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METR 415/715

This document explores Planck's function, detailing the distinction between intensity (W m⁻² sr⁻¹) and radiative flux (W m⁻²). It emphasizes the significance of wavelength in maximum emission, governed by Wien’s Displacement Law (λ_max = 2897 μm K). The laws of gray bodies and the Stefan-Boltzmann Law are also discussed, highlighting the constant emissivity of gray bodies and integrating Planck’s function to derive the total emitted radiation (σ = 5.67 x 10⁻⁸ W m⁻² K⁴). Additionally, it covers Kirchhoff's Law and the concept of brightness temperature in radiative equilibrium.

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METR 415/715

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  1. METR 415/715 MondayFeb 18 2013

  2. Planck’s function

  3. Intensity vs. radiative flux Remember the units used in Intensity (Wm-2sr-1) and in Flux (Wm-2). Intensity refers to radiation travelling in a certain direction, and Flux to radiation emitted in all directions The left hand side of Planck function refers to the intensityof radiation for a particular wavelength

  4. Wien’s Displacement Law • Refers to the wavelength of maximum emission of Planck’s Function • Obtained by taking the derivative with respect to wavelength and setting it = 0 • ΚW= 2897μm K

  5. Wien’s Displacement Law • Refers to the wavelength of maximum emission of Planck’s Function • Obtained by taking the derivative with respect to wavelength and setting it = 0 • ΚW= 2897μm K

  6. Gray Bodies You assume the emissivity (and hence absorptivity) is a constant fraction of black body emissivity across all wavelengths

  7. Stefan – Boltzmann Law • Obtained by integrating Planck’s function over all wavelengths (eq. 6.4) p.122. • σ = 5.67 X 10-8 Wm-2K4

  8. Monochromatic emissivity – Graybodyemissivity

  9. Krichhoff’s Law

  10. Brightness temperature

  11. Discussion of Fig 6.6 p.129

  12. Discussion of Section 6.4 Radiative equilibrium in a vacuum

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