuing a dual objective: to conduct an in-depth study of animal life and to observe the physical properties of ocean waters. Volume 3 focuses on measurements and modeling of liquid compressibility. Based on the work initiated by the physicist Peter Tait, a detailed presentation of liquid equations-of-state is proposed. The physical interpretation of the parameters of these equations is discussed, leading to a description of the "structure" of liquid media. From Deep Sea to Laboratory is available in three volumes for curious readers drawn to travel, history and science. Students, researchers and teachers of physics, fluid mechanics and oceanography will find material to deepen their knowledge.

Auteur

Frédéric Aitken is a CNRS researcher who has previously worked at the Electrostatics and Dielectric Materials Laboratory (LEMD) and is currently working at the Grenoble Electrical Engineering Laboratory (G2Elab). He is the former President of the Alps section of the French Society of Physics.

Jean-Numa Foulc is Honorary Professor at Grenoble Alpes University in France. He has had successive positions as an Assistant Professor and then Professor at the Universities of Rouen, Montpellier and Grenoble (Polytech Grenoble). He is currently a researcher at G2Elab.

Contenu

Foreword vii

Preface xi

Notations xv

Chapter 1. The Compressibility of Liquids and Tait's Equation-of-State 1

1.1. Introduction 2

1.2. Concepts of compressibility 3

1.3. The first instruments to measure the compressibility of liquids 5

1.4. The piezometers used onboard the Challenger 21

1.5. Sources of pressure measurement errors 24

1.5.1. Apparent compressibility of water and mercury 24

1.5.2. Apparent compressibility of liquid and piezometer 27

1.6. Compressibility of fresh and salt water 32

1.6.1. Results on fresh water compressibility 34

1.6.2. Results on seawater compressibility 38

1.6.3. Results on the compressibility of saline solutions 40

1.6.4. Equilibrium of a water column 42

Chapter 2. Interpretations of the Parameters of Tait's Equation 45

2.1. Introduction 46

2.2. Comparison and analogy with the BoyleMariotte equation-of-state 46

2.3. Comparison and analogy with the Hirn equation-of-state 54

2.4. Comparison and analogy with the van der Waals equation-of-state 84

2.4.1. The molecular motion model 88

2.4.2. Establishing the van der Waals equation 94

2.4.3. The different expressions and interpretations of covolume 111

Chapter 3. TaitTammannGibson Equations-of-State 147

3.1. Introduction 148

3.2. Examples of compressibility equations-of-state 150

3.3. Evolution of the parameters of the mixed modulus 155

3.3.1. Application in the case of fresh water 160

3.3.2. Application in the case of standard seawater 168

3.3.3. Application in the case of helium-4 179

3.3.4. Application in the case of helium-3 192

3.3.5. Density anomalies 199

3.3.6. Compressibility anomalies 201

3.4. Discussion and conclusion 207

Chapter 4. The Modified Tait Equation 245

4.1. Introduction 246

4.2. Development of a complete equation-of-state 249

4.3. Study of the adiabatic elastic modulus 255

4.3.1. Application in the case of fresh water 255

4.3.2. Application in the case of helium-3 264

4.3.3. Application in the case of helium-4 271

Conclusion 279

Appendices 283

Appendix A. Compressibility of a Straight Tube 285

Appendix B. Virial Theorem 291

References 335

Index 343

Summary of Volume 1 347

Summary of Volume 2 351