Chapitre 7 :Transfert d`énergie par rayonnement

Transcription

Chapitre 7 :Transfert d`énergie par rayonnement
T his work is licensed under a Creative Commons
“Attribution-ShareAlike 4.0 International” license.
" ! #
" !
$%
(
" &
) ')
!
'('
!
#
*+
=
"ω −
,
*
"
"
". *
"0
#
*+
#
)
-
-
#
/
+
(
ω
1 =
π
1λ =
π
ω
#
!
*+"
$
3
#
#
%
2
)
(
* +!
)
=
ω
#
!
λ=
=
ν
#
$
= ε,
=
+
µ,
+
Ismaël Bouya http://melusine.eu.org/syracuse/immae/
#
2 4
• 5
•
)
#
*
ν
-
' ε = ν 6 = 8!8 # , −.0 7#
= ν )
9
'
ν
=
: ;
4
)
#
= #
)
% <
=
•
$
)
(
' =
%
#
"
)
>!
) 9
' =
4
' =
• +
' +
γ "
)
?) 9
)
3
'
!
"
' @
3
#
9 )
!
#
(
"
4 (
#
!
#
!
#$
9 )
% !
#
=4
*
!
)
)
)
!
)
9
)
A !
9
9
!9
!
$
/ *
#
)
!
9 #
)
#
#
9
•
$
)
#
!
=4
B C → B + ν " ν = ε −ε
@
B + ν →B C
)
+ ν
∆ε
•
#
+
" !
D
= " + ∧
E
(
!
)
*
#
4
4
#
9 9
!
)
)
% !
>
) !
#
.
%
• 3
' =4
ϕ"
:
= ϕ ",
"φ =
− #
<:
<3
! 6ϕ "
=
!
9
φ"
!
4
#
⋅
ϕ
φ"
φ ",
4
"
$
9
δ=
9
#
1
9
9 9#
' ;
ϕ
=−
ϕ
!ϕ
G!
)
(
=−
$
F
" 6 ϕ
!
"
−
4
!ϕ
4
9
=
)
# "−
9
9
.
!
99
9 9
H
(
#=
)
'
"
3
9
#
:
ϕ"
$
"
ϕ"
−
= ϕ ",
= ϕ ", ,
−
(
ε
(
1
4
)
3 ε
". 9 9
ϕ ",
α
)
α
=
!
"
)
)
#
! 6ε = α
4
"
'
'
3#
ϕ"
ϕ"
=(
ϕ ",
=
"0
=
!
ε
)
(
!
4
= "ε + ε
#
! )
)
#
4
λα !
λβ !
%
!
ε "λα = ,
J
• @
' $
D
D
'
!
λβ
4
J
α
β
= "ε "λα
= "ε "λβ
+ ε "λα
+ ε "λβ
I ε "λ
!
ε "λ β = , #
#
λα
4
#
= +∞ #
= ,#
4
! ∀ !ϕ " = , " δ = ,
! ∀ ! ϕ " = ϕ ", " δ = +∞
!
4
#
'
9
* δ <<
ϕ
3
E
#
0
* δ >>
ϕ
3
'
E
δ
4
#
λ#
E
)
#
!
'
δ
#
!
3
9 9
)
2 4L
#
4
9 9#
L
@
Σ
2 4L
L
4
#
2 4
•
@
δ .φ
λ
4
Ω
' 3
λ+ λ!
#
λ
δ .φ =
θ # # λ # Ω 6!
λ
θ
θ
"
λ
=
λ
"λ ! !
" O λ N = M# − #µ
' 3
3 9
"
!
D
)
−
#
−
#
λ
)
3
9 #
K
+
)
E
)
F
θ
G
λ
#
)
% ! &
! δ φ = λ "λ
θ#
#
!
4
9 !
λ#
λ
θ # # λ# Ω
.
"
'('
3
(
(
9 )
)
(
#
2 4
•
+∞
δ φ =
"λ λ
λ
,
θ# # Ω
3
=
+∞
" λ λ " O N = M#
λ
,
!δ φ =
−
−
#
θ# # Ω #
. 2 4
•
@
δ φ =
θ Ω
?
λ
"λ #
# λ
λ
θ Ω=
?
!
λ
•
θ# π
,
λ
#
)
3
9
# λ#
4
2 4
#
+∞
δφ =
θ# θ = π
= π λ "λ "
= δ φ =
λ
π
λ
,
# λ #
=4
=
+∞
,
λ
# λ = π#
: 2 4 J
2 4
Σ
8
δ .φ
λ
λ+ λ
δφ
9
!
4
)
Ω
4
#
)
#
4
4
' *
' *
%
9 9#
δ .φ = δ .φ + δ .φ #
•
9
δ .φ
αλ = . #
δ φ
αλ
;
)
4
9
λ!
"
%
!
αλ
!
αλ
!
"
#"
6
4
'
9
+
9
α=
δφ
δφ
4
4
+
4
J
2 4
$
# "=4
%
# "=4
!
(
4
4
2 4
δφ
•
"
, ≤ αλ ≤
'
•
%
%
) 9 !
3
4
9
E
4
$
9
(
)
#
"3
%
%
!
δ φ = δφ − δφ
•
$
δ φ = δφ − δφ " δφ
4
4
! &
'('
(
•
4
=
+
+
+
⋅ =ϕ =
⋅ = −λ #
•
δφ
∂
∂
⋅ = " −
<
4 δ φ = δ φ "ϕ = ϕ
$
δφ − δφ = δφ − δφ !
δφ − δφ = δφ − δφ #
∂
∂
∂
−λ
= −λ
−λ
= " −
∂ ,−
∂ ,+
∂ ,−
•
;
4
#
4
4
#
;
ϕ
ϕ
δ →,
δ
3
@
#
+
$
−λ
+
∂
∂
!
=ϕ −λ
,−
∂
∂
,+
+
P
+
9
$
•
3
)
!
9 9
#
R
R
(
9
)
%
(
"
1
!
!
9 9
4
•
9
R#
)
4
%
(
9
#
•
' 3
'
" =
" =
(
%
E
%
9
9
$
#
E
!
#
)
!
=
)
•
$
9
τ
!
=
τ
!
τ#
!=
"
= ε,
"
=
•
+
ν
τ
∈ τ
@
)
'
µ,
)
λ
ν
ν=
λ
λ
δ !=
!
λ
=
λ τ "
+∞
,
λ
!= δ !
λ
λ
λ
λ
Q
'
ν
δ !=
ν τ!
ν
' +
λ
ν=
λ
,
=
!
$
λ
ν
λ#
λ
ν
λ
+∞
=
. 3
−
ν
,
ν
−
ν=
#$
+∞
=
λ=
+∞
,
λ
λ#
ν
ν
λ
S
•
=4
(
ν
=
Pπ
ν
.
ν
•
'
' 3
' ν =
"
ν
9 (
.
−
#
ν
#
"ν !
"ν
ν
ν"
"
)
∝ν .
ν "ν
ν
<
<
.
! ν"
T
ν"
+∞
=
!
,
ν
ν
#
#
S
=
•
' T
' +
' *
"
=
"
)
"
"
Q,,!
)
H(
ν
=
ν
"ν !
!
,
1
)
)
(
J
<=
:
"
•
'
%#
#
2
ν
4
Pπ
=
ν "
.
"
3
"
=
+
<7
" Q,,
)
%
+∞
ν
,
)
ν = +∞
ν <<
9
"
S
)
4
'
ν
= ν
M
(
" PQ.
. − #ν
)
ν >>
9
'
λ"
=
#
ν
!
=
=
!
λ
=
λ
Pπ
.
! #=
#
#
λ"
= .,,U ! λ = 0Pµ
= .,,,U ! λ = 0!Pµ
0 3
*
•
<: R
=4
=
=
+∞
ν
,
ν #=
Pπ
0
.
'('
σ =
Pπ K
K . .
<: R
#
=
ν
!
9
−
,
π0
K
Pπ K
=
K . .
0
9
.
+∞
=
&
)
0
×
0
=σ
*
0
•
σ = ,! K8080# , − K 7# −. #U −0 #
= .,,U ! = 8# , −8 7# −.
.
.
"
R
!!=
=
$!
R
= ,,, U ! = ! # , − 7# −. #
= 8,,,U "
! = 7#
.
! = , 7# −. #
= , U "
=
−.
.
!
9
K 3
9
•
$
δ .φ = , "
δ .φ , =
)
θ
,
λ
%
(
9
(
# Ω# λ
)
9
"(
• =4
V
%
)
)
!
#
Ω
θ
' 5
'
4
'
)
λ
λ
,
=
,
λ
λ
"λ !
=
0π
λ
θ # # Ω# λ
#
θ#
λ
4
)
9
,
δφ , =
,
σ
,
θ
#
' 4
=
θ# Ω =
λ
3
=σ
=
Ω
# #
0π
λ
H
' =4
•
λ
,
δ φ, =
,
λ
0π
+
• "
' $
λ
%
(
)
!δ φ =
,
Ω
(
#
.
"
)
Ω
"
0π
λ
λ
*
θ
# #
,
,
!
π?
θ# π#
λ ,
=
,
λ
λ=
θ# θ = π#
,
λ
0
*
0
,
#$
*
=
= σ 0 =σ 0 #
0
0
! σ = K!8 # , −P M#
−
#U −0 #
=
0
λ
4
•
(
δφ =
δφ , =
4
#
= δφ + δφ
= , + δφ !
,
$
≤
,
" )
≥,
9 9
3
!
8 3
M
•
=
"
"
=
λ
,
λ
ν
λ
=
Pπ
λ
"λ
Pπ
.
=
λ.
.
−
λ
λK
λ
−
λ
∆λ
λ
λ"
)
λ
λ
=,⇔
*
"
=
9
− =
= 0!Q8K
λ
#
K
λ" = PQPµ #U #
! λ"
";+!
) 9 !
= P! , !
∆λ# = . PPµ #U #
$ 6
M
!
D5
= ! .!
λ
! " = ,!P. #
∆λ
$
P#λ"
λ"
λ
λ = ,!QP#
+∞
,
λ
λ#
•
λ"
.,,µ
•
.0 µ
+
Q80 M
3
,µ
! µ
,!Kµ
R
)
.# , − 0 µ
)
)
!
!
.
"
= !
)
U
λ
λ" =
9
)
)
)
W
"
9 '9
4
)
X " Q0P
%
)
#
: 3
$
αλ =
!
"αλ =
9 9
#
#
δφ
δ .φ
.
=
(
• 3
δ .φ =
9
θ # # Ω# λ
%&
λ
= δ φ =
.
λ
,
θ # # Ω# λ = δ .φ + δ .φ
,
λ
=,
$
'
' 3
•
=
%&
λ
,
λ
#
!
3
9 #
9 9
#
!
=4
%&
λ
•
3
,
λ
=
0
λ
=
M
%&
,
λ
%&
!
λ
=
=
0
,
λ
!
=σ
0
!
*
)
#
λ" = PQPµ #U #
. =
9
•
V
%
#
3
•
3
4 '" (
!
=4
9
%&
H
)
E
=
,
!
%&
=
,
=σ
0
!
λ" = PQPµ #U #
#
0
"
! λ" ≈ QPQµ #U "
λ" = ,!Kµ "H
>
9
< #
=
=
≈ 8,,,U #
!
0 +
!
•
•
•
*
3
#
) 9 #
αλ =
A
9
#
3
9
9
#
$
' D
!
E
E
9 9 )
#
' 3
9 #
3
αλ ≠ #
=
)
•
$
δ .φ =
= δ .φ , =
$
λ
≤
θ # # Ω# λ
λ
θ # # Ω# λ = δ .φ + δ .φ
,
λ
,
λ
#
)
λ
= ελ
,
λ
#
λ
λ
ελ =
•
, ≤ ελ ≤
ελ
%
#
#
K
! ελ =
#
•
=4
λ = π#
,
=
λ
"
λ
= π#
$
=4
=
λ
3
,
λ
#
= ελ#
,
#
λ
λ = ελ
λ
9
λ#
,
λ
= ε#
)
= ε #σ #
!
0
#
#
(
!
"
3
,
9 !
(
)
9
9 #
U
αλ = ε λ
$
%
(
!
•
:
"
9
δφ = δφ "
δφ =
λ λ#
(
δφ = α λ
$
9
H( )
,
λ
(
=
(ε
λ#
#
H
( ελ
)
,
λ
9
)
λ
λ#
λ = αλ
λ
• :
ε λ λ, = α λ λ,
9 9
! ε λ = αλ #
•
) #
,
λ
#
λ
,
(
)
E
E
9 !
#
(
9 !
.
= αλ
9 9 #
λ
!
' *
αλ = , !
,
λ
#
λ
!
=,
4
#
8
,
' *
J
λ
(
=,
" 4
%
9H
) 9 !
H
) 9
0
•
5
$X
αλ = ,
ελ = , !
$
9
)
!
) 9
#
#
9
"αλ = ,
9
"ελ = , #
)
• *
ελ ≈ !
9
αλ ≈ !
@
4
3
(
#
9
#
B X
:
!
'
≠
' T
'
'
,
<<
#
= ,!
1
→ +∞ !
9
φ = φ −φ
#
9 #
→ ,
% (
"
"
9
*
=
9
9
• φ = φ = ,( = σ
•
φ
'@
φ = " , #
0
× 0π
! φ =φ
9
φ =σ
$
"
× 0π
0
,
=σ
,
0
,
=
,
#
#
× 0π
#
'@
δ φ =
θ × Ω#
,
α
$
δ φ = ,
* δφ = ,π #
= δφ = π # , ×
θ × π#
α#
α
θ# θ#
,
= 0π #
=
•
φ =σ "
*
Y
,
−
0
0
,
#
"
!
= φ = 0σ #(
.
,
" −
0
=
0
,
+0
.
,
" −
,
!
,
Γ
=
0σ #(
.
,
#
@
φ
0σ #
.
,
. :
•
V
%
9
" & '('
9
•
) = "# #
) = −φ # #
P
$
*
" #
= −0 ,.σ #(#" −
−
− 0 σ #(
"#
=
,
−
• $
3
•
ρ =
•
,
.
,
,
,,S #
) τ=
−.
=
π # . ρ#
0 ,.σ #0π #
0
.
λ
=
ρ
%
−
)
=
ρ# #
σ
.
,
#
#
!
,
= ,°
9 #
#
%
ρ # #*
.
,σ
λ = ,,M#
)
#U − !
=
τ* #
*Z
*
0 σ #(
.
,
−
!
= Q,,7#S
8, Z .,& #
%
"/
* τ * << τ !
3
"#
6τ =
(
+
O *N =
!
− ?τ
=" −
,
)
<<
*
λ
<<
−
τ*
σ
.
,
τ* Z
!
<<
*
#
ρ# #
σ
.
,
#
#U − #
<< 0 #
: =)
V
%
'
' =
'
*
4!
#
)
#
#
= 80,,S !
= KP,,U !
= # ,K S
= K,# ,8 S #
φ = φ −φ = ,
' φ = σ # 0 × 0π #
'
φ
2 4
=
σ#
0
× 0π #
φ = σ#
0
#
× 0π #
×
Ω
0π
Q
π#
Ω≈
)
! φ = σ#
0
× 0π #
×
=
#
= P,U = ° !
9 ) #
*
φ
$
φ =φ
0
!
= −λ
=
!
−
0
)
0
×
×
(
Ω
0π
(
λ
σ
= .,U#S
!
−
#
= Q# ,−. U #
) #
&−
&= P,U !
%
H
)
!
−σ#
0
9
#
"
0
)
=
[
φ = φ −φ = σ#
@
.
0
φ =φ !
H
⋅
! Ω=
"
[
"
*
=
9
T
=
)
=
⋅ =
δ
ν
"
)
θ
=
$
δ
ν
θ#
ν
=
)
)
+
"
%
ν
θ −
θ
)
−
(
ν
θ =
+
9
,
θ
ν ν+ ν
9
δ 0&
θ
δ
ν
%#
ν
=
θ #δ 0 & #
ν θ
B 9
& = & "ν
ν "
ν
"ν
9
)
)
$
T
)
9
! δ 0 & = & "ν
δ
$
=
=
&
$
ν θ
+∞
ν =,
θ#
#
ν×
ν
Ω= π
δ
ν+ ν
S
θ#
#
θ ( θ
)
ν ( ν
%
θ+ θ
Ω
0π
×
$
θ #& "ν ν ×
Ω
0π
θ#
#
$
×
Ω
0π
θ# θ
ν "ν ν
π?
θ
,
&
θ# θ
?.
!
=
!
×
$ .
=
$
.
=
.
#
=
=
σ
0
.
#
. =
! = $ = . $ = $σ
! %$ =
∂!
∂
0
"
= 0$σ
$
R
.
#
!!=
.
$
0 =
0
) = ! + $ = 0 $ = σ 0$
.
∂)
% =
!
∂
#
K =
=4
!
=
$ = 0σ
+
= 0σ
0
+ σ
.
$
→,
=,
+σ
$
.
$+ σ
.
.
.
$
$
0
= σ
.
$+
.
#
".%
B
0
= σ
.
!
.
$#
$=
.
' $
' *
)
8 =
$ 0?. =
× =
!
9
#
9 !
•
0
= σ
.
+=)−
•
+=−
β
$
+µ
+$
$× =,
.
∂+
∂
#$
µ=
$α +
µ !α / !α
=,#
α
!α =
$
0
$− σ
.
0
α
α
−
α
! !α + ! β = , !
,="
α
−
β
α
+ µβ
α
β
!
+
β
!β =
β
=,#
α
=
β
µβ = ,
β
−
β
$β + µ β
β

Documents pareils