Table Of ContentAnatoliy I. Fisenko · Vladimir F. Lemberg
Black-body Radiative,
Thermodynamic, and
Chromatic Functions:
Tables in Finite Spectral
Ranges
Black-body Radiative, Thermodynamic,
and Chromatic Functions: Tables in Finite
Spectral Ranges
Anatoliy I. Fisenko (cid:129) Vladimir F. Lemberg
Black-body Radiative,
Thermodynamic,
and Chromatic Functions:
Tables in Finite
Spectral Ranges
AnatoliyI.Fisenko VladimirF.Lemberg
ONCFEC,Inc. ONCFEC,Inc.
St.Catharines,ON,Canada Etobicoke,ON,Canada
ISBN978-3-319-38994-3 ISBN978-3-319-38995-0 (eBook)
DOI10.1007/978-3-319-38995-0
LibraryofCongressControlNumber:2016935860
©SpringerInternationalPublishingSwitzerland2016
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Vladimir F. Lemberg dedicates this book
to the memory of his father,
Felix A. Lemberg (1936–2015)
Anatoliy I. Fisenko dedicates this book
to the memory of his friend Dr. Tatyana
V. Lokotosh (1957–2015)
Preface
Black-bodyradiationisawell-studiedareainmodernphysics.Thethermalradia-
tiveandthermodynamicpropertiesofblackbodieswereextensivelystudiedtheo-
reticallyinthepast.Asaresult,thetemperaturedependencesofthetotalradiation
power per unit area, total energy density, number density of photons, Helmholtz
free energy density, entropy density, and others are described by well-known
equations.Itisessentialtonotethatthesepropertiesofblack-bodyradiationwere
investigatedinthesemi-infiniterangeoftheelectromagneticspectrum.
However,inpracticallyalldevicesorinstrumentsthatdealwiththermalradia-
tion(detectors,receivers,incandescentsourcesoflight,etc.),onlyasmallregionof
theelectromagneticspectrumisused.Therefore,whendesigningthesedevicesthe
knowledgeoftheblack-bodythermalradiativeandthermodynamicpropertiesina
finitespectralrangeisnecessary.
Overtheyearswe,theauthors,havebeencloselyinvolvedwiththestudyofthis
phenomenon. This book accumulates our own results obtained in this area. The
main purpose of this book is to present the calculated values for the black-body
radiative, thermodynamic, and chromatic functions in the various finite spectral
rangesatdifferenttemperaturesintheformoftables.
The book conceptually consists of two major parts. The first part (Chaps. 1–5)
describes the analytical formulas and methods used for the calculation of the
numerous black-body functions. The second part (Chap. 6) of the book presents
thetableswiththeobtainednumericalresults.
The tables presented in this book are primarily meant to be used by engineers,
scientists,researches,lecturers,universityandcollegestudents,andotherswhoare
interestedintheblack-bodyfunctionsinafinitespectralrange.
InChap.1,theexactanalyticalexpressionsforthethermalradiativefunctions,
such as the total radiation power per unit area, total energy density, and number
densityofphotons,arepresented.
Chapter 2 is devoted to obtaining exact analytical expressions for the thermo-
dynamic functions in the finite spectral range. These functions are (a) Helmholtz
free energy density, (b) enthalpy density, (c) entropy density, (d) heat capacity at
vii
viii Preface
constantvolume,and(e)pressure.Black-bodyradiativeandthermodynamicfunc-
tions for different domains are discussed. Tables 6.1–6.3 are calculated using the
exactanalyticalexpressionsforthethermalradiativeandthermodynamicfunctions
of black-body radiation in the various finite spectral ranges at different tempera-
tures.Weperformedthecalculationsoveraverywiderangeoftemperatures(upto
1K), considering the possible applications in astrophysics, for example, those
whichusetheFIRASinstrumentdata.
In Chap. 3, we present examples of the use of Tables 6.1–6.3 for different
measurement devices. Special attention is given to the calculation of the thermal
radiativeandthermodynamicfunctionsofCosmicMicrowaveBackground(CMB)
radiation.
The chromatic functions of black-body radiation, such as the chromaticity
coordinates and R (red), G (green), and B (blue) values, are investigated in
Chap.4.InTables6.5–6.14,thetemperaturedependenceofthelinearandnonlinear
RGBvaluesfordifferentcolorspaces(Rec.709(HDTV),sRGB,andAdobeRGB)
is presented. In Chap. 5, a number of optimization problems are formulated for
variousthermalblack-bodyradiativeandthermodynamicfunctionsinafiniterange
offrequencies.Anewgenericapproachforsolvingtheseoptimizationproblemsis
proposed. The universal numerical results for the solutions of these optimization
problems are obtained. In Chap. 6, the tables of black-body radiative, thermody-
namic, and chromatic functions in the various finite spectral ranges at different
temperaturesarepresented.
ThederivationsoftheformulasforthetotalenergydensityandHelmholtzfree
energydensityinagivenspectralrangeareprovidedinAppendices.
St.Catharines,ON,Canada AnatoliyI.Fisenko
Etobicoke,ON,Canada VladimirF.Lemberg
Contents
1 Black-BodyRadiativeFunctionsinaGivenSpectralRange. . . . . . . 1
1.1 TotalEnergyDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Stefan-BoltzmannLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 NumberDensityofPhotons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 ThermodynamicsofBlack-BodyRadiation
inaFiniteSpectralRange. .. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. 5
2.1 GeneralRelationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 HelmholtzFreeEnergyDensity. . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 EntropyDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 HeatCapacityatConstantVolumeDensity. . . . . . . . . . . . . . . . . 7
2.5 Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 EnthalpyDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Black-BodyRadiativeandThermodynamicFunctions
forDifferentDomains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 ExamplesoftheUseoftheTables6.1–6.3for
PracticalApplications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 FourierTransformInfraredRadiantSpectrometer(FT-IR). . . . . . 11
3.2 FarInfraredAbsoluteSpectrophotometer(FIRAS). . . . . . . . . . . . 13
3.3 HighTemperatureRadianceSpectroscopy. . . . . . . . . . . . . . . . . . 14
3.4 CosmicMicrowaveBackgroundRadiation(CMB). . . . . . . . . . . . 16
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 ChromaticityPropertiesofBlack-BodyRadiation
forDifferentColorSpaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 GeneralApproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Step1.ObtainingRGBTristimulusValues. . . . . . . . . . . . . . . . . 20
Step2.GettingNormalizedChromaticityCoordinates. . . . . . . . . 25
ix
