Termisk Strålning; Thermal radiation
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1 Termsk Strålnng; Thermal radaton Termsk strålnng är den elektromagnetska strålnng som en kropp emtterar p.g.a. sn temperatur. Thermal radaton s the electromagnetc radaton a body s emttng due to ts temperature elektromagnetsk strålnng (vågrörelse) fortplantar sg med ljusets hastghet : electromagnetc radaton (a wave moton) s progressng wth the speed of lght; m/s c ν c ljushastghet (speed of lght) våglängd (wavelength) ν frekvens (frequency)
2 Termsk Strålnng- spektrum; Thermal radaton - spectrum. Termsk strålnng Solstrålnng Sun radaton ν Våglängd (μm) Wave length Frekvens (/s) Frequency Infraröd Infrared ultravolett Synlga området Vsble range
3 Termsk Strålnng betecknngar Thermal radaton-notatons E (W/m ) totalt emtterad energ (effekt) per ytenhet; total emtted energy (power) per unt area G (W/m ) nfallande strålnng rradans; ncdent radaton rradance J (W/m ) totalt utsänd strålnng från en yta radans: total radaton from a surface radance J E + ρg I strålnngsntenstet; radaton ntensty F vnkelfaktor formfaktor; vew factor shape factor
4 Termsk Strålnng betecknngar Thermal radaton - notatons Reflektans reflectance ρ - andelen reflekterad strålnng fracton reflected radaton Absorptans absorptance α - andelen absorberad strålnng fracton absorbed radaton Transmttans transmttance τ - andelen transmtterad strålnng fracton transmtted radaton Emttans emttance (emssvty) ε strålnngsförmåga relatvt en s.k. svart kropp rato of emtted radaton from a body and emtted radaton from a smlar black body
5 Termsk Strålnng; Thermal radaton nfallande ncdent reflekterat reflected absorberat absorbed transmtterat transmtted ρ + α + τ
6 Termsk Strålnng; Thermal radaton opaque surface opak yta (τ 0) En opak yta (τ 0) som nte reflekterar någon strålnng (ρ 0) säges vara en svart kropp därför att den absorberar all nfallande strålnng och på grund av att en sådan yta uppfattas av det mänsklga ögat som svart. An opaque surface (τ 0) whch s not reflectng any radaton (ρ 0) s sad to be a black body. It absorbs all ncdent radaton and t s observed as black by the human eye.
7 Termsk Strålnng; Thermal radaton E 0 E d E monokromatska strålnngsenergn monocromatc radant energy
8 Termsk Strålnng; Thermal radaton En perfekt emttator av strålnngsenerg är en yta som emtterar maxmal energ varje våglängdsntervall vd gven yttemperatur. Det är också klart från ekvaton (-6) att en sådan yta också emtterar maxmal total strålnngsenerg vd gven yttemperatur. A perfectly emttng body emts maxmum radant energy for every wavelength at a certan surface temperature. Such a body wll also emt the maxmum total radant energy (see eq. (-6)) Man kan lätt vsa att en perfekt absorbator (svart kropp) också är en perfekt emttator. Följaktlgen kallas också en perfekt emttator för en svart kropp. Fortsättnngsvs gäller för svarta kroppar att alla storheter ges ett ndex B (blackbody). It can easly be shown that a perfect absorber (black body) also s a perfect emtter. Thus a perfect emtter s also sad to be a black body. Propertes/Varables for black bodes are gven a subscrpt B (black body)
9 Termsk Strålnng; Thermal radaton / 5 B T C e C E 6 Wm C K m C ) ( } { ) ( / 5 5 B T f e T C T E T C
10 Termsk Strålnng; Thermal radaton K E π B [ W/cm ] 4000 SYNLIGT SPEKTRUM max T 898 μm K 00 K 600 K 000 K K Vsble range 600 K Våglängd [μm] wavelength
11 Termsk Strålnng; Thermal radaton E B 0 [ W/(m /T μmk 5 5 ] T 0 3 [ μmk] max T [m]
12 Termsk Strålnng; Thermal radaton ( ) 0 / / / 5 B } { Introduce Inför } { x C T C T C e x T dx C T Td dx T x e T C d T d e C E 4 B T E σ Stefan-Boltzmann s lag/law σ W/m K 4
13 Termsk Strålnng; Thermal radaton ε E E B ε Fe Cu Al Au Ag μm
14 Termsk Strålnng; Thermal radaton ε E E B lera clay ε Portland cement kakel vt 0. magnesum oxde μm
15 Termsk Strålnng; Thermal radaton grå kropp grey body E g εσ T 4 60 o 40 o 0 o 0 o 0 o 40 o 60 o N (polerad) N (matt) Cr Mn Al ε θ
16 Termsk Strålnng; Thermal radaton 40 o o 0 o o 0 (b) (c) (a) (d) (e) 0 (g) (f) 40 o (a) våt s wet ce (b) trä wood (c) glas glass (d) papper paper (e) lera clay (f ) kopparoxd copper oxde (g) alumnumoxd alumnum oxde 80 o 60 o o 80 o ε θ
17 Termsk Strålnng; Thermal radaton Krchhoff's lagar/laws α ε α ε
18 Termsk Strålnng-Begreppet Intenstet Thermal radaton - Intensty θ dθ da' r I da φ dφ
19 Termsk Strålnng-rymdvnkel Thermal radaton-sold angle Rymdvnkel dω Sold angle dω da r
20 Termsk Strålnng-Intenstet Thermal radaton-intensty Strålnngsntensteten defneras som strålnngsenergn per ytenhet projcerad vnkelrätt mot en gven rktnng och per rymdvnkelenhet sett från den strålande ytan. The radaton ntensty s defned as the radant energy per unt area projected perpendcular to a gven drecton and per sold angle unt vewed from the radatng surface. d( EdA) da I dacosθ dω I dacosθ r
21 Termsk Strålnng-Intenstet Thermal radaton-intensty EdA d( EdA) dω sn θ dθ dφ d( EdA) I dacosθ sn θ dθ dφ EdA π 0 π / I da dφ cosθ snθ dθ 0 I daπ E π I
22 Termsk Strålnng-Vnkelfaktor Thermal radaton vew factors da A n da r θ θ n da da A dφ dω I da cosθ dω da cosθ r
23 Termsk Strålnng-Vnkelfaktor Thermal radaton vew factors Φ A A A A r I cosθ cosθ da da Φ A E A π IA Φ A F Φ A A F A A A cosθ cosθ π r da da
24 Termsk Strålnng-Vnkelfaktor Thermal radaton vew factors F A A A cosθ cosθ π r da da A F A F j n j F j F + F F n
25 Termsk Strålnng-Utbyte svarta kroppar/ytor; Thermal radaton- exchange black surfaces k J G Q A J EB A G ( J G ) Ak J k Fk k k A J k F k
26 Termsk Strålnng-Utbyte svarta kroppar/ytor; Thermal radaton- exchange black surfaces Q A ( J F k k J k ) Q A k F k ( J J k ) A Fk ( EB EB k k )
27 Termsk Strålnng-Utbyte cke-svarta kroppar/ytor; Thermal radaton exchange non-black surfaces k J G Q A ( J G ) J EB ε + ρ G ρ ε
28 Termsk Strålnng-Utbyte cke-svarta kroppar/ytor; Thermal radaton exchange non-black surfaces Q A ε ( E ε B J ) Q A F ( J J ) k k k
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