Transcript Lecture Notes 3a - Black Body Distribution Function and Emissivity

Black Body Distribution
Function and Emissivity
S W McKnight
C A DiMarzio
Blackbody Distribution Function
4
10
2
T=6000 K
0
10
e
M (W cm-2 -1)
10
-2
10
-4
10
-1
10
0
1
10
10
Wavelength ()
2
10
Meaning of Distribution Function
• How much energy is emitted at =550
nm?
– =550.0?
– =550.000000000…?
Me, d = energy emitted between
 and +d per unit area
Me, = dNe, / d where Ne, is energy
emitted for wavelengths less than 
Effect of Emissivity
• ε≤1
• ε=1 → “blackbody”
• ε<1 → “greybody”
Radiative Thermal Equilibrium
Greybody in thermal equilibrium with enclosure
T1
T2
Thermal Equilibrium → T1 = T2
Relation between Emissivity and
Absorption: A(, T)
For optically thick sample, A=1-R
(R=reflectivity)
Detailed Balance
Greybody in thermal equilibrium with enclosure
T1
T2
Wavelength selective filter
Detailed Balance
• Second Law of Thermodynamics implies
that T1 must remain equal to T2
– (Cannot create heat gradient without applying
work)
• At each wavelength: ε(, T) = A (, T)
• Same argument applies to non-normal
incidence: ε(, Θ, T) = A (, Θ, T)
• For optically dense object:
ε(, Θ, T) = 1 - R(, Θ, T)
Emissivity of Materials
• Highly reflective materials are low
emissive materials
(Reflective materials in visible are not
necessarily reflective in IR)
• Vacuum thermos bottles are coated with
reflective metal
• So why are house radiators painted silver?
To look nice?