Chapter - 2 Thermophysical Properties of Fluids & Materials Chemical Engineering Notes | EduRev

Chemical Engineering : Chapter - 2 Thermophysical Properties of Fluids & Materials Chemical Engineering Notes | EduRev

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BOOKCOMP, Inc. — John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan
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CHAPTER 2
Thermophysical Properties of Fluids
and Materials
*
R.TJACOBSEN
IdahoNationalEngineeringandEnvironmentalLaboratory
IdahoFalls,Idaho
E.W.LEMMON
PhysicalandChemicalPropertiesDivision
NationalInstituteofStandardsandTechnology
Boulder,Colorado
S.G.PENONCELLOandZ.SHAN
CenterforAppliedThermodynamicStudies
CollegeofEngineering
UniversityofIdaho
Moscow,Idaho
N.T.WRIGHT
DepartmentofMechanicalEngineering
UniversityofMaryland
Baltimore,Maryland
2.1 Introduction
2.2 Thermophysicalpropertiesof?uids
2.2.1 Thermodynamic properties
Equationofstate
Calculationofproperties
Thermodynamicpropertiesofmixtures
2.2.2 Transport properties
Extended corresponding states
Dilute-gas contributions
Density-dependent contributions
Transportpropertiesofmixtures
2.3 Thermophysicalpropertiesofsolids
2.3.1 Conservationofenergy
2.3.2 Behaviorofthermophysicalpropertiesofsolids
*
ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology,
not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use
portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions
ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology.
43
Page 2


BOOKCOMP, Inc. — John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan
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CHAPTER 2
Thermophysical Properties of Fluids
and Materials
*
R.TJACOBSEN
IdahoNationalEngineeringandEnvironmentalLaboratory
IdahoFalls,Idaho
E.W.LEMMON
PhysicalandChemicalPropertiesDivision
NationalInstituteofStandardsandTechnology
Boulder,Colorado
S.G.PENONCELLOandZ.SHAN
CenterforAppliedThermodynamicStudies
CollegeofEngineering
UniversityofIdaho
Moscow,Idaho
N.T.WRIGHT
DepartmentofMechanicalEngineering
UniversityofMaryland
Baltimore,Maryland
2.1 Introduction
2.2 Thermophysicalpropertiesof?uids
2.2.1 Thermodynamic properties
Equationofstate
Calculationofproperties
Thermodynamicpropertiesofmixtures
2.2.2 Transport properties
Extended corresponding states
Dilute-gas contributions
Density-dependent contributions
Transportpropertiesofmixtures
2.3 Thermophysicalpropertiesofsolids
2.3.1 Conservationofenergy
2.3.2 Behaviorofthermophysicalpropertiesofsolids
*
ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology,
not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use
portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions
ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology.
43
BOOKCOMP, Inc. — John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan
44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS
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2.3.3 Propertyvaluesofsolidmaterials
2.3.4 Measuringthermophysicalpropertiesofsolids
Thermal conductivity
Speci?c heat
Thermal diffusivity
Thermal expansion
Nomenclature
References
Graphsofthermophysicalproperties
2.1 INTRODUCTION
The need for accurate thermophysical properties in the design and analysis of en-
gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking
?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom
crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It
is particularly true that small errors in properties for custody transfer of ?uids can
result in signi?cant costs or bene?ts to those involved in commercial transactions. It
istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora
particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis
inlightoftheaccuracyofthepropertiesused.
In addition to the individual properties for system design and analysis, there is a
need for combined heat transfer parameters and dimensionless groups that occur in
equations for conduction, convection, and radiation. These include:
Biot number Boussinesq number Eckert number
Fouriernumber Graetznumber Grashofnumber
Lewis number Nusselt number P´ eclet number
Prandtl number Rayleigh number Reynolds number
Schmidt number Sherwood number
Only the Prandtl number is a ?uid property; the others incorporate system character-
istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this
book and are not discussed in this chapter.
The termthermophysicalproperties is used here to refer to both thermodynamic
(equilibrium) properties and transport properties. The thermodynamic properties de-
?ne equilibrium states ofthe system and include such properties as temperature,
pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en-
tropy. The transport properties are those such as thermal conductivity, viscosity, and
thermal diffusivity which pertain to the transfer of momentum or energy within the
system. In a practical sense, design and analysis ofheat transf er systems require
information about both transport and thermodynamic properties. The thermodynamic
properties are generally well de?ned by measurement for most common ?uids and
Page 3


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CHAPTER 2
Thermophysical Properties of Fluids
and Materials
*
R.TJACOBSEN
IdahoNationalEngineeringandEnvironmentalLaboratory
IdahoFalls,Idaho
E.W.LEMMON
PhysicalandChemicalPropertiesDivision
NationalInstituteofStandardsandTechnology
Boulder,Colorado
S.G.PENONCELLOandZ.SHAN
CenterforAppliedThermodynamicStudies
CollegeofEngineering
UniversityofIdaho
Moscow,Idaho
N.T.WRIGHT
DepartmentofMechanicalEngineering
UniversityofMaryland
Baltimore,Maryland
2.1 Introduction
2.2 Thermophysicalpropertiesof?uids
2.2.1 Thermodynamic properties
Equationofstate
Calculationofproperties
Thermodynamicpropertiesofmixtures
2.2.2 Transport properties
Extended corresponding states
Dilute-gas contributions
Density-dependent contributions
Transportpropertiesofmixtures
2.3 Thermophysicalpropertiesofsolids
2.3.1 Conservationofenergy
2.3.2 Behaviorofthermophysicalpropertiesofsolids
*
ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology,
not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use
portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions
ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology.
43
BOOKCOMP, Inc. — John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan
44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS
1
2
3
4
5
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7
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11
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PgEnds: T
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[44], (2)
2.3.3 Propertyvaluesofsolidmaterials
2.3.4 Measuringthermophysicalpropertiesofsolids
Thermal conductivity
Speci?c heat
Thermal diffusivity
Thermal expansion
Nomenclature
References
Graphsofthermophysicalproperties
2.1 INTRODUCTION
The need for accurate thermophysical properties in the design and analysis of en-
gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking
?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom
crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It
is particularly true that small errors in properties for custody transfer of ?uids can
result in signi?cant costs or bene?ts to those involved in commercial transactions. It
istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora
particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis
inlightoftheaccuracyofthepropertiesused.
In addition to the individual properties for system design and analysis, there is a
need for combined heat transfer parameters and dimensionless groups that occur in
equations for conduction, convection, and radiation. These include:
Biot number Boussinesq number Eckert number
Fouriernumber Graetznumber Grashofnumber
Lewis number Nusselt number P´ eclet number
Prandtl number Rayleigh number Reynolds number
Schmidt number Sherwood number
Only the Prandtl number is a ?uid property; the others incorporate system character-
istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this
book and are not discussed in this chapter.
The termthermophysicalproperties is used here to refer to both thermodynamic
(equilibrium) properties and transport properties. The thermodynamic properties de-
?ne equilibrium states ofthe system and include such properties as temperature,
pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en-
tropy. The transport properties are those such as thermal conductivity, viscosity, and
thermal diffusivity which pertain to the transfer of momentum or energy within the
system. In a practical sense, design and analysis ofheat transf er systems require
information about both transport and thermodynamic properties. The thermodynamic
properties are generally well de?ned by measurement for most common ?uids and
BOOKCOMP, Inc. — John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan
INTRODUCTION 45
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mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor
the same ?uids and mixtures. This is, in part, because the experimental methods for
measuring transport properties are generally less accurate than those for the thermo-
dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements
(see Wakeham et al., 1991).
Current practice in the design and analysis of?uid systems requires the use of
computer programs in various forms for thermophysical properties. Based on the ex-
perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor
engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases
available to the engineer. Such sources of highly accurate properties are often referred
to asstandardreferencequality sources, and many are the result ofinternational
agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical
accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If
special applications require equations with fewer terms for rapidly estimating proper-
ties or for calculating abbreviated tables, these can be developed based on properties
calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin
the properties used in design can be determined by comparisons to values from the
source,theaccuraciesofwhicharegenerallywellspeci?ed.
We have assumed that the user ofthis book has access to a reasonably current
personal computer and to the World Wide Web. Because the National Institute of
Standards and Technology (NIST) databases generally incorporate the best available
?uid properties algorithms and equations, we rely heavily on those sources in the
recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties
ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter,
graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection
ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues
for ?uid properties that are readily available in other sources, including common
engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty
values at common conditions are given for completeness.
Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof
?uids may be calculated using several comprehensive computer programs from NIST,
including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer
program is included in this book for use in calculating properties for design and
analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare
also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry.
Although the NIST programs provide the most accurate values currently avail-
able, additional research, experimentation, and correlation activities worldwide will
increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe
covered ?uids. The full programs with source code and mixture capabilities are avail-
able from NIST at a nominal cost and are updated periodically. Details concerning
the current databases available from the Standard Reference Data Of?ce of NIST are
located at the Web address http://www.nist.gov/srd by searching for the key words
NIST10, NIST12, NIST14, or NIST23.
There are fewer sources of properties of solids for design than there are for ?uids,
and the data available have not yet been incorporated into evaluated wide-range com-
puter models. The uncertainties associated with published values for many properties
Page 4


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Normal Page
PgEnds: T
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[43], (1)
CHAPTER 2
Thermophysical Properties of Fluids
and Materials
*
R.TJACOBSEN
IdahoNationalEngineeringandEnvironmentalLaboratory
IdahoFalls,Idaho
E.W.LEMMON
PhysicalandChemicalPropertiesDivision
NationalInstituteofStandardsandTechnology
Boulder,Colorado
S.G.PENONCELLOandZ.SHAN
CenterforAppliedThermodynamicStudies
CollegeofEngineering
UniversityofIdaho
Moscow,Idaho
N.T.WRIGHT
DepartmentofMechanicalEngineering
UniversityofMaryland
Baltimore,Maryland
2.1 Introduction
2.2 Thermophysicalpropertiesof?uids
2.2.1 Thermodynamic properties
Equationofstate
Calculationofproperties
Thermodynamicpropertiesofmixtures
2.2.2 Transport properties
Extended corresponding states
Dilute-gas contributions
Density-dependent contributions
Transportpropertiesofmixtures
2.3 Thermophysicalpropertiesofsolids
2.3.1 Conservationofenergy
2.3.2 Behaviorofthermophysicalpropertiesofsolids
*
ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology,
not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use
portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions
ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology.
43
BOOKCOMP, Inc. — John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan
44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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[44], (2)
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———
Long Page
PgEnds: T
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[44], (2)
2.3.3 Propertyvaluesofsolidmaterials
2.3.4 Measuringthermophysicalpropertiesofsolids
Thermal conductivity
Speci?c heat
Thermal diffusivity
Thermal expansion
Nomenclature
References
Graphsofthermophysicalproperties
2.1 INTRODUCTION
The need for accurate thermophysical properties in the design and analysis of en-
gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking
?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom
crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It
is particularly true that small errors in properties for custody transfer of ?uids can
result in signi?cant costs or bene?ts to those involved in commercial transactions. It
istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora
particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis
inlightoftheaccuracyofthepropertiesused.
In addition to the individual properties for system design and analysis, there is a
need for combined heat transfer parameters and dimensionless groups that occur in
equations for conduction, convection, and radiation. These include:
Biot number Boussinesq number Eckert number
Fouriernumber Graetznumber Grashofnumber
Lewis number Nusselt number P´ eclet number
Prandtl number Rayleigh number Reynolds number
Schmidt number Sherwood number
Only the Prandtl number is a ?uid property; the others incorporate system character-
istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this
book and are not discussed in this chapter.
The termthermophysicalproperties is used here to refer to both thermodynamic
(equilibrium) properties and transport properties. The thermodynamic properties de-
?ne equilibrium states ofthe system and include such properties as temperature,
pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en-
tropy. The transport properties are those such as thermal conductivity, viscosity, and
thermal diffusivity which pertain to the transfer of momentum or energy within the
system. In a practical sense, design and analysis ofheat transf er systems require
information about both transport and thermodynamic properties. The thermodynamic
properties are generally well de?ned by measurement for most common ?uids and
BOOKCOMP, Inc. — John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan
INTRODUCTION 45
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2
3
4
5
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[45], (3)
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[45], (3)
mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor
the same ?uids and mixtures. This is, in part, because the experimental methods for
measuring transport properties are generally less accurate than those for the thermo-
dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements
(see Wakeham et al., 1991).
Current practice in the design and analysis of?uid systems requires the use of
computer programs in various forms for thermophysical properties. Based on the ex-
perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor
engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases
available to the engineer. Such sources of highly accurate properties are often referred
to asstandardreferencequality sources, and many are the result ofinternational
agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical
accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If
special applications require equations with fewer terms for rapidly estimating proper-
ties or for calculating abbreviated tables, these can be developed based on properties
calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin
the properties used in design can be determined by comparisons to values from the
source,theaccuraciesofwhicharegenerallywellspeci?ed.
We have assumed that the user ofthis book has access to a reasonably current
personal computer and to the World Wide Web. Because the National Institute of
Standards and Technology (NIST) databases generally incorporate the best available
?uid properties algorithms and equations, we rely heavily on those sources in the
recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties
ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter,
graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection
ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues
for ?uid properties that are readily available in other sources, including common
engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty
values at common conditions are given for completeness.
Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof
?uids may be calculated using several comprehensive computer programs from NIST,
including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer
program is included in this book for use in calculating properties for design and
analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare
also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry.
Although the NIST programs provide the most accurate values currently avail-
able, additional research, experimentation, and correlation activities worldwide will
increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe
covered ?uids. The full programs with source code and mixture capabilities are avail-
able from NIST at a nominal cost and are updated periodically. Details concerning
the current databases available from the Standard Reference Data Of?ce of NIST are
located at the Web address http://www.nist.gov/srd by searching for the key words
NIST10, NIST12, NIST14, or NIST23.
There are fewer sources of properties of solids for design than there are for ?uids,
and the data available have not yet been incorporated into evaluated wide-range com-
puter models. The uncertainties associated with published values for many properties
BOOKCOMP, Inc. — John Wiley & Sons / Page 46 / 2nd Proofs /HeatTransferHandbook / Bejan
46 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS
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ofsolidsaregenerallylargerthanthoseforpropertiesof?uids,inpartbecauseofim-
purities or compositional variations in experimental samples. In this chapter we have
includedselectedpropertiesofsolidsfromreliablepublishedsources.
Thischaptercontainsaminimumoftheoryandnodetailsonthecorrelationand
analysis of thermophysical property data for determining the recommended values for
both ?uids and solids. Literature references are given for the best available sources
known for the various properties. The references should be useful to the reader who is
interested in greater detail about the correlation methods and about the data on which
the correlations and recommended values are based.
2.2 THERMOPHYSICAL PROPERTIES OF FLUIDS
Thethermodynamicandtransportpropertiesof?uidsarediscussedseparatelyinthis
section.Sourcesofcalculatedvaluesandbriefdescriptionsofthemethodsusedto
determine values in the tables and graphs in this book are given. References to original
worksthatcontaindetailsofbothcorrelationandmeasurementtechniquesarealso
included.
2.2.1 Thermodynamic Properties
Apropertyformulationisthesetofequationsusedtocalculatepropertiesofa?uid
at speci?ed thermodynamic states de?ned by the appropriate independent variables.
A typical thermodynamic property formulation is based on an equation of state that
allowsthecorrelationandcomputationofallthermodynamicpropertiesofthe?uid,
including properties such as entropy that cannot be measured directly.
The general termequationofstate in this chapter refers to an empirical model
developed for calculating thermodynamic properties of ?uids. The termfundamental
equation is often used in the literature to refer to empirical descriptions of one of
four fundamental relations: internal energy as a function of volume and entropy,
enthalpy as a function of pressure and entropy, Gibbs energy as a function of pressure
and temperature, and Helmholtz energy as a function of density and temperature.
Modernequationsofstateforthethermodynamicpropertiesofpure?uidsareusually
fundamental equations explicit in the Helmholtz energy as a function of density and
temperature.
The equation of state for a pure ?uid using the Helmholtz energy as the fundamen-
tal property is given by
a(?,T)= a
0
(?,T)+a
r
(?,T) (2.1)
where a is the molar Helmholtz energy, a
0
(?,T) is the ideal gas contribution to the
Helmholtz energy, anda
r
(?,T) is the residual Helmholtz energy that corresponds to
thein?uenceofintermolecularforces.Allthermodynamicpropertiescanbecalcu-
latedasderivativesoftheHelmholtzenergy.Forexample,thepressurederivedfrom
this expression is
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CHAPTER 2
Thermophysical Properties of Fluids
and Materials
*
R.TJACOBSEN
IdahoNationalEngineeringandEnvironmentalLaboratory
IdahoFalls,Idaho
E.W.LEMMON
PhysicalandChemicalPropertiesDivision
NationalInstituteofStandardsandTechnology
Boulder,Colorado
S.G.PENONCELLOandZ.SHAN
CenterforAppliedThermodynamicStudies
CollegeofEngineering
UniversityofIdaho
Moscow,Idaho
N.T.WRIGHT
DepartmentofMechanicalEngineering
UniversityofMaryland
Baltimore,Maryland
2.1 Introduction
2.2 Thermophysicalpropertiesof?uids
2.2.1 Thermodynamic properties
Equationofstate
Calculationofproperties
Thermodynamicpropertiesofmixtures
2.2.2 Transport properties
Extended corresponding states
Dilute-gas contributions
Density-dependent contributions
Transportpropertiesofmixtures
2.3 Thermophysicalpropertiesofsolids
2.3.1 Conservationofenergy
2.3.2 Behaviorofthermophysicalpropertiesofsolids
*
ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology,
not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use
portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions
ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology.
43
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2.3.3 Propertyvaluesofsolidmaterials
2.3.4 Measuringthermophysicalpropertiesofsolids
Thermal conductivity
Speci?c heat
Thermal diffusivity
Thermal expansion
Nomenclature
References
Graphsofthermophysicalproperties
2.1 INTRODUCTION
The need for accurate thermophysical properties in the design and analysis of en-
gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking
?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom
crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It
is particularly true that small errors in properties for custody transfer of ?uids can
result in signi?cant costs or bene?ts to those involved in commercial transactions. It
istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora
particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis
inlightoftheaccuracyofthepropertiesused.
In addition to the individual properties for system design and analysis, there is a
need for combined heat transfer parameters and dimensionless groups that occur in
equations for conduction, convection, and radiation. These include:
Biot number Boussinesq number Eckert number
Fouriernumber Graetznumber Grashofnumber
Lewis number Nusselt number P´ eclet number
Prandtl number Rayleigh number Reynolds number
Schmidt number Sherwood number
Only the Prandtl number is a ?uid property; the others incorporate system character-
istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this
book and are not discussed in this chapter.
The termthermophysicalproperties is used here to refer to both thermodynamic
(equilibrium) properties and transport properties. The thermodynamic properties de-
?ne equilibrium states ofthe system and include such properties as temperature,
pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en-
tropy. The transport properties are those such as thermal conductivity, viscosity, and
thermal diffusivity which pertain to the transfer of momentum or energy within the
system. In a practical sense, design and analysis ofheat transf er systems require
information about both transport and thermodynamic properties. The thermodynamic
properties are generally well de?ned by measurement for most common ?uids and
BOOKCOMP, Inc. — John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan
INTRODUCTION 45
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mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor
the same ?uids and mixtures. This is, in part, because the experimental methods for
measuring transport properties are generally less accurate than those for the thermo-
dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements
(see Wakeham et al., 1991).
Current practice in the design and analysis of?uid systems requires the use of
computer programs in various forms for thermophysical properties. Based on the ex-
perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor
engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases
available to the engineer. Such sources of highly accurate properties are often referred
to asstandardreferencequality sources, and many are the result ofinternational
agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical
accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If
special applications require equations with fewer terms for rapidly estimating proper-
ties or for calculating abbreviated tables, these can be developed based on properties
calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin
the properties used in design can be determined by comparisons to values from the
source,theaccuraciesofwhicharegenerallywellspeci?ed.
We have assumed that the user ofthis book has access to a reasonably current
personal computer and to the World Wide Web. Because the National Institute of
Standards and Technology (NIST) databases generally incorporate the best available
?uid properties algorithms and equations, we rely heavily on those sources in the
recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties
ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter,
graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection
ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues
for ?uid properties that are readily available in other sources, including common
engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty
values at common conditions are given for completeness.
Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof
?uids may be calculated using several comprehensive computer programs from NIST,
including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer
program is included in this book for use in calculating properties for design and
analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare
also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry.
Although the NIST programs provide the most accurate values currently avail-
able, additional research, experimentation, and correlation activities worldwide will
increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe
covered ?uids. The full programs with source code and mixture capabilities are avail-
able from NIST at a nominal cost and are updated periodically. Details concerning
the current databases available from the Standard Reference Data Of?ce of NIST are
located at the Web address http://www.nist.gov/srd by searching for the key words
NIST10, NIST12, NIST14, or NIST23.
There are fewer sources of properties of solids for design than there are for ?uids,
and the data available have not yet been incorporated into evaluated wide-range com-
puter models. The uncertainties associated with published values for many properties
BOOKCOMP, Inc. — John Wiley & Sons / Page 46 / 2nd Proofs /HeatTransferHandbook / Bejan
46 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS
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ofsolidsaregenerallylargerthanthoseforpropertiesof?uids,inpartbecauseofim-
purities or compositional variations in experimental samples. In this chapter we have
includedselectedpropertiesofsolidsfromreliablepublishedsources.
Thischaptercontainsaminimumoftheoryandnodetailsonthecorrelationand
analysis of thermophysical property data for determining the recommended values for
both ?uids and solids. Literature references are given for the best available sources
known for the various properties. The references should be useful to the reader who is
interested in greater detail about the correlation methods and about the data on which
the correlations and recommended values are based.
2.2 THERMOPHYSICAL PROPERTIES OF FLUIDS
Thethermodynamicandtransportpropertiesof?uidsarediscussedseparatelyinthis
section.Sourcesofcalculatedvaluesandbriefdescriptionsofthemethodsusedto
determine values in the tables and graphs in this book are given. References to original
worksthatcontaindetailsofbothcorrelationandmeasurementtechniquesarealso
included.
2.2.1 Thermodynamic Properties
Apropertyformulationisthesetofequationsusedtocalculatepropertiesofa?uid
at speci?ed thermodynamic states de?ned by the appropriate independent variables.
A typical thermodynamic property formulation is based on an equation of state that
allowsthecorrelationandcomputationofallthermodynamicpropertiesofthe?uid,
including properties such as entropy that cannot be measured directly.
The general termequationofstate in this chapter refers to an empirical model
developed for calculating thermodynamic properties of ?uids. The termfundamental
equation is often used in the literature to refer to empirical descriptions of one of
four fundamental relations: internal energy as a function of volume and entropy,
enthalpy as a function of pressure and entropy, Gibbs energy as a function of pressure
and temperature, and Helmholtz energy as a function of density and temperature.
Modernequationsofstateforthethermodynamicpropertiesofpure?uidsareusually
fundamental equations explicit in the Helmholtz energy as a function of density and
temperature.
The equation of state for a pure ?uid using the Helmholtz energy as the fundamen-
tal property is given by
a(?,T)= a
0
(?,T)+a
r
(?,T) (2.1)
where a is the molar Helmholtz energy, a
0
(?,T) is the ideal gas contribution to the
Helmholtz energy, anda
r
(?,T) is the residual Helmholtz energy that corresponds to
thein?uenceofintermolecularforces.Allthermodynamicpropertiescanbecalcu-
latedasderivativesoftheHelmholtzenergy.Forexample,thepressurederivedfrom
this expression is
BOOKCOMP, Inc. — John Wiley & Sons / Page 47 / 2nd Proofs /HeatTransferHandbook / Bejan
THERMOPHYSICALPROPERTIESOFFLUIDS 47
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p= ?
2

?a
??

T
(2.2)
Also, the thermodynamic properties at saturation conditions can be calculated with-
out additional ancillary equations through the use ofthe Maxwell criterion (equal
pressures and Gibbs energies at constant temperature during phase changes).
Thequalityofathermodynamicpropertyformulationisdeterminedbyitsability
to model the physical behavior ofthe ?uid as represented by the available data as
well as by its conformance to theory (to assure reasonable extrapolation behavior).
Publishedcorrelationsshouldincludeestimatesoftheaccuracyofcalculatedproper-
tiesaswellasacarefulde?nitionoftherangeofvalidity.Amodernthermodynamic
property formulation is generally capable of representing all data values within the
estimatedexperimentaluncertaintyofthemeasurements(seeTable2.1).Thepracti-
calmodelsoftodayareempiricalorsemiempiricalinnature,althoughvirtuallyall
arebasedonsoundtheoreticalprinciples.Thelimitationsofthemodelselectedmust
be understood by the user for effective system optimization and related work.
Correctbehavioroftheequationofstateinthecriticalregion(boundedby ±0.25?
c
and ±0.05T
c
) is sometimes a concern ofusers ofproperty f ormulations. Classical
equations (those that do not use an additional scaling theory) cannot represent the
theoretically expected behavior at the critical point. However, state-of-the-art multi-
parameterequationsofstatearesuf?cientlyaccurateinthecriticalregiontosatisfy
TABLE2.1 GeneralStandardUncertaintyEstimatesforVariousFluidProperties
Uncertainty
State-of-the-Art to Be Expected
Experimental from a Modern
CalculatedProperty Region Uncertainty(%) EquationofState(%)
Pressure — 0.02
Temperature — 0.001 K
Density — 0.02 0.1
Isochoric heat capacity ? > ?
c
0.5 0.5
? < ?
c
11
Isobaric heat capacity ? > ?
c
0.5 1
? < ?
c
21
Speedofsound ? > ?
c
0.1 0.5
? < ?
c
0.01 0.1
Vapor pressure p< 0.1 MPa 0.05 0.5
p> 0.1 MPa 0.01 0.2
Thermal conductivity ? > ?
c
0.5 0.5
? < ?
c
22
Viscosity ? > ?
c
22
? < ?
c
0.5 0.5
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