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ASTRONOMYDEPT,

THETHEORYOFHEATRADIATION

PLANCKANDMASIUS

Li

THETHEORY

OF

HEATRADIATION

BY

DR.MAXPLANCK

AUTHORISEDJTRANSLATION

BY

MORTONJVUSIUS,M.A.,Ph.D.(Leipzig)

WITH7ILLUSTRATIONS

PHILADELPHIA

P.BLAKISTONSSON&CO.

1012WALNUTSTREET

SEP29

ASTRONOMYDEFT;

COPYRIGHT,1914,BYP.BLAKISTONSSON&Co.

THE.MAPLHPRESS-YORK-PA

TRANSLATORSPREFACE

ofreasoninginaforeignlanguage. toobriefortopresentsomedifficulties. viTRANSLATORSPREFACE scriptandthegalleyproof.MORTONMASIUS.

WORCESTER,MASS.,

February,1914.

PREFACETOSECONDEDITION

vii viiiPREFACETOSECONDEDITION

PREFACETOSECONDEDITIONix

discussalldifferingopinions. quantumofactionpromisestothrowsomelight. generation.

THEAUTHOR.

BERLIN,

November,1912.

PREFACETOFIRSTEDITION

asregardsspecialdetails. XI

TABLEOFCONTENTS

PARTI

FUNDAMENTALFACTSANDDEFINITIONS

CHAPTERPAGE

I.GeneralIntroduction1

BlackRadiation22

PARTII

,I.MaxwellsRadiationPressure49

II.Stefan-BoltzmannLawofRadiation59

III.WiensDisplacementLaw69

PARTIII

ENTROPYANDPROBABILITY

II.IdealMonatomicGases127

III.IdealLinearOscillators135

Equilibrium144

PARTIV

ASYSTEMOFOSCILLATORSINASTATIONARYFIELDOF

RADIATION

II.AbsorbedEnergy155

III.EmittedEnergy.StationaryState161

QuantaofMatterandofElectricity167

xiii xivTABLEOFCONTENTS PARTV

IRREVERSIBLERADIATIONPROCESSES

I.FieldsofRadiationinGeneral189

II.OneOscillatorintheFieldofRadiation196

III.ASystemofOscillators200

bytheAuthor216

Appendices218

Errata..225

PARTI

FUNDAMENTALFACTSANDDEFINITIONS

RADIATIONOFHEAT

CHAPTERI

GENERALINTRODUCTION

conduction. 1

2FUNDAMENTALFACTSANDDEFINITIONS

speakofthe " giverisetoanyparticulardifficulty.

GENERALINTRODUCTION3

wespeakof phenomenatobeconsidered.

4FUNDAMENTALFACTSANDDEFINITIONS

randomundirectedheatmotioncannotbemade. firstthethreeprocessesjustmentioned. otherformsofenergy(heat,

1chemicalorelectricenergy,etc.)

lessintenseradiations. "heat."(Tr.)

GENERALINTRODUCTION5

r >v.The

6FUNDAMENTALFACTSANDDEFINITIONS

the alsobefinite. prism. elementdrto dtdT-dttdv2*,.(1) conicalelementsdttis4,w,weget: CO dt-dr.SwI<,dv.t(2)

GENERALINTRODUCTION7

weaker,BastrongeremitterthanA. giventhecommonname "phenomenaofluminescence."We shalldealwithpure pletelydeterminedbythetemperature. nonof " chemically. p.155,1904.

8FUNDAMENTALFACTSANDDEFINITIONS

erlyregardedasopticallyhomogeneous,

1providedonlythatthe

turbidbythepresenceofmolecules. phereasbytheairmoleculesthemselves. tionisproportionaltos,say fts(3) radiationandiscalledthe appliedtoanymaterialsubstance.

GENERALINTRODUCTION9

forraysofshorterwavelength;

1hencethebluecolorofdiffuse

skylight. anyfurtherdiscussionofthesequestions. andrefractionmaybe " regular,"therebeingasinglereflected medium. iLordRayleigh,Phil.Mag.,47,p.379,1899.

10FUNDAMENTALFACTSANDDEFINITIONS

called "black."

Inadditionto

used.AccordingtoG.Kirchhoff

1itdenotesabodywhichhas

thesurface.2 definition. body.

GENERALINTRODUCTION11

12.Absorption.Heatraysaredestroyedby

" absorption." isused. andmaybewritten a,s(4)

Hereavisknownasthe

peratureT,andthenatureofthemedium. small,containsmanywavelengths(Sec.2).

12FUNDAMENTALFACTSANDDEFINITIONS

ray,butonadefinitepositioninspace. when >=!

GENERALINTRODUCTION13

surface. andbyanazimuth coneis d!2=sin0-d6-d<i>.(5) do-inthedirectionoftheconedttis: dtdo-cosddttK=Ksin6cosdd d<t>do-dt.(6) stitutingTTforandTT+ <for precedingone. integratingwithrespectto (/>fromto2irandwithrespectto

7Tfromto-

27T2
I <*0f t/ot/o ddKsincos8do-dt.

14FUNDAMENTALFACTSANDDEFINITIONS

TTKd<jdt.(7)

Fromapencilofrayscalled

"parallel "afiniteamountofenergyof narrowcone. homogeneousormonochromatic. intensitymaybewrittenintheform

K.cosV+K/sinV

andK.sinV+K/cosV(8)

GENERALINTRODUCTION15

the v.

Hencewecallthesevaluesthe

"principalvaluesoftheintensi maywritegenerally I (9) CO dtdo-cos6dQIdv(K.+K/)(10)I K,:

ForunpolarizedraysK,=K/,andhence

oo

K=2CdvK,,(12)=2CdvK

2dtdo-cos$dtiK,dv=2dtdo-sin6cosdd

d<j>K,dv.(13) foundfrom(7)and(12);itis

27rdadt1Kvdv.(14)I

16FUNDAMENTALFACTSANDDEFINITIONS

Thiswillbefurtherdiscussedlateron.

from v=\(15)A qdXdv--* isobtained.Hencewegetbysubstitution:

E,=.(16)

GENERALINTRODUCTION17

lineardimensionsoftheelementsdaandda fbutstillsosmall manousmedia. angleis dacos(/,r)^-

I"

where/denotesthenormalofda fandtheangle(v 1 ,r)istobe ofthevertexoftheconeonda. radiationrequiredisfoundtobe:

ArArcos(r,r)-cos(/,r)K----at.(17)

energywillbe,accordingtoequation(11), dadacos(v,r)cos(i>,r)

K,,dv--dt.(18)r2

ifwechoosedalargecomparedwithda.

18FUNDAMENTALFACTSANDDEFINITIONS

"focalplanes"ofthepencil. thatcasethe "cross-section "ofthewholepencilatadefinite

GENERALINTRODUCTION19

liesataninfinitedistance. ofradiusr,rbeinglargecompared withthelineardimensionsofvbut stillsosmallthatnoappreciable absorptionorscatteringoftheradia tiontakesplaceinthedistancer (Fig.1).Everyraywhichreaches vmustthencomefromsomepoint onthesurfaceofthesphere.If, then,weatfirstconsideronlyallthe raysthatcomefromthepointsofan morethanonce.

20FUNDAMENTALFACTSANDDEFINITIONS

sis: certainelementofa hencetheenergyis: -f-f rdaJ~K=-S

2-Kda.(19)

fromdaandentervwehave

Kda_Kdo-

r2qr2q -ofa thesphere,wegetforthewholeenergy: -IKdQ. dividingbyv.Itis =-KdQ. lj (20)

GENERALINTRODUCTION21

onintegrationweget: trumweget: (22) -(K.+K/)dfi,(23)u,=Ii ij directions: STTK, u,=-(24)

CHAPTERII

inentropyispossible. significance. (Sec.52). 22

RADIATIONATTHERMODYNAMICEQUILIBRIUM23

scattering. theelementofarea.

24FUNDAMENTALFACTSANDDEFINITIONS

volume-elementv. CO dtVS-JTIdvV-STTI Jo chemicalnatureofthemedium. intensity(energyradiatedperunittime) da-~ 2-K spectrumseparately: 2da

Hencetheintensityofamonochromaticrayis:

2da*K,dv.

r2 thetimedtis,accordingto(4), dta,,s2da9K,dv. r2

RADIATIONATTHERMODYNAMICEQUILIBRIUM25

Cda= Jr*= 00 f,K, Jo dtvSirIavK,dv.(25) Jo oo =IOLK,,dv.f*,^=r JotJo frequencytherelation: e,=a,K,,or(26)

K,=(27)av

tionofthemediumforthisfrequency.

26FUNDAMENTALFACTSANDDEFINITIONS

whateverofthatcolor. raysofthefrequencyv.

RADIATIONATTHERMODYNAMICEQUILIBRIUM27

finitecoefficientofabsorption. similarto(25),namely, CO ftK,dv.(28) sionby-r-.Thisgives 00 fJo K,dv, dtvdSlhK,,dv.(29)

28FUNDAMENTALFACTSANDDEFINITIONS

otherrays. ousisotropicmediumwhichisinthermodynamic thiscasedt=l,6=0,by dadfiK,dv. .(30) mediumwereperfectlydiathermanous.

RADIATIONATTHERMODYNAMICEQUILIBRIUM29

byputting do- dt=l,dr=drr2dtt,dtt=-^TO andomittingthenumericalfactor2.Wethusget

E=drdttdae,dv.(31)

distances=drwehave or, dr and,byintegration, whichreachesisfoundtobe

E=Ee-(a

"+^ro=drdfido-c,*-**+**dv.(32) 00 d!2dadve,fdre-(a >+ft >)r=dttda^dv.(33)f 1

30FUNDAMENTALFACTSANDDEFINITIONS

fromwithout.TheradiationE fthuscollectedbythevolume- elementatrisfound,byputtingin(29), dt=1,v=drdQ,r do- tobe

E=drdQdaftK,dv.

rwefind:

E+E=drdttdo-(e,+ftK,)dv.

Thepartofthisreachingis,similarto(32):

drdtida(e,+ftK.)dve~ ro(a-"W theenergyultimatelyreachingdo- dtidafe+ftK,)d asmaybeseenbycomparisonwith(26).

RADIATIONATTHERMODYNAMICEQUILIBRIUM31

32FUNDAMENTALFACTSANDDEFINITIONS

ever.

RADIATIONATTHERMODYNAMICEQUILIBRIUM33

mediumandfallingontheboundingsurface.

BoundingSurface

FIG.3.

containedintheconicalelementdtt,quotesdbs_dbs47.pdfusesText_47

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