Black Body Distribution Function and Emissivity S W McKnight C A DiMarzio

Blackbody Distribution Function

Meaning of Distribution Function How much energy is emitted at =550 nm? – =550.0? – = …? M e, d = energy emitted between and +d per unit area M e, = dN e, / d where N e, 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 T1T1 T2T2 Thermal Equilibrium → T 1 = T 2

Relation between Emissivity and Absorption: A(, T) For optically thick sample, A=1-R (R=reflectivity)

Detailed Balance Greybody in thermal equilibrium with enclosure T1T1 T2T2 Wavelength selective filter

Detailed Balance Second Law of Thermodynamics implies that T 1 must remain equal to T 2 –(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?