Black Body Distribution Function and Emissivity

S W McKnight

C A DiMarzio

Blackbody Distribution Function

10-1

100

101

102

10-4

10-2

100

102

104

Wavelength ()

Me (

W c

m-2

-1

)

T=6000 K

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?