(Blackbody Radiation) (Stefan-Boltzmann s Law) (Wien s Displacement Law)
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- ぜんすけ あきくぼ
- 7 years ago
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1 ( ) ( )
2 (Blackbody Radiation) (Stefan-Boltzmann s Law) (Wien s Displacement Law) (Kirchhoff s Law) ( Radiative Equilibrium Temperature ) ( Sun ) (Solar radiation) (Solar constant) (Terrestrial Radiation) (Greenhouse effect) A 19 B (1) (2) 25 I
3 1 1.1 (Blackbody Radiation) (black body) ( ) 500K ν ( λ ) T Planck Planck Planck B ν (T ) B ν dν = 2hν 3 c 2 {exp( hν (1) kt ) 1}dν B λ dλ = h = [Js] k = [J/K] c = [m/s] T [K] ν λ ( ν = c λ ) 2hc 2 λ 5 {exp( hc (2) λkt ) 1}dλ 1.2 (Stefan-Boltzmann s Law) T Stefan-Boltzmann Planck B λ (T ) B(T ) = = 0 0 = 2k4 T 4 h 3 c 2 B λ (T )dλ 2hc 2 λ 5 {exp( hc 0 λkt x 3 e x 1 dx ) 1}dλ ( x = hc λkt ) 1
4 = 2k4 T 4 x 3 h 3 c 2 0 e x (1 e x ) dx = 2k4 T 4 h 3 c 2 x 3 (e x + e 2x + + e nx )dx 0 = 2k4 T 4 h 3 c n 4 n=1 = 2k4 T 4 h 3 c 2 π 4 15 = 2k4 π 4 15h 3 c 2 T 4 = bt 4 πb(t )=πbt 4 = σt 4 (3) 1 Boltzmann σ = 2π5 k 4 15c 2 h 3 = [W/m 2 K 4 ] σ Stefan- 1.3 (Wien s Displacement Law) W.Wien Wien Planck B λ (T ) λ 2hc 2 ( 5+ hc λ 6 {exp( hc λkt ) 1} λkt λ = λ max 1 5+ x me xm e xm 1 db λ (T ) =0 dλ ) =0 exp( hc λkt ) exp( hc λkt ) 1 = 0 hc λ maxkt = x m 0 x s e x 1 dx = n=1 0 x s dx = s! e nx n=1 1 = s! ζ(s +1) ns+1 (s =1, 2, 3, ) ζ s ζ(s) ζ(2) = π2 π4, ζ(3) = 1.202, ζ(4) =
5 e xm = 5 5 x m x m = Wien x m = hc λ max kt = λ max = /T [m] = 2897/T [µm] (4) 1.4 (Kirchhoff s Law) ( j ν ) ( k ν ) B ν (T ) j ν = k ν B ν (T ) (5) ν ε ν = α ν (6) ε ν B ν (T )=α ν B ν (T ) (7) ε ν = α ν =1 (8) ε ν = α ν < 1 (9) Kirchhoff Kirchhoff 40 km Kirchhoff ( local thermodynamic equilibrium : LTE ) 3
6 1.5 ( Radiative Equilibrium Temperature ) (Radiative equilibrium temperature ; T e ) S (2.2.2 ) (S) (A) 0.30 S (1 A) πr 2 e = 4 πr 2 e σt 4 e (10) r e : T e : σ : [Wm 2 K 4 ] πr 2 e ( ) T e T e = 4 S (1 A) 4 σ = 255 [K] (11) 288 K : 4
7 1.6 2: 6000 K 255 K 2(a) 6000 K 255 K (1.2 ) (1.3 ) 0.4 µm (ultraviolet ; UV) µm (visible) µm (infrared ; IR) 100 µm µm (near-infrared) 3 6 µm (midinfrared) 6 15 µm (far-infrared) 15 µm (ultra far-infrared) µm 0.5µm µm 15 µm 4 6 µm (Short wave ; SW) (Long wave ; LW) 2(b) (c) 11 km 0.3µm UV 11 km O 2 O 3 2 H 2 O CO 2 H 2 O CO µm O 3 2 O 2 O 3 (photo dissociation) ( )(photo ionisation) 5
8 (d) O 3 CH 4 N 2 O H 2 O CO 2 H 2 O 6
9 2 2.1 ( Sun ) km km g K 5800 K 150 g cm gcm 3 90% (H) 75% (He) 25% (Fe) (Si) (Ne) (C) (4H He ) (photosphere) 500 km K (sunspot) 2000 K (faculae) km K (choromosphere) (10 6 K) (corona) (absorption line) (Fraunhoferline) ( ) 69 (Fe) 388nm (Na 589.6nm Mg) 518.4nm (H) 656.3nm ( ) 3 1 (Astronomical Unit ; AU) 7
10 3: : (Solar radiation) 6000 K 6000 K ( µm) 46 % ( 0.7 µm 100 µm) 46 % ( 0.4 µm) 7% K (1) (absorption) ( 0.4 µm ) O 2 O 3 0.3µm ( µm ) N 2 O 2 ( 0.7 µm ) 4 H 2 O CO 2 O 3 ( ) (scattering) 4 8
11 4: [nm] [Wm 2 nm 1 ] 6000 K (Rayleigh Scattering) (Mie Scattering)
12 2.2.2 (Solar constant) L = W (solar luminosity) S 1 (AU) km = R R S S = L 4πR 2 = [W km 2 ] = [W m 2 ] (12) S = 1386Wm 2 (Solar Constant) C.G.Abbot % 10
13 O 2 CO 2,H 2 O,N 2 (78 %) (20 %) 2% A CO 2 O 2 15 C A (E t ) (E r ) (E v ) (E e ) (Translational Energy) (photon) ( ) (collision/pressure broadening ) (Lorents width) (Lorentz profile/shape) (Doppler broadening) 11
14 (Doppler profile/shape) (Void profile/shape) (Rotational Energy) OH GHz 3 (Vibrational Energy) 300K (Electronic Energy) ( 2 ) 1. (H 2 O) (asymmetric top) - 6.3µm (8 12µm) 2. (CO 2 ) - 15µm 3. (O 3 ) 12
15 - 9.6µm 14µm UV-A( nm), UV-B ( nm), UV-C ( nm) UV-C UV-B UV-A 4. (CH 4 ) 7.6µm 6.5µm 5.2µm 3.3µm 7.6µm (N 2 O) N-N-O 17µm 7.8µm 4.5µm 7.8µm 7.6µm ( ( ) ) 2 Rayleigh Mie ( (2) ) Mie Rayleigh ( ) 3.2 (Terrestrial Radiation) (Greenhouse effect) 288 K K 13
16 ε ν % 39 % (H 2 O) (CO 2 ) (CH 4 ) (greenhouse effect) CO 2 90 atm ( 5) 5: ( ε =1.0) I αi (1 α)i σt 4 g ( T g ) σt 4 ( T ) 14
17 (1 α)i + σt 4 σt 4 g = 0 (13) αi 2σT 4 + σt 4 g = 0 (14) (13) (14) T = 4 I σ, T g = 4 (1 + (1 α))i σ I α T g = 4 I/σ ( 6) 6: T 1, T 2,T 3 σt2 4 2σT 1 4 = 0 (15) σt1 4 + σt3 4 2σT2 4 = 0 (16) σt2 4 + σtg 4 2σT3 4 = 0 (17) I + σt3 4 σt g 4 = 0 (18) 15
18 ,, I T 1 = 4 σ, T 2 = 2 Iσ 4 T 3 = 3 Iσ 4 T g = 4 4 I σ n T g = 4 n +1(I/σ) 1/4 n : (Goody,1964) τ<1, =1, 4 τ 6.5 Kkm Kkm 1 ( 7 ) 16
19 8: ( Manabe and Strickler, 1964) (L+S) ( ) H 2 O(L+S), CO 2 (L+S), H 2 O+CO 2 (L+S) 8 H 2 O,CO 2 H 2 O+CO 2 7(Goody 1964) O 3 10 km 9 H 2 O H 2 O+CO K km 1 O 3 17
20 9: ( Manabe and Strickler, 1964) H 2 O,H 2 O+CO 2,H 2 O+CO 2 +O 3 18
21 A (%) N O Ar 0.93 CO Ne CH He Kr H N 2 O CO Xe O H 2 S NH SO NO H 2 O ( ) 78 % ( ) 19
22 NO x (15µm) (2.7, 4.3µm) ( 10) 20 20
23 10: km 60 N 90 % 10 % CO 2 H 2 O 3 ( ) 21
24 (Aerosol) µm 10 7 m ( ) m 10 6 m 11 11: (Mie Rayleigh ) 12 ( ) ( ) ( ) 13 22
25 12: (CH 4 ) (rainout) 1991 SO
26 13: ( &, 1980) 14: 24
27 B (1) : ( 1) 16: ( 2) Kiehl and Trenberth, % % 25
28 % W m 2 ( 1364W m 2 ) % 26
29 (2) [ ] (CO 2 ) ( ) ( ) (= σt 4 T ) [ ] (CO 2 ) ( ) CO 2 27
30 MACS 28
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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4.2 4.2.1 [ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 S i S j (4.39) i, j z 5 2 z = 4 z = 6 3 z = 6 z = 8 zn/2 1 2 N i z nearest neighbors of i j=1
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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