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Black Body Distribution Function and Emissivity

Black Body Distribution Function and Emissivity. S W McKnight C A DiMarzio. Blackbody Distribution Function. M e,  = dN e, / d where N e, is energy emitted for wavelengths less than . Meaning of Distribution Function. How much energy is emitted at =550 nm? =550.0?

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Black Body Distribution Function and Emissivity

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

  2. Blackbody Distribution Function

  3. Me, = dNe, / d where Ne, is energy emitted for wavelengths less than  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

  4. Effect of Emissivity • ε ≤ 1 • ε=1 → “blackbody” • ε<1 → “greybody”

  5. Radiative Thermal Equilibrium Greybody in thermal equilibrium with enclosure T1 T2 Thermal Equilibrium → T1 = T2

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

  7. Detailed Balance Greybody in thermal equilibrium with enclosure T1 T2 Wavelength selective filter

  8. 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)

  9. 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?

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