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u 0 Œ u E £ν Ýn;ºÿÕv«Ý%9``a9ìÝ«”›ŒÝë 3®ðÝÀۗu tot™ÿ#ë ÝÀۗ|C Àú—Ñfy¸Ý–Eá—ݰg℄9Ì®úúú™™™777

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(1)

é®õήή›ÝÎl»¬¡¼I.s¨3ذ¨é

¸Æbv«Ôݕ ¯î×6®›K×ÌÔÝP²

#

##ëëë

(

TAݑ

)

Î ¾ Õ # ¿ ÉÝ é  ë  . ‚ ¸ Æ b  Ý á

—3›á—ìÝ#ë Í£b=Ý5µ

uàŒë 3&£

ν

Ýë ú—

I(ν)

XÿÕÝ`aÌ®9ë ÝH™ÿ–Eá—

T

Ý#ë ÝHAì%Xî

`a9ìÝ«”›ŒÝë 3®ðÝÀú—

I tot

%iŒÝ3

×Í´{Ýá—

T

ÝH

(

ÌaI

)



v I

(4.1)

ë ú —

I

Ñ f y ë Ý   Û —

u



I = uc/4

 . ‚  u 0 Œ

u

E

ν

Ýn;ºÿÕv«Ý%9``a9ìÝ«”›ŒÝë 3®ðÝÀۗ

u tot

™ÿ#ë ÝÀۗ|C Àú—Ñfy¸Ý–Eá—ݰg℄9Ì®úúú™™™777ŸŸŸ

u tot = aT 4 , I tot = c

4 u tot = σT 4 . (4.2)

îPÝf»ðó

a

õ

σ = ac/4

5½Ì®ëëë ðððóóóõúúú™™™77ððóóó

(2)

uŠ.0ŒG–Ý”Œ´Ä60ŒÝÎ3›Ýë £

ν

ì

!ÝM›ÿP

(

ETy!Ýé®Fê℄'õǑM

)

Ýóê3

N Ž › › ”   ƒ ë 3  £

ν

‹

ν + ∆ν

 Ý M › ÿ P Ý ó ê

g(ν) ∆ν

9Í

g(ν)

Ì Vۗó¸Ñfy£

ν

Ý¿℄

g(ν) = Aν 2 , (4.3)

Í

A

Îðó©Š.îP¶|N×M›ÿPÝ ¿í 

E(ν) ¯

ÿÕۗó

u(ν) = g(ν) ¯ E(ν)





ííí555§§§

3ŽÑ<®›+²5Ú ®×º›ÝMuƒMÝ

²õÄPðó5½

m

õ

k

JMÎ

E = 1 2 mv 2 + 1 2 kx 2

ïžÎ#ٌÝí5§Eyãœ9Í9øÝMXxWÝ

–Eá—

T

Ý#æÙîPN׿℄4Ý¿íÎ

1

2 k B T

Í

k B

Ì®««++££ðððóóó

k B = 1.381 × 10 −23 J K −1 = 8.617 × 10 −5 eV K −1 . (4.4) (

îPÿ

1 eV/k B = 11600 K

9Î|

eV

Ž›îÝ; |á

—Ž›î`Ý»ð.

)

.‚î–MÝ¿íÎ

E ¯ cl = k B T . (4.5)

9Êàyé®ÝM›ÿP‚&ÆÿÕ#ë Ýۗ

u(ν) = g(ν) ¯ E cl = Ak B T · ν 2 . (4.6)

AhJ#ë ÝHÞÎ\?îÝeÎa‚ë ÝÀJºÎ

PM9G«G–Ý™H`a«ðI8nÇ

(3)

#ë H`a

(4.1)

« y#¿É݇›Ý5>—5µ`abv

«ÝÏÑA‡›Îã5XàW%

(4.1)

›&ÆÝîÎ

&éÂë Îã¸Ý

5

XxWÝ/$

Ý Š 0 Œ # ë ÝHûk¸ èŒÝë Ý

(



)

Ý F &

Æ Ì ®

(

T é Â ®

)

Ý     . ‚ ®  Ú  ‡ ›  ‚#

ë Jξl#¿ÉÝ ‡›£

ν

Ý ®Í Î

ǫ = hν = hc

λ . (4.7)

9 Í 

λ = c/ν

Î ® Ý ®   . | > º›X |¸Ý

² ë

(3.6)

Pá ›

p = ǫ/c

ùÇ

p = h

λ . (4.8)

GPÝf»ðó

h

Ì®ûûûkk¸¸ðððóóó¸|Cà)

hc

ÝóÂÎ

h = 6.626 × 10 −34 J s = 4.136 × 10 −15 eV s, (4.9a) hc = 1.986 × 10 −25 J m = 1.240 × 10 −6 eV m. (4.9b)

;ðºàÕûk¸ðóݨ×P

¯h ≡ h/2π



¯h = 1.055 × 10 −34 J s = 6.582 × 10 −16 eV s, (4.9c)

¯hc = 3.162 × 10 −26 J m = 1.973 × 10 −7 eV m. (4.9d)

Ê–Eá—

T

Ý#ë uë Îãî–Ý XàW݇

›JN×M›ÿPÝ¿íÎ

(4.5)

‚Î

E = ¯ hν

e hν/k B T − 1 . (4.10)

t&£

ν

œîPX›ŒÝ

E ¯

Þºí5§ Ý ” Œ

(4.5)

b•½Ý-²

(4)

 £

ν

Ý    Î

  ó ©  Î

0, 1, 2, . . .

 E T  $ Î

0, hν, 2hν, . . .



¶ïžÎ#ΧÝi

(Maxwell-Boltzmann)

5µ2PÙ y$

ǫ n

Ý^£

Ñfy

e ǫ n /kBT

.‚×ÍM›ÿPÝ¿íÎ

E(ν) = ¯ 0 + hν · e hν/kBT + 2hν · e −2 hν/kBT + · · · 1 + e hν/kBT + e −2 hν/kBT + · · ·

≡ P

n=0 nhν · e nhν/kBT P

n=0 e nhν/kBT

= hν P

n=0 nx n P

n=0 x n x ≡ e hν/kBT 

= hν e hν/kBT (1 − e hν/kBT ) 2

 1

1 − e hν/kBT

= hν

e hν/kBT − 1 .

îP¨×ÍÌF

(

‘ÙŒ°

)

0Œ

êÞ

1

3±Á§ì™J

(4.10)

PݔŒ«

(4.5)

P×l

AGX–#ë Ýۗ

u(ν) = g(ν) ¯ E(ν)

”)G–Ý

(4.3)

õ

(4.10)

ËPµÿÕ

u(ν) = Ahν 3

e hν/k B T − 1 = αν 3

e βν/T − 1 , (4.11)

Í3tŸ℄ÆLðó

α ≡ Ah

õ

β ≡ h/k B

îPµÎûk¸Ý#

ë 2P¸«™”Œ

(4.1)

Î)Ý

êÞ

2

3›Ýá—

T

ìH5µ`a

(4.1)

îETyÁÂÝ

ν max

Î9K

.ûk¸2P

(4.11)

E£”5ǝÿú™7Ÿ

(4.2)

Tï

à# ÝP

(4.7)

0Œ9ן

êÞ

3



(4.7)

P|C#ٌ݁0Œf»P

u tot ∝ T 4

£

Œë ðó

a

ÝóÂ

(5)

ü›æÝ#º››Œþ}ÝM›ùÇ9ü›ÝήksM

›æÚ ëîݍ×Mí5§áNÍæÝ¿

í

E ¯ atom = 3k B T

Í

T

Îü›Ý–Eá—×͸5

(mole)

ü›Ýæó‡yhó

N 0 = 6.022 × 10 23

.‚Í/Î

U = N 0 E ¯ atom = 3RT , (4.12)

Í

R = N 0 k B = 8.315 J K −1 mol −1

·›ðó

uü›Ýá—Ǒ

∆T

J¸Ý/Ý

∆U = 3R∆T

.‚&Æ

ÿÕü›Ý¸5# 

C = ∆U

∆T = 3R = 24.9 J K −1 mol −1 , (4.13)

«ü›ÝC℄Pnî–n;δ™”Œhû‚ÿÝ

½±á*Ýs"I.Æs¨ á—#–Eë—`×6

ü›Ýf#í á—Ý쪂 yë.‚2P

(4.13)

Wñ

.ú´¼Œuή«éÂ®×øÎ;ÝG–ݯµ

|ÿÕ)§ÝŠÕ*F&ÆÌήÝ Î

. ή«é®b8« &Ɲ|àG«ny Ý2P

©½2£

ν

ÝήÍM›ÿPÝ¿íã

(4.10)

P›Œ

E = ¯ hν

e hν/k B T − 1 . (4.14)

{áì

e hν/k B T − 1 ≃ hν/k B T

.‚

E ≃ k ¯ B T

׸5ü›b

N 0

Í

曌

3N 0

ÍM›ÿP.‚·›/

U = 3N 0 E = 3RT ¯



9«G–í5§XÿݔŒ×l

(6)

¨×℄«3±áìã

(4.14)

PX›Ý

E ¯

ÞGy

k B T

.ú

ƒ'ü›Ýþ}G|Ž×£M›ÿÕÝü›f# á—쪂

yëݔŒ¬€XÕÿÝf#ìª TQG"yjÝ

¯î«#ë v«ü›þ}ÝM›£b=Ý5µ¬«é

 ®  !  Î ® ®      y Ø Í t  Â

λ min

 » A  3 ì % X î Ýή÷®N×Íæí›y®;î.‚÷®‡yë

|îÝB–áήÝ£yØÍtÂ

ν max ∼ v s /λ min



9Í

v s

ή>׸5ü›Ýή©b

3N 0

ÍM›ÿPÍ

 £ Ý ã  P š  ë Õ

ν max

 9 µ Î # ‚ 3 ‡ á ì Î  ‡ ›Ý /  õf#« ‡›Ý×ø

ü›Ýá—

T

yë`JÎ!ݵ9`©b£ÝM

›ÿPbΪAt£

ν max

Ú PM.‚·›Ý

• y ‡›‚&Ɲ|2àv«y#ë Ý2P9

ÿÕݔŒÎ3±áìü›f#Ñfy

T 3



C = bT 3 ,

T

œ`

(4.15)

(

!Ýü›b×øÝf»ðó

b



)

îP«™óAÎ8Ý

êÞ

4

·›õ ‡›Ývf0Œ

(4.15)

P

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