InfRec Thermo Gear G100, Руководство по эксплуатации

Страница: 127 / 141

Chapter 7 Appendix
＜
Blackbody radiation
＞
Blackbody is an object which absorbs all the incident energy and the radiant intensity becomes
maximum at full wavelengths and temperatures.
In a blackbody, Absorptance
α
equals Emissivity
ε
, and
α
=
ε
= 1.
Practical existing object is not like this, but it is described with transmittance
τ
and refrectance
ρ
as follows,
α
+
ρ
+
τ
= 1
Energy radiated from the blackbody is described as follows and called “Plank’s law”.
) 1 ...(
1 exp
2
5
1
⎭
⎬
⎫
⎩
⎨
⎧
−
⎟
⎠
⎞
⎜
⎝
⎛
=
T
c
c
W
λ
λ
λ
In order to obtain whole radiant emittance of the blackbody, integrate the equation (1) through
the full the full wavelengths (0 to infinity). The result is as follows and called
“Stefan-Bolzmann’s equation”.
W T
=
σ
4
2 ...( )
The temperature of blackbody can be obtained directly from the radiant energy of blackbody by
this equation. In order to find out the wavelength on the maximum spectral radiant emittance,
differentiate lank’s law and make the value to 0.
.
[
) 3 ...( 8 2897
K m T
m
⋅ =
μ λ ]
This equation is called “Wien’s displacement law”.
Where in above (1) to (3),
W λ :
S pectral radiant emittance per unit wavelength and unit area
[ W / c m
2
· μ m ]
λ
m :
Wavelength of maximum spectral radiant emittance [ μ m ]
λ : Wavelength [ μ m ]
h : Plank’s constant = 6 . 6 2 6 1 × 1 0
- 3 4
[ W · s
2
]
T : Absolute temperature [K ]
c : Light velocity = 2 . 9 9 7 9 × 1 0
1 0
[ c m / s ]
k : Bolzmann constant = 1 . 3 8 0 7 × 1 0
- 2 3
[ W · s / K ]
σ : Stefan-Bolzmann constant = 5 . 6 7 0 5 × 1 0
- 1 2
[ W / c m
2
· K
4
]
c
1 :
Fist radiation constant = 3 . 7 4 1 8 × 1 0
4
[ / c m
2
· μ m
4
]
c
2 :
Second radiation constant = 1 . 4 3 8 8 × 1 0
4
[ μ m · K ]
95691-2935-0000
8 - 2