Muutke küpsiste eelistusi

E-raamat: Physics of Liquid Water [Taylor & Francis e-raamat]

  • Formaat: 186 pages, 9 Tables, black and white; 55 Illustrations, color; 80 Illustrations, black and white
  • Ilmumisaeg: 25-Mar-2021
  • Kirjastus: Jenny Stanford Publishing
  • ISBN-13: 9781003056164
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 175,41 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 250,59 €
  • Säästad 30%
Physics of Liquid WaterSuurem pilt
  • Formaat: 186 pages, 9 Tables, black and white; 55 Illustrations, color; 80 Illustrations, black and white
  • Ilmumisaeg: 25-Mar-2021
  • Kirjastus: Jenny Stanford Publishing
  • ISBN-13: 9781003056164
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003056164

Unraveling the mystery of the negative thermal expansion of liquid water has been a challenge for scientists for centuries. Various theories have been proposed so far, but none has been able to solve this mystery. Since the thermodynamic properties of matter are determined by the interaction between particles, the mystery can be solved fundamentally if the thermodynamic physical quantities using the laws of thermodynamics and statistical mechanics are determined, the experimental results are reproduced, and the phenomena in relation to the shape of the interaction between particles are elucidated. In this sense, this book has fundamentally unraveled this mystery. In addition, it discusses the mysteries of isothermal compressibility, structural diversity, as well as liquefaction and boiling points of water in relation to the shape of the interaction between particles. It carefully explains the analysis and calculation methods so that they can be easily understood by the readers.

Preface xi
1 Statistical Mechanics and Thermodynamics of Fluids
1(6)
1.1 Statistical Mechanics
1(2)
1.2 Thermodynamics
3(2)
1.2.1 Pressure from Energy Equation
3(1)
1.2.2 Chemical Potential from Energy Equation
4(1)
1.2.3 Pressure and Chemical Potential from Compressibility Equation
5(1)
1.3 Consistency between Energy Equation and Compressibility Equation
5(2)
2 Strange Temperature Change of Water Density
7(4)
2.1 Positive Thermal Expansion
7(1)
2.2 Negative Thermal Expansion
8(3)
3 Fundamental Clarification of Thermodynamic Phenomena in Water
11(12)
3.1 Function Form of Interaction between Water Molecules
12(1)
3.1.1 Water Molecule Shape
12(1)
3.2 Method by Solving the Basic Equation of Quantum Mechanics
13(1)
3.3 Method by Using Realistic Water Model
14(1)
3.4 Simplified Model (Core-Softened Model)
15(1)
3.5 Method by Self-Consistent Ornstein-Zernike Approximation
16(1)
3.6 Multi-Yukawa Type Intermolecular Interaction
17(1)
3.7 Thermodynamic Mechanism of Negative Thermal Expansion
18(5)
3.7.1 Shape of Intermolecular Interaction That Causes Negative Thermal Expansion
22(1)
4 Variety of Shapes of Water Molecule Interactions
23(8)
4.1 Soft-Repulsive Tail Slope and Isothermal Compression Ratio
25(1)
4.2 Problems with Existing Ideas on Negative Thermal Expansion
26(5)
5 Ornstein-Zernike Equation
31(64)
5.1 Hyper-netted Chain Approximation
32(1)
5.2 Percus-Yevick Approximation
32(1)
5.3 Mean-Spherical Approximation
32(1)
5.4 OZ Equations in Baxter Form
33(6)
5.4.1 Baxter Function Q[ r)
33(3)
5.4.2 Baxter's First Equation
36(1)
5.4.3 Baxter's Second Equation
37(2)
5.5 Analytical Solution of the Percus-Yevick Equation for Hard Sphere Fluids
39(9)
5.5.1 Direct Correlation Function
40(1)
5.5.2 Equation of State Derived from Virial Theorem
41(1)
5.5.3 Equation of State Derived from Compressibility
41(6)
5.5.4 Carnahan-Starling's Empirical Formula
47(1)
5.6 Self-Consistent OZ Approximation
48(11)
5.6.1 SCOZA Closure
49(1)
5.6.2 Laplace Transformation of Baxter-Type OZ Equation
50(1)
5.6.3 Laplace Transformation of Baxter's Second Equation
50(7)
5.6.4 Laplace Transform of Baxter's First Equation
57(1)
5.6.5 Analytical Solution of Baxter-Type OZ Equation
58(1)
5.7 MSA Analytic Display of Diffusion Equation for u
59(4)
5.7.1 Boundary Conditions
61(1)
5.7.2 Initial Conditions
61(1)
5.7.3 The Spinodal Curve
62(1)
5.8 Numerical Calculation Method of Diffusion (Heat Conduction) Type Equation
63(11)
5.8.1 In the Case of T ≥ Tc
64(1)
5.8.1.1 Predictor
64(1)
5.8.1.2 Corrector
64(1)
5.8.1.3 Simultaneous linear equations for uj [ 1 ≤ j ≤ J)
65(1)
5.8.1.4 Solution method of linear equations Au=r
66(1)
5.8.1.5 LU decomposition of matrix A
66(1)
5.8.1.6 Solution of Au = r
67(1)
5.8.2 In the Case of T < Tc and 0 < ρ ≤ ρL
68(1)
5.8.2.1 Predictor
68(1)
5.8.2.2 Corrector
69(1)
5.8.2.3 A system of linear equations for U j (1 ≤ j ≤ L)
69(1)
5.8.2.4 Solutions of Au = r
70(2)
5.8.3 In the Case of T < Tc and ρR *le; ρ ≤ ρj
72(1)
5.8.3.1 Predictor
72(1)
5.8.3.2 Corrector
72(1)
5.8.3.3 A system of linear equations for ρR ≤ ρ ≤ ρj
73(1)
5.9 Numerical Calculation Method with Two Different Step Sizes of Δρa and Δρt
74(1)
5.10 Method to Mark Density
75(20)
5.10.1 In the Case of T ≥ Tc
75(1)
5.10.1.1 Predictor
75(1)
5.10.1.2 Interpolation of um ja+1
76(2)
5.10.1.3 Corrector
78(1)
5.10.1.4 Simultaneous linear equations for uj (1 ≤ j ≤ J)
79(1)
5.10.1.5 LU decomposition of matrix A
80(2)
5.10.1.6 Solutions of Au = r
82(3)
5.10.2 In the Case of T < Tc
85(1)
5.10.2.1 Predictor for 1 ≤ j ≤ L
85(1)
5.10.2.2 Corrector for 1 ≤ j ≤ L
86(1)
5.10.2.3 Simultaneous linear equations for Uj (1 ≤ j ≤ L)
87(1)
5.10.2.4 LU decomposition of matrix A
87(2)
5.10.2.5 Solutions of Au = r
89(4)
5.10.2.6 Solutions for R ≤ j ≤ J
93(2)
6 Calculation Procedure of SCOZA
95(12)
6.1 Method to Determine the Potential Tail
95(1)
6.2 k(1)(ρ) and z1(ρ)
96(11)
6.2.1 Calculation of u(ρ β = 0)
99(2)
6.2.2 Calculation up to Critical Temperature Tc
101(1)
6.2.3 Calculation below Critical Temperature
102(2)
6.2.4 Calculations of Gas Phase Water below the Critical Temperature
104(2)
6.2.5 Calculations of Liquid Phase Water below the Critical Temperature
106(1)
7 Pressure and Chemical Potential
107(14)
7.1 Pressure Derived from Energy Equation
107(2)
7.2 Pressure Derived from Compressibility Equation
109(1)
7.3 In the Case of T > Tc
110(5)
7.3.1 Spinodal Curve
110(3)
7.3.1.1 Isotherms
113(2)
7.4 Chemical Potential Derived from the Energy Equation
115(1)
7.5 Chemical Potential at β = β
115(3)
7.6 Chemical Potential Derived from Compressibility Equation
118(3)
8 Thermodynamic Properties of Subcritical Fluids
121(22)
8.1 Method to Find Liquefaction Point G and Vaporization Point L
122(7)
8.2 Absence Temperature Region of Liquefaction Point and Vaporization Point (βc < β < β†)
129(1)
8.3 Necessity of Two Density Step Sizes
130(2)
8.4 Comparison of Theory and Experiments
132(5)
8.4.1 Units of Length σu and Energy εu
132(3)
8.4.2 Pressure, Temperature, and Density at Critical Point
135(1)
8.4.3 Comparison of Theoretical and Experimental Vaporization Points
136(1)
8.5 Simplest and Most Optimum Interactions between Water Molecules
137(3)
8.6 Concluding Remarks
140(3)
Appendix A Integration Region
143(6)
A.1 Integration Region 1
143(1)
A.2 Integration Region 2
143(2)
A.3 Integration Region 3
145(4)
Appendix B Q0(n), q1(n, k), q2(n, k)
149(2)
Appendix C F0(k), F1(k), F2(k, n), F3(k, n), F4(k, n), F2(k, n)
151(2)
Appendix D A, B
153(2)
Appendix E δxj/δu
155(2)
Appendix F Stability of Solutions of Diffusion Equations
157(4)
F.1 In the Case of λ > 0
158(1)
F.2 In the Case of λ = 0
158(1)
F.3 In the Case of λ < 0
159(1)
F.4 Principle of Superposition of Solutions of Diffusion Equation
159(2)
Appendix G Solutions of Dn and Gn (1 ≤ n ≤ 6) for Water below Tc for φc1
161(12)
G. 1 Solutions of Dn and Gn (1 ≤ n ≤ 6) for Gas-Phase Water
161(3)
G.2 Solutions of Dn and Gn (1 ≤ n ≤ 6) for Liquid-Phase Water
164(9)
Index 173
Makoto Yasutomi is a lecturer at the University of the Ryukyus, Japan.
Püsilink: https://www.kriso.ee/db/9781003056164_pe.html
Märksõnad: