A Study of Fundamental Law of Thermal Radiation and Thermal Equilibrium Process

Transcription

1 Itratoal Joural of Hgh Ergy Physcs 5; (3): Publshd ol May 6, 5 ( do:.648/j.jhp.53. ISSN: (Prt); ISSN: (Ol) A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss Ch Dayou Shaax Socty of Optcs, Photolctro ad Quatum Elctrocs, X a, Cha Emal addrss: Chdayou668@63.com To ct ths artcl: Ch Dayou. A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss. Itratoal Joural of Hgh Ergy Physcs. Vol., No. 3, 5, pp do:.648/j.jhp.53. Abstract: Th fudamtal law of thrmal qulbrum radato cluds two lmts: th law of rgy dstrbuto of mattr vbrators th radato fld ad th law of rgy xchag btw vbrators ad th radato fld. Ths papr dscovrs th law of how vbrators stmulat ad absorb radato, by a study of th black-body radato law ad th charactrstcs of vbrators absorpto of radato. As for th fudamtal law of thrmal qulbrum radato, ts complt xprsso should b: th rgy dstrbuto of vbrators th thrmal qulbrum radato fld follows th rgy dstrbuto law by L. Boltzma; th probablty of vbrators stmulatg radato s drctly proportoal to thr stat of rgy lvls ad that of thr absorbg radato s drctly proportoal to thr rgy dstrbuto probablty. Th author, o th bass of th fudamtal law of thrmal radato, proposs codtos for thrmal qulbrum radato ad aalyss th mcro momtum thory ad charactrstcs th procss of thrmal qulbrum. Kywords: Thrmal Equlbrum Radato, Stat of Ergy Lvls, Probablty of Ergy Lvls, Thrmal Equlbrum Procss, Fudamtal Law of Thrmal Radato. Itroducto Th thortc study ad lab xprmt of thrmal radato s of spcal sgfcac th hstory of dvlopmt of physcs. Espcally th study of black-body radato law rsults th foudg of quatum physcs. Hstorcally, thr hav b two ma mthods. O s to drv th black-body radato formula by calculatg th avrag rgy of vbrators o cavty, as was do by M. Plack; th othr s adoptd by L. Raylgh ad J. H. Jas to calculat th avrag rgy of stadg wavs cavty. Accordg to modr radato thory, th thrmal radato s th lctromagtc radato of som spcal wavs ad th photo (wav packt) s of wav artcl dualty. A mpty cavty s a radato fld. If th radatg body rachs a balacd stat wth th cavty tmpratur, th Plack formula may b drvd by calculatg th avrag rgy of th stadg wavs cavty. From th comparatv study of Plack s ad Raylgh s work, w fd that th black-body radato law has mor profoud cott. If w do furthr rsarch o ths bass, w ca rval th fudamtal law of thrmal radato. Th fudamtal law of thrmal radato cluds two aspcts of th vbrators rgy dstrbuto law ad th rgy xchag law th radato fld, th formr bg dscrbd by Boltzma s rgy dstrbuto law whl th lattr awats furthr study. Our study s focusd o rvalg th rgy xchag law btw th body ad th radato fld. Th rgy xchag also covrs two lvls of vbrators stmulatg ad absorbg radato. Lt s frst of all aalys th law of vbrators stmulatg radato.. Law of Vbrators Stmulatg Radato Th Plack s formula s of mmdat sgfcac for rvalg th law of vbrators stmulatg radato. W ca v clam that t mplctly cotas th law. Plack holds th vw that th rgy spctrum dsty th radato fld u(v, T) s dtrmd by th stat dsty of th radato fld ad th avrag rgy of vbrators. O th ssu of how to calculat th avrag rgy of vbrators, Plack advacd th rvolutoary cocpt of quatum of rgy ad thus foudd hs quatum thory. Accordg to ths thory th vbrator s rgy s dscotuous ad has ts mmal ut. For vbrators whos frqucy s v, th mmal

2 39 Ch Dayou: A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss ut of rgy ε ad vbrators ca oly locat thmslvs ε, ε, 3ε,. o of a srs of dscotuous stats of rgy. Accordg to Boltzma s law of rgy dstrbuto, th cavty frqucy s v ad th ormalzd dstrbuto law of ε rgy vbrators s B T D () ε / ( ε, ) (,, ) I th formula D stads for th ormalzato coffct D / ε ε Now that th rgy lvls ar sparat, w caot but drctly calculat th avrag rgy of vbrators. Notcg ε, th avrag rgy s ε / / ε ε ε / / ε ε / I( ) / (/ ) Th dsty th v v+dv ara s rprstd by g(v)dv. [] Wh th rsult of Raylgh ad Jas calculato s usd So th Plack formula () (3) 8πv dv g( v)dv (4) 3 c u( v, T) g( v) εdv 8 v d π v 3 / kt c Bfor Plack, Raylgh calculatd th stat dsty of lctromagtc stadg wavs th cavty ad offrs th formula of black-body rgy spctrum, o th bass of th xstc of lctromagtc mdum vacuum. u( v, T) (5) 8πν (6) 3 c Ths formula coforms to th xprmt log wavs, but dffrs a lot short wavs. Th Raylgh formula s a atural rsult of th classc lctromagtc thory ad th rgy qual dstrbuto law. Th what s wrog wth th Raylgh-Jas formula? I our vw, frst of all th stat dsty ca ot srv as th bass of calculatg th umbr of stadg wavs. Othrws, t wll rsult th ultravolt dsastr that th hghr th frqucy s, th gratr th umbr of stadg wavs bcoms, ad th radato rgy td to b ft. As a mattr of fact, th umbr of stadg wavs th cavty s dtrmd by two dpdt factors. It s rlatd ot oly to th stat dsty, but also to th vbrators th cavty whos frqucy s v. Ths cocluso s asy to udrstad. Th xprmts rval that th strogst cosmos ray rcvd so far s o hghr tha 6 frqucy. [][3] Th vbrator whos frqucy s hghr tha th lmt caot possbly xst ay kow body. But th stat dsty gv th Raylgh-Jas formula s astoshgly hgh. Bsds, whl calculatg th rgy of stadg wavs, classc thory s usd to gv th avrag rgy of vbrators. To fd th law of vbrators stmulatg radato, w rpat our calculato of th umbr of stadg wavs th v v+dv ara. For th cavty radato fld wth th T tmpratur, p (v, T) stads for th probablty of radato stmulato by vbrators wth v frqucy ad rgy. It s also th probablty of th umbr of trasmttd photos. W hold th vw that, although vbrators whos frqucy s v ad whos rgy lvls ar rspctvly,, 3, tc. hop ad shft btw rgy lvls of th sam basc frqucy, thy all stmulat photos wth v frqucy. But th probablts of dffrt rgy lvl vbrators stmulatg radato ar dffrt. It s asr for vbrators of hgh rgy stat to trasfr ad stmulat radato tha thos of low rgy stat. Ad th probablts of vbrators stmulatg radato ar surly drctly proportoal to thr rgy lvl stat. That s to say, for vbrators whos rgy lvls ar rspctvly,, 3, tc., th probablty rlatoshp of th umbr of stmulatd radato ut tm s : : 3 : : 3 (7) Th radato stmulato probablty of vbrators wth v frqucy ad rgy lvl s dtrmd by th two factors of rgy lvl stat ad rgy dstrbuto probablty. That s to say p ( v, T ) (8) So th avrag probablty of radato stmulato of vbrators wth v frqucy s f ( v, T ) If P(v, T) stads for th umbr of stadg wavs th aras ghborg ut volum frqucy v, obvously th umbr of stadg wav cavty s dtrmd by th product of th dsty of stat multpld by avrag stmulatg probablty. π P( v, T) g( v) f ( v, T) 8 v 3 c (9) () Formula () s multpld by th rgy of wav packts ad w hav Plack Formula. Th Plack formula compltly agrs wth th xprmt. Ths mas that th umbr of stadg wavs show Formula () coforms to th xprmt. Ad furthrly, th

3 Itratoal Joural of Hgh Ergy Physcs 5; (3): rlatoshp of th radato probablty rvald by Formula (7) s drctly proportoal to th vbrators stat of rgy lvls, whch coforms to th ralty. That s why w clam that Plack formula ot oly rvals th law of black-body radato, but also cotas th rlatoshp of th probablty of vbrators stmulatg radato bg drctly proportoal to thr stat of rgy lvls. So, as for th fudamtal law of thrmal stmulato, our cocluso s: th probablty of stmulatg radato of vbrators thrmal qulbrum radato fld s drctly proportoal to thr stat of rgy lvls. Th radato stmulatg probablty of vry spcfc vbrator s drctly proportoal to ts stat of rgy lvl. For larg umbrs of vbrators, thr avrag radato stmulatg probablts ar drctly proportoal to thr avrag rgy. 3. Law of Vbrators Absorbg Radato Tabl. Ergy Lvl ad Frqucy Dstrbuto of Vbrators. W v alrady studd th law of vbrators stmulatg radato. Now o th bass of Boltzma s rgy dstrbuto law ad th law of vbrators stmulatg radato, w ll aalyz th law of vbrators absorbg radato. Th rgy ad frqucy dstrbuto of vbrators s show Tabl [4]. I Tabl, th vrtcals ar th Boltzma dstrbuto of vbrators rgy ad horzotals ar th Plack dstrbuto of vbrators frqucs. N ad ar rspctvly corrspodg to th umbr of vbrators. Th horzotal ls th mddl of th tabl stad for rgy lvls. Boltama dstrbuto rgy Dstr-buto m ε+dε B(ε ) N ε+dε B(ε ) N ε+dε B(ε ) N ε+dε B(ε ) N ε+dε B(ε ) N v +dv v +dv v +dv... v +dv... v m+dv Froqucy P(v ) P(v ) P(v )... P(v )... P(v m) Plack dstrbuto I Tabl B(ε, T) stads for ormalzd Boltzma rgy dstrbuto coffct. Ad P(v, T) rprst th Plack frqucy dstrbuto coffct. A. Est dvdd th rgy xchag of thrmal radato to 3 dffrt procsss: spotaous radato, stmulatd radato ad stmulatd absorpto radato. Spotaous radato rfrs to th radato of spotaous trasto wth o rlato btw vbrators ad th radato fld. At ths momt th photos stmulatd by vbrators mata radomss a stat of polarzato, phas posto or drcto of propagato. Stmulatd radato rfrs to photos st out wh vbrators ar stmulatd by th st- photos th radato fld. It kps cosstt wth th frqucy, phas posto, polarzato stat ad propagato drcto of st- photos. [5] Th radato fld th cavty s th rsult of th two kds of radatos. Th procss of absorpto s just oppost. Vbrators ca oly rsoatly absorb photos of sam frqucy. Sc th dsty of stat cavty s dpdt ad thr s o dgracy btw photos, vbrators ca oly absorb sam-frqucy photos o by o. Ths s th sstal charactrstc of vbrators absorbg photos. [6] Th rgy lvls of harmoc vbrators ar charactrstc of qual trvals. If vbrators wth v frqucy ad rgy lvl trast to th stat of m rgy lvl, thy strd ovr (-m) rgy lvls ad stmulat (-m) photos of v frqucy, stad of o photo of (-m)v products. Ths s dffrt from th hop of atom rgy lvls. [7] I th tabl k (,,3, ) dcats th umbr of rgy lvls of vbrators of dffrt frqucs th sam rgy dvso. Th low-frqucy vbrator k s grat umrcal valu ad ds rgy lvls. Th hgh-frqucy vbrator k s small umrcal valu ad th trvals ar bg btw rgy lvls. To fd out th law of how vbrators absorb radato, lt s cosdr such a stat of xtrmty. Suppos th mattr vbrators th cavty sd out, a prod of tm, all th photos of corrspodg frqucs whch thy carry ad all rtur to th groud stat. Th w lt th cavty absorb photos th formr vromt so as to abl rgy to rdstrbut from th groud stat ad ultmatly rach th formr stat of qulbrum. Ev so, accordg to Boltzma s law of rgy dstrbuto, vbrators wll choos th formr stat of dstrbuto. Accordg to quatum mchacs, vbrators of groud stat hav th mmum rgy E (E /). At ths momt thy do ot stmulat photos. I accordac wth th supposto that vbrators sd out all photos of varous frqucs thy carry, th probablty o groud stat at ths momt s (G ). If th probablty of vbrators absorbg at last o photo s G, th G D ε D ε ( ) () I th formula, D stads for ormalzd factor. It s th sam as Formula (). Formula () mas th probablty that vbrators absorb at last o photo,.. th probablty of vbrators ot bg

4 4 Ch Dayou: A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss th groud stat. Th da s slf-vdt. To absorb o photo s absorpto, so s to absorb umbr of photos. Accordg to th charactrstcs of vbrators absorbg photos, to absorb umbr of photos s always a r-absorpto aftr absorbg o. Thrfor, all vbrators whos rgy lvls ar abov groud stat ar wth ths probablty. So th probablty of groud-stat vbrators absorbg radato s gv by Formula (). Th probablty of how vbrators absorb photos s show Fg.. th probablty of th vbrators absorbg radato whos rgy stat s E. Grally, th radato absorbg probablty of th vbrators whos rgy lvl s E m-- s m G D ε m m m m ( + ) ( ) ( ) ε ε (3) m ( + ) ( + ) I th formula,, + s th hghst rgy lvl of vbrators. Plas otc, wh, (+)/kt. Thrfor, Formula (3) may b xprssd as Gm m (4) Th probablty of th oscllator absorbg at last o photo,.. th dstrbuto probablty of th oscllator th o-groud stat, as s show th shadow of Fg. (a) Formula (4) s tru wth vbrators of varous frqucs. It dcats that th radato absorbg probablty of vbrators s drctly proportoal to thr rgy dstrbuto probablty. Also bcaus G + G + G + + G + + G + m m m m m (5) th ormalzd factor rmas to b D. Aftr ormalzato, th radato absorbg probablty of vbrators whos rgy lvl s E m s D -m/. Howvr, vbrators wth E m rgy lvl ar thos whch hav absorbd (m-) umbr of photos. Thrfor, th radato absorbg probablty of vbrators wth E m rgy lvl s xactly th probablty of vbrators whch hav absorbd m umbr of photos. So th avrag probablty of vbrators absorbg radato may b wrtt as Th photo-absorpto probablty of th oscllator of Em- rgy lvl,.. th dstrbuto probablty of th oscllator whos rgy lvl s grat tha Em-. Fg.. Sktch of How Vbrators Absorb Photos. Lkws, th probablty of oscllators o th E stat absorbg radato s G D( + ) ε ( + )( ) () Formula () mas th probablty of vbrators absorbg at last two photos. Thrfor, ay vbrator whos rgy lvl s abov E blogs to ths catgory. Lkws, w call G m m m m G m m m (6) Formula (6) s Formula (9), rfrrg to th avrag radato absorbg probablty of vbrators. Lkws, th probablty of radato absorpto of vbrators s also rlatd to th dsty of stat of th sam frqucy th cavty. Multply th avrag absorbg probablty wth th dsty of stat, w gt th umbr of vbrators absorpto of radato. W kow ε. Multply t wth, w gt th Plack formula of black-body radato. Now ths formula s obtad through th oppost procss of absorpto. I ths way w ca xpla thory th law of rgy xchag durg thrmal qulbrum radato.

5 Itratoal Joural of Hgh Ergy Physcs 5; (3): Fudamtal Laws of Thrmal Radato Boltzma s law of rgy dstrbuto may b drvd o th bass of laws of vbrators stmulatg ad absorbg radato. W start wth th vstgato to vbrators stmulatg radato. B(ε, T) stll stads for th rgy dstrbuto coffct. Th probablty of vbrators stmulatg radato s drctly proportoal to thr stat rgy lvls. I th v v+dv ara, th probablty rlatoshp of vbrators stmulatg radato s p ( v, T)d v B(, T)dv (7) Multply Formula (7) wth C so as to wrt t to a quato. Th p ( v, T) CB(, t)dv (8) Howvr, w also kow that th v frqucy vbrators ad rgy vbrators corrspod wth ach othr. Thy show th sam dstrbuto. Wh vbrators stmulat radato, thr rgy dstrbuto vtably chags. W ca fr that p (v, T)dv s xactly th full dffrtal of rgy dstrbuto coffct B(ε, T) at ÄT. Aftr r-orgazato, th formula bcoms DB ( T. ) Cdv B (, T ) () Th tgrals of both sds of Formula () rsult So I B (, T ) Cv () cv B (, T) D (3) D stads for ormalzd costat. Formula(3) alrady has th form of Boltzma rgy dstrbuto fucto. Coffct C awats furthr aalyss. Th rgy dstrbuto fucto s th rsult of both vbrators stmulato ad absorpto of radato. Thrfor, w stll hav to aalyz th fluc of vbrators radato absorpto o th dstrbuto fucto. From th lvl of vbrators absorbg radato, smlar cocluso coms about. W us J - (v, T) to rprst th probablty of vbrators wth E - rgy lvl absorbg photos. Now w kow that th probablty of vbrators (E - rgy lvl) absorbg photos s drctly proportoal to B (, T). W also kow that th probablty of vbrators (E - rgy lvl) absorbg radato s xactly th probablty of absorbg umbr of photos. So th dv ara, th probablty rlatoshp of vbrators absorbg radato s J ( v, T)dv CGd v CB (, T)dv (4) Th shadow part of th fgur shows th chag of rgy D(B(, T)) wth Ät tm. Fg.. Sktch to Show th Rlatoshp btw Ergy Dstrbuto ad Frqucy. Th rlatoshp btw vbrators rgy spctrum ad frqucy s show Fg.. I th formula B (, T) s th spctrum l at t ad B (, T) s th spctrum l at t+ät. Bcaus Ät s suffctly small, B (, T) may b dmd as a ty paralll shft of B (, T). Radato rducs th rgy of mattr, th spctrum ls mov to lowr frqucy. Th shadow part of th fgur shows th chag of rgy D(B(, T)) wth Ät tm. Gv that rgy oly xchags by way of radato, wh ÄT ad furthr ÄT, th chag s xprssd by B(, T) vrsus v dffrtal. Th B(, T) B(, T) p ( v, T) dv lm D( B(, T)) dv + lm dt t v t T (9) D B(, T) r Notcg that vbrators stmulatg radato rducs th rgy, hc th followg rlatoal xprsso p ( v, T) D B (, T) CB (, T)dv () Th absorpto of radato by vbrators may also chag th orgal dstrbuto fucto, whch s qual to lookg at th rlatoshp show Fg. th othr way roud. Th vbrators absorpto of radato crass rgy, so J ( v,t) D B(, T ) CB (, T) (5) Compard wth Formula (), o gatv symbol s mssg. Th fuctos of avrag probablts of vbrators stmulatg ad absorbg radato ar th sam. Th avrag probablty s th fucto of frqucy. Th frqucy chags th dv ara, whch vtably flucs th avrag probablty. I rtur th chag of avrag probablty also flucs th vbrators absorpto radato. Thrfor, w hav to vstgat th chag rato of frqucy by avrag probablty. So w do dffrtal o Formula(9). h d ( ) dv ( ) (6) Th drvatv of avrag absorpto rato s gatv, whch mas th lowrg of absorpto rato as frqucy rss. Ths coforms to fact. To fd th chag rato of absorpto, w approxmat Formula (6) ormal

6 43 Ch Dayou: A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss tmpratur. I ormal tmpratur T3K, aftr Plack costat ad Boltzma costat ar put v v (7) I ormal tmpratur, thrmal rgy s coctratd th fra-rd ara whch th charactrstc frqucs ar hghr tha 3, />, / >>. I hgh tmpratur,.g. T3K, th thrmal rgy movs towards th volt d ad th charactrstc frqucs ar hghr tha 4, / >>. [8] So Formula (6) may b xprssd as.. d h h ( ) d v ( ) d( ) h dv ( ) (8) (9) Formula(9) mas that th chag of frqucy by avrag absorpto rato s drctly proportoal to (-h/). So, wh frqucy chags th dv ara, th probablty of vbrators absorbg radato s drctly proportoal to (-h/). Hr w rplac C Formula(5) wth (-h/). Aftr tgral DB(, T) h d v B(, T ) I B (, T ), B (, T ) D (3) Formula (3) s Boltzma dstrbuto fucto of vbrators rgy lvls. But w kow that Plack formula s also a xprmt law. If w do t rgard vbrators avrag rgy ad th avrag probablty as th thortc rsult of Boltzma s rgy dstrbuto law, oly as a xprmt law, w may clam that Boltzma s rgy dstrbuto law s th rsult of rgy xchag law th radato fld. 5. Aalyss of Thrmal Equlbrum Radato Procss bass of th fudamtal law of thrmal radato. A solatd matral systm s boud to dvlop to a thrmal qulbrum systm. If th rgy chag of th systm s ffctd oly by way of radato, t s a systm of thrmal qulbrum radato. Aga lt s tak th spcal cas of cavty radato as a xampl. Suppos th cavty s hat sulatd ad thr ar kds of bods cludg th cavty whch ar m, m,, m,, m. Th tmpraturs ar T, T,, T,, T ad th moochromatc radato dgrs ar r (v, T ), r (v, T ),, r (v, T ),, r (v, T ). Th hols of th cavty ar mat to masur th cavty s radato rgy. Th hat-sulatd cavty s a solatd systm, as s show Fg.(3).Suppos th body tmpraturs of th cavty bar th followg rlatoshp T>T > >T > > T (3) Th stmulato ad absorpto of radato by a body s rlatd to ts structur, spcally to ts surfac codtos (color, class ad brghtss). Dffrt bods hav dffrt moochromatc radato dgrs r (v, T) ad dffrt moochromatc rradato dgrs (v, T). But o th othr had th r (v, T) of th sam body s closly rlatd to ts (v, T). C.R. Krchhoff law tlls us r ( v, T) r ( v, T) r ( v, T) r( v, T) ( v, T ) α ( v, T ) α ( v, T ) α ( v, T ) (3) I th formula á (v, T) stads for th absorpto coffct of th body; r(v, T) ad (v, T) rspctvly rprst th moochromatc radato dgrs ad th rradato dgrs of th absolut black-body; ts absorpto coffct s á(v, T). Formula(3) s tru wth a tmpratur T. It s a xprsso of th body s faturs ad has othg to do wth radato tslf. [9] I Formula(3) th moochromatc radato dgrs of dffrt bods ar smplfd to th moochromatc radato dgrs of black-bods. Notcg r( v, T) cu( v, T) 4, [] th c ( r v, T) αr( v, T) αu( v, T) 4 c 8πv α 3 4 c παv (,,, ) c (33) Formula (33) s a gral formula of moochromatc radato dgrs. It may b prdctd that gv log ough tm, ths solatd systm tds to b thrmal qulbratd. Suppos ts qulbrum tmpratur s T a. At ths momt th moochromatc radato dgrs of th cavty s Th v(v, T) th cavty s dtrmd by th avrag r v(v, T) of bods. Fg. 3. Thrmal Equlbrum Radato of Hat-sulatd carty. W coduct a aalyss of thrmal radato procss o th c πv r( v, Ta ) u( v, Ta ) 4 c a (34) Th probablty of vbrators absorbg radato s drctly proportoal to that of vbrators rgy dstrbuto. Ths

7 Itratoal Joural of Hgh Ergy Physcs 5; (3): rlatoshp s tru wth ay hat-xchag procss, rgardlss of th strgth of radato o th surfac. Th probablty of radato absorpto by vbrators of low rgy s always hghr tha thos of hgh rgy lvl. But obvously, how may photos ar absorbd by a body s drctly proportoal to th umbr of photos trasmttd to th surfac of th body,.. to th moochromatc radato dgrs v (v, T). Th v (v, T) th cavty s dtrmd by th avrag r v (v, T) of bods. For ths purpos w calculat th avrag dgrs of th bods th cavty. Suppos th umbr of vbrators of body m ad frqucy v s N ad th absorbg coffct s á. Th probablty of stmulatg radato s of th sam ffct wth á N v black-body vbrators. So th avrag probablty of stmulatg radato by body m v s F ( v, T ) α N f( v, T ) αn (,,, ) (35) Th total probablty of stmulatg radato by bods s F( v, T ) (36) Th avrag probablty of stmulatg radato by bods s F( v, T ) ( ) (37) For th purpos of brvty, oly two body systms ar vstgatd. Bcaus T >T, f (v, T )> f (v, T ). Lt s agr that f( v, T ) f( v, T ) a, ad a s a ral umbr smallr tha f (v, T ). So th avrag probablty of stmulatg radato of th systm s Bcaus αn f( v, T ) + αn f( v, T ) f ( v, T) + f ( v, T ) f ( v, T ) + f ( v, T ) α α α α N + N N + N f ( v, T ) + f ( v, T ) a α α α α ( ) N + N N + N a f ( v, T ) >f ( v, T ) αn + αn At th sam tm f ( v, T) f ( v, T ) + f ( v, T ) α α α α N + N N + N N + N N + N a + + f ( v, T ) <f ( v, T ) (38) (39) ( f ( v, T ) + a) + f ( v, T ) (4) α α α α From Formula (39) ad (4) w kow f ( v, T ) >f ( v, T) > f ( v, T ) (4) Notcg th charactrstc that th radato probablty kps chagg wth th tmpratur, w blv thr must xst a tmpratur T a [T,T ] dgr ara. Satsfy So that f ( v, T) f ( v, T a ) a + ( + ) a (4) (43) Ths rsult may b appld to a systm wth may bods. For th systm show Formula (3), thr s f ( v, T ) >f ( v, T ) >f ( v, T ), a αn( ) a (44) Sc f(v, T a ) s th avrag probablty of stmulatg radato by bods th cavty, th moochromatc radato dgr th cavty s c 8πv v, Ta ) 3 4 c πv c ( a 8 a (45) Notcg that th radato dgr of ay body may b qually xprssd by th radato dgr of th black-body ad that th radato absorbg ablty of a body s drctly proportoal to á, w thk t provds a bass for judgmt. Compard wth Formula(33), at ay tm for ay body whos T s bggr tha T a, ts radato dgr s bggr tha ts radato llumac; ts radato rgy s bggr tha ts absorbg rgy; th body tmpratur drops. For ay body whos T s smallr tha T a, ts radato dgr s smallr tha ts radato llumac; ts absorbg rgy s bggr tha ts radato rgy; th body tmpratur rss. If w cotuously masur th tmpraturs of m ad m, th T shows a cotuous dcl squc whl th T shows a rsg srs. Bsds, T> T >T >T > > T (46) s a s Accordg to th prcpl of std trvals mathmatcs, th systm s boud to bcom qulbratd at a crta tmpratur, say T a, th tmpratur ara. At th frst glac, th qulbratd tmpratur s a procss quatty whch chags wth th procss of qulbrum. Furthr aalyss provs t s ot tru. If th umbr of bods th cavty s grat ough ad th tmpratur dffrc s bg ough, th tmpratur rlatoshp shows th followg chag f th varato dt a of th qulbrum tmpratur s bggr tha T a :

8 45 Ch Dayou: A Study of Fudamtal Law of Thrmal Radato ad Thrmal Equlbrum Procss Momt t T>T > >T >Ta>T + > > T, Momt t+dt T>T > >Ta >T>T + > > T. From th abov tmpratur rlatoshp, w s that f T a s a procss quatty, th body m may probably rlas hat a t tm ad absorb hat at t+dt tm. But th fudamtal of thrmal radato tlls us that ths phomo wo t tak plac spotaously. Ths s bcaus, f ay body m th radato fld chags from rlasg hat to absorbg hat, t vtably gos past th qulbrum pot of hat chag dq, at whch th rgy radatd by th body (á r(v, T ) ds dt) quals ts absorbd rgy (á (v, T a ) ds dt). Wh th body shfts from rlasg hat to absorbg hat, t dcats that th rlatoshp btw radato dgr ad radato llumac udrgos a rvrs. Howvr, th radato dgr s dtrmd by th rgy dstrbuto of m vbrator ad th radato llumac dpds o th systm. Th fluc of th radato dgr of m body s sgfcat. Rlatv to th radato llumac cavty, f th radato dgr of m rvrss, t must b a spotaous act, whch s obvously mpossbl. If body m chags from absorbg hat to rlasg hat, t lkws gos past th balac pot of dq. Th chag shows th chag of radato dgr from bg smallr to bg bggr tha th radato llumac. But th llumac dpds o th systm, so th strgth of ay body th cavty absorbg radato caot possbly b gratr tha th llumac. Thrfor, for ay body whos radato dgr s smallr tha llumac, th rvrs phomo caot possbl tak plac. Our aalyss shows that, a crta body wll always mata a balac stat f t s a balac stat wth th radato fld, ulss trfrd by outsd codtos. Ths charactrstc s vry much rvalg for us to udrstad th charactrstcs of thrmal qulbrum radato. As s statd abov, f th umbr of th body sampls th cavty s bg ough ad th tmpratur dffrc dt s suffctly small, f th balac tmpratur T a of th systm s locatd btw T ad T +, o varato of absorbg ad rlasg hat of th bods wll tak plac th qulbrum procss. As tm gos o, th [T, T + ] ara arrows dow, whch dcats that th qulbrum tmpratur Ta of th systm s th mmobl pot of th [T, T + ] ara, ad also th mmobl pot of th [T, T ] ara. Thrfor, w arrv at th followg cocluso about th charactrstcs of thrmal qulbrum procss: th qulbrum tmpratur T a of th thrmal qulbrum procss s oly dtrmd by th tal codtos of th systm, s charactrstc of a mmobl pot ad has othg to do wth th qulbrum procss. Ths s tru mcroscopcally. O th o-qulbrum pot th avrag rgy of vbrators ad th rgy of th radato fld ar a stat of o-balac, so that th rgy trasfr s matad. O th qulbrum pot th avrag rgy of vbrators ad th rgy of th radato fld ar a stat of balac ad ay subtl chag th dstrbuto stat of vbrators rgy s rsstd by th balac stat. Th shft of a body from th balac stat to th stat of stmulato bggr tha absorpto mpls that th rgy dstrbuto of vbrators hops towards hghr rgy lvl. Ad mmdatly aftr, th radato rgy crass, so that t rturs to th low lvl. Th shft of a body from th balac stat to th stat of absorpto bggr tha stmulato mpls that th rgy dstrbuto of vbrators hops towards lowr rgy lvl. Th rsult s vtably th cras of absorbd rgy, so that t rturs to th hgh lvl. Hr, th fudamtal law of thrmal radato matas th balac of th radato fld ad prvts th systm stat from dvlop to th oppost drcto. Thrfor, w clam that th rrvrsblty of thrmal qulbrum radato s a form of xprsso of th fudamtal law of thrmal radato. Th codtos for thrmal qulbrum radato may b drvd from th avrag probablty. Th avrag probablts of vbrators stmulatg ad absorbg radato ca both b xprssd by Formula(9). Th two qual ach othr th stat of thrmal qulbrum. At ths momt th chagg possblty of avrag probablts tds to b zro,.. Df(v, T). ( ) D f ( v, T) D ( ) ( ( ) ) dv + ( ( ) ) dt v T hdv dt + Lt Df(v, T), so Aftr r-orgazato ( ) ( ) (47) hdv dt (48) dv dt (49) v T Formula (49) shows th basc codtos for thrmal qulbrum radato. W hav coductd a vstgato to th thrmal qulbrum procss of th solatd systm th spcal form of mpty cavty radato. But th matral systms ar uvrsally assocatd ad th absolut solatd systm s rar. Ral ad cocrt thrmal qulbrum procsss hav thr cocrt complxty, but ths dos ot hdr our udrstadg of th atural charactrstcs of thrmal qulbrum procss. 6. Cocluso A complt fudamtal law of thrmal radato should cota two lvls of rgy dstrbuto ad xchag. Our cocluso o th fudamtal law of thrmal qulbrum radato s: th rgy dstrbuto of mattr vbrators th

9 Itratoal Joural of Hgh Ergy Physcs 5; (3): thrmal qulbrum radato fld follows Boltzma s law of rgy dstrbuto; th probablty of vbrators stmulatg radato s drctly proportoal to thr stat of rgy lvls ad th probablty of vbrators absorbg radato s drctly proportoal to th probablty of thr rgy dstrbuto. Boltzma s law of rgy dstrbuto ad th law of vbrators stmulatg ad absorbg radato srv as causalty codto for ach othr. Th formr rvals th law of vbrators rgy dstrbuto ad s charactrstc of statc, whl th lattr rvals th law of rgy xchag btw vbrators ad th radato fld ad s charactrstc of dyamc. Both costtut th basc laws of thrmal qulbrum radato. Th abov cocluso s dducd from thrmal qulbrum radato ad s also tru wth o-qulbrum radato. As for th procss of thrmal qulbrum radato, our cocluso s that th thrmal qulbrum tmpratur th solatd systm s dtrmd oly b th tal codtos of th systm ad has othg to do wth th qulbrum procss. Th rrvrsblty of thrmal radato s th xprssg form of th fudamtal law of thrmal radato. Rfrcs [] ZHAO Ka-hua, LUO W-y, Quatum Mchacs (Nw Cocpt Coursbook of Physcs). Bjg: Hghr Educato Prss,, 9-. [] [Russa]B. Λ. Kgsbough, traslato by Wag Zhsog,Wag Lg ad Luo Ku,som Importat Issus Physcs ad Astrophyscs. Bjg: Scc Prss, [3] CHEN Da-you. O Grato ad Sgfcac of Mass. X a: Northwst Uvrsty Prss. 7, [4] Stv Adams (US), Physcs th Ctury, traslatd by ZHOU Fu-x, XUAN Zh-hua, SHAN Zh-guo. Shagha: Shagha Prss of Scc ad Tchology, 6, 7-9. [5] Stv Adams (US), Physcs th Ctury, traslatd by ZHOU Fu-x, XUAN Zh-hua, SHAN Zh-guo. Shagha: Shagha Prss of Scc ad Tchology, 6, [6] A. Est[us] Aal dr Physk 7 [95] -3. [7] Zhou Shxu A Cours of Ouatum Mchacs, Bjg, Hghr Educato Prss, 979, [8] Xu Xu du, Ch Xao yu, L Luo, A Cours of Physcs [M], Bjg, Hghr Educato Prss, 988: [9] Xu Xu du, Ch Xao yu, L Luo, A Cours of Physcs [M], Bjg, Hghr Educato Prss, 988: [] ZHAO Ka-hua, LUO W-y, Quatum Mchacs (Nw Cocpt Coursbook of Physcs). Bjg: Hghr Educato Prss,, -5.