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.
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 Boyle–Mariotte 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. Tait–Tammann–Gibson 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
Jean-Numa Foulc
