The science of construction materials

327 Pages·2009·9.021 MB·English

by  Per Freiesleben Hansen (auth.), Ole Mejlhede Jensen (eds.)

Per Freiesleben Hansen
edited by Ole Mejlhede Jensen
The Science of
Construction Materials
1 C
Prof. Ole Mejlhede Jensen
Technical University of Denmark
Dept. Civil Engineering
2800 Kgs. Lyngby
Brovej, Bldg. 118
Denmark
[email protected]
This book is scientifically sponsored by the Educational Activities Committee, EAC, of the International
Union of Laboratories and Experts in Construction Materials, Systems and Structures, RILEM.
ISBN: 978-3-540-70897-1 e-ISBN: 978-3-540-70898-8
DOI 10.1007/978-3-540-70898-8
Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2009935456
Translation from the Danish edition: Materialefysik for Bygningsingeniører - Beregningsgrundlag by Per Freiesleben
Hansen, © Statens Byggeforskningsinstitut, Hørsholm, Denmark 1995. All rights reserved.
© Springer-Verlag Berlin Heidelberg 2009
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on
microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is per-
mitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and
permission for use must always be obtained from Springer. Violations are liable to prosecution under the German
Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not
imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and
regulations and therefore free for general use.
Photographs: The photos in this book come from different sources and are reproduced by permission. For a list of
the origin of these illustrations see Appendix E.
Cover illustration: Paul Stutzman, Nat. Inst. of Sci. and Techn., USA; for details please refer to Appendix E.
Cover design: eStudio Calamar S.L, Figueres/Berlin
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Contents
List of symbols ......................................................... xii
Preface ................................................................. xv
Introduction ........................................................... xvii
1. Systems of matter
1.1 Atoms .............................................................. 1.2
Structure of the atom 1.2
Elements 1.2
Isotopes 1.3
1.2 Relative atomic mass .............................................. 1.3
1.3 Relative molecular mass ........................................... 1.4
1.4 Amount of substance - the mole .................................. 1.5
The Avogadro constant 1.5
1.5 Molar mass ......................................................... 1.6
1.6 Mixture of substances ............................................. 1.7
Concentration 1.7
1.7 The ideal gas law .................................................. 1.8
1.8 Ideal gas mixture .................................................. 1.9
Atmospheric air 1.9
Humidity 1.9
1.9 Real gases ......................................................... 1.10
The van der Waals equation 1.11
The van der Waals constants 1.11
1.10 Intermolecular forces ............................................ 1.12
The Lennard-Jones potential 1.12
The Lennard-Jones parameters 1.13
Hydrogen bond 1.13
1.11 Critical temperature ............................................ 1.14
The van der Waals isoterms 1.14
The critical point 1.15
Critical constants 1.16
1.12 SI units .......................................................... 1.17
Base units 1.17
Derived units 1.17
Prefixes 1.17
Special units 1.18
List of key ideas ...................................................... 1.19
Examples ............................................................. 1.20
1.1: Corrosion of iron – stray current 1.20
1.2: Air hardening of lime mortar 1.21
1.3: Foaming of aerated concrete 1.22
1.4: Accelerated testing of concrete 1.23
page v
Contents
1.5: Molar mass of atmospheric air 1.24
1.6: Chemical shrinkage by hardening of Portland cement 1.25
Exercises .............................................................. 1.27
Literature ............................................................. 1.30
2. Thermodynamic concepts
2.1 Thermodynamic system ........................................... 2.2
System types 2.2
2.2 Description of state ................................................ 2.3
2.3 Thermodynamic variables ......................................... 2.4
2.4 Temperature ....................................................... 2.6
Thermodynamic temperature scale 2.6
Other temperature units 2.6
2.5 Work ............................................................... 2.7
Work and heat 2.7
The concept of work 2.8
Mechanical work 2.8
Volume work 2.9
Surface work 2.10
Electrical work 2.10
2.6 Heat ............................................................... 2.11
Heat capacity of a system 2.12
Specific heat capacity 2.12
Heating of a system of substances 2.13
Symbols and units 2.13
2.7 Thermodynamic process ......................................... 2.14
Process conditions 2.15
Process types 2.15
List of key ideas ...................................................... 2.16
Examples ............................................................. 2.18
2.1: Measuring the adiabatic heat development of concrete 2.18
2.2: Mechanical work in tensile testing of a steel rod 2.19
2.3: Volume work by evaporation of water 2.20
2.4: Surface work by atomization of water 2.21
2.5: Electrical work by galvanizing of steel 2.22
2.6: Heating of mortar by employing hot mixing water 2.24
Exercises............................................................... 2.24
Literature.............................................................. 2.28
3. First law
3.1 Energy ............................................................ 3.2
Energy and energy conservation 3.2
Energy forms 3.2
Kinetic energy 3.2
Potential energy 3.3
Chemical energy 3.3
Summary 3.3
3.2 First law ........................................................... 3.4
Internal energy as a state function 3.5
page vi
Contents
3.3 Internal energy U .................................................. 3.6
Symbols and units 3.7
Internal energy and heat capacity 3.7
3.4 Enthalpy H ......................................................... 3.8
Enthalpy H as a state function 3.8
Symbols and units 3.9
Enthalpy and heat capacity 3.9
3.5 Ideal gas .......................................................... 3.10
Joule’s law 3.11
3.6 Isothermal change of state ....................................... 3.12
3.7 Adiabatic change of state ........................................ 3.13
Adiabatic equations 3.14
Course of adiabats 3.15
3.8 Thermochemical equation ........................................ 3.16
Reaction enthalpy 3.16
Reaction equations 3.16
Reaction heat 3.17
Thermochemical calculation 3.17
Calculation rules 3.18
3.9 Standard enthalpy ................................................ 3.19
Pressure-dependence of enthalpy 3.20
Temperature-dependence of enthalpy 3.20
3.10 Reaction enthalpy ............................................... 3.21
Calculation procedure 3.22
List of key ideas ...................................................... 3.23
Examples ............................................................. 3.24
3.1: Temperature rise in hardening plaster of Paris 3.24
3.2: Computerized calculation of the evaporation heat of water 3.26
3.3: Heat development and hydration of clinker minerals 3.27
3.4: Fire resistance of plaster 3.28
3.5: Measurement of hydration heat with a solution calorimeter 3.30
3.6: Computerized enthalpy calculation 3.32
Exercises .............................................................. 3.33
Literature ............................................................. 3.38
4. Second law
4.1 Introduction ....................................................... 4.2
Spontaneous processes 4.2
Thermodynamic equilibrium 4.2
Thermodynamic process 4.3
4.2 The Carnot cycle ................................................. 4.4
Thermal efficiency 4.4
The Carnot cycle 4.5
4.3 Second law ......................................................... 4.7
Entropy S 4.7
4.4 Temperature dependence of entropy .............................. 4.9
4.5 Entropy change, ideal gas ........................................ 4.10
4.6 Entropy change by phase transformation ........................ 4.12
4.7 Standard entropy ................................................. 4.13
4.8 Reaction entropi .................................................. 4.15
page vii
Contents
Calculation procedure 4.16
4.9 Chemical equilibrium ............................................. 4.17
The constant growth of entropy 4.17
Thermodynamic equilibrium condition 4.18
4.10 The concept of entropy ......................................... 4.19
Micro states 4.19
The probable disorder 4.20
The Boltzmann relation 4.20
Can entropy decrease? 4.21
Phase transformation and disorder 4.21
List of key ideas ...................................................... 4.22
Examples ............................................................. 4.24
4.1: Transformation of tin at a low temperature – ”tin pest” 4.24
4.2: Dehydration of gypsum when grinding Portland cement 4.26
4.3: Computerized calculation of the partial pressure of sat. water vap. 4.27
4.4: Differential thermal analysis of cement paste – DTA 4.29
4.5: Vapour pressure of mercury – occupational exposure limit 4.31
4.6: Control of relative humidity RH by salt hydrates 4.32
Exercises .............................................................. 4.34
Literature ............................................................. 4.37
5. Calculations of equilibrium
5.1 The Gibbs free energy ............................................. 5.2
Definition of free energy G 5.2
The G function differential 5.2
Spontaneous processes 5.3
Free reaction energy 5.4
5.2 The Clapeyron equation ........................................... 5.5
Phase equilibrium in single-component system 5.6
Integration of the Clapeyron equation 5.6
5.3 The Clausius-Clapeyron equation ................................. 5.7
Integration of the Clausius-Clapeyron equation 5.8
5.4 Activity ............................................................ 5.9
5.5 Thermodynamic equilibrium constant ........................... 5.12
Equilibrium condition 5.13
Determination of activity 5.13
5.6 Temperature dependence of equilibrium ........................ 5.14
List of key ideas ...................................................... 5.16
Examples ............................................................. 5.17
5.1: Loss of strength by high-temperature curing of concrete 5.18
5.2: Steel manufacture – reduction of iron ore in blast furnace 5.19
5.3: Capillary condensation in porous construction materials 5.21
5.4: Computerized calculation of the partial pressure of sat. water vap. 5.23
5.5: Adsorption of water in hardened cement paste 5.25
5.6: Precipitation of salt in porous materials – salt damages 5.28
Exercises .............................................................. 5.31
Literature ............................................................. 5.35
page viii
Contents
6. Electrochemistry
6.1 Electric current and charge ...................................... 6.2
Electric current 6.2
Electric charge 6.3
The Faraday constant 6.3
6.2 Electric potential ................................................. 6.4
Field strength 6.4
Electric potential 6.4
Electric work 6.5
6.3 Electric conductivity .............................................. 6.6
Conductivity 6.6
Conductance 6.7
6.4 Electrochemical reaction .......................................... 6.8
Electrochemical cell 6.8
Redox reaction 6.9
Electrochemical process 6.9
6.5 Electrochemical potential ....................................... 6.11
The electrochemical potential 6.11
Daniell cell 6.12
6.6 The Nernst equation ............................................ 6.13
Electric work contribution 6.13
The Nernst equation 6.13
6.7 Temperature dependence of the potential ...................... 6.15
6.8 Notation rules ................................................... 6.16
Cell diagram 6.16
Cell reaction 6.17
6.9 Standard potential ............................................... 6.19
Standard hydrogen electrode 6.19
Potential of single electrode 6.19
6.10 Passivation ...................................................... 6.21
Anode reaction with passivation 6.21
Reinforcement corrosion 6.22
List of key ideas ...................................................... 6.23
Examples ............................................................. 6.25
6.1: Oxidation of metals in water – pH dependence 6.25
6.2: Calculating and producing a Pourbaix diagram for iron Fe 6.27
6.3: Measurement of pH with glass electrode – membrane potential 6.29
6.4: Electrochemical measurement of thermodynamic standard values 6.30
6.5: Hydrogen reduction with polarization – hydrogen brittleness 6.32
Exercises .............................................................. 6.34
Literature ............................................................. 6.38
APPENDIX A
Mathematical appendix
1. Numerical calculations ............................................. A.2
Input data A.2
Specification of uncertainty A.2
Significant digits A.2
Mathematical uncertainty calculation A.3
page ix
Contents
Approximate uncertainty calculation A.4
Example:
Thermodynamic calculation of the ion product and pH of water A.6
Literature A.8
2. Dimensional analysis ............................................... A.8
Fields of application A.8
Limitations A.8
Physical dimension A.9
Types of dimension A.9
Dimensional-homogeneous equation A.10
The Buckingham pi teorem A.10
Determination of pi parameters A.11
Rewriting of pi parameters A.12
Synthetic base units A.13
Calculation examples A.14
Examples:
Non-steady convective cooling of concrete cross-sections A.14
Capillary cohesion in particle systems A.17
Literature A.19
3. Newton-Raphson iteration ........................................ A.19
Example:
Calculation of amount of substance, the van der Waals equation A.20
Literature A.20
4. Cramer’s formula ................................................. A.20
Example:
Solution of linear equation system A.22
Literature A.22
5. Linear regression .................................................. A.22
Example:
Influence of the force-fibre angle on the compressive strength of wood A.24
Literature A.25
6. Exact differential .................................................. A.26
Example:
Change of state, ideal gas A.27
Literature A.28
7. Gradient field ..................................................... A.28
Example:
Calculation of gradient and curve integral A.30
Literature A.30
8. Maxwell’s relations ................................................ A.31
State quantities A.31
Fundamental equations A.31
Maxwell’s relations A.32
Substance parameters A.33
Examples:
Joule’s law for ideal gas A.34
Influence of pressure on the entropy of condensed substances A.35
Temperature change for adiabatic compression of substances A.35
Pressure increase in case of heating with delayed expansion A.36
Literature A.37
9. Debye-Hu¨ckel’s law ............................................... A.37
Ions in solutions A.37
Activity coefficient A.38
page x
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(cid:22)(cid:14) (cid:34)(cid:61)(cid:55)(cid:53)(cid:69)(cid:67)(cid:64)(cid:53)(cid:58)(cid:55)(cid:62)(cid:59)(cid:68)(cid:69)(cid:67)(cid:74) (cid:32)(cid:14)(cid:25)
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Acknowledgeme(cid:16)n(cid:16)t(cid:16)s(cid:16) f(cid:16)o(cid:16)r(cid:16) (cid:16)i(cid:16)ll(cid:16)u(cid:16)s(cid:16)t(cid:16)r(cid:16)a(cid:16)t(cid:16)i(cid:16)o(cid:16)n(cid:16)s(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16)(cid:16) (cid:21)E(cid:7)(cid:9)
(cid:12)(cid:2)(cid:6)(cid:4) (cid:16)(cid:7)
List of symbols
List of symbols
Thelistcontainssymbolsandindicesusedthroughoutthebook. Note:insomecases
the same symbol has been used for a mole-specific and a mass-specific quantity,
for example for specific heat capacity (c). In such cases, the value concerned will be
specifiedbytheunit.Also,thermodynamicstatefunctionssuchasU,H,GandS,which
may occur as both extensive and intensive quantities, are described by the same
symbol.Again,theappliedunitshallbenoted.Thesenotationruleshavebeenchosen
to limit the use of indices and thus further the legibility. In the list, non-dimensional
andabstractquantitiesareindicatedby(–).
A area of cross-section ......................................... (m2)
A nucleon number in atom nucleus (mass number) ............... (−)
A the Helmholtz free energy ............................ (J); (J/mol)
A relative atomic mass m/m ................................... (−)
r u
a activity of substance component .............................. (−)
a the van der Waals constant (correction of pressure) .. (m6Pa/mol2)
a stoichiometric coefficient in reaction equation ................. (−)
(aq) ions or gases in aqueous solution .............................. (−)
b the van der Waals constant (correction of volume) ....... (m3/mol)
b stoichiometric coefficient in reaction equation ................. (−)
C heat capacity of system ..................................... (J/K)
c mole-specific heat capacity ............................. (J/molK)
c mass-specific heat capacity ............................... (J/kgK)
c molar concentration of component (i) .......... (mol/m3); (mol/ℓ)
i
c heat capacity at constant pressure (isobaric) ............ (J/molK)
p
c heat capacity at constant volume (isochoric) ............ (J/molK)
V
c⊖⊖ standard concentration 1 mol/ℓ .......................... (mol/ℓ)
c stoichiometric coefficient in reaction equation ................. (−)
d stoichiometric coefficient in reaction equation ................. (−)
det() determinant of () ............................................. (−)
dim() physical dimension of () ...................................... (−)
E electric field strength ...................................... (V/m)
E modulus of elasticity ....................................... (MPa)
e electric elementary charge ∼1.602·10−19 C ................. (C)
eV electron volt, energy unit ∼1.602·10−19 J ................. (eV)
e− symbol for electron in reaction equation ....................... (−)
F force (vector quantity) ........................................ (N)
F force, component in x direction ............................... (N)
x
F the Faraday constant ∼96500 C/mol ................... (C/mol)
G the Gibbs free energy in thermodynamic system ...... (J); (J/mol)
G⊖⊖ standard free energy at temperature T ................... (J/mol)
T
Δ G free reaction energy .................................. (J); (J/mol)
r
G electric conductance ......................................... Ω−1
(g) gaseous state (”gas”) ......................................... (−)
H enthalpy content in thermodynamic system ........... (J); (J/mol)
H⊖⊖ standard enthalpy at temperature T ..................... (J/mol)
T
Δ H reaction enthalpy ..................................... (J); (J/mol)
r
I electric current ........................................ (A); (C/s)
K thermodynamic equilibrium constant .......................... (−)
a
k Boltzmann constant R/N ∼1.38·10−23 J/K .............. (J/K)
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