--- theme: default class: text-center title: Laws of radiation --- # Laws of radiation Unit 3, Lecture 25 --- ## Fundamental Laws of Radiation - Course: Heat and Mass Transfer (DI05019071) - Unit 3: Radiation - Lecture 25: Laws of Radiation --- ## Lecture Agenda - 1. Planck's Law of Distribution - 2. Wien's Displacement Law - 3. Stefan-Boltzmann Law - 4. Kirchhoff's Law - 5. Lambert's Cosine Law --- ## 1. Planck's Distribution Law - Formulated by Max Planck (1900). - Describes the spectral emissive power of a black body (E_bλ) as a function of wavelength (λ) and temperature (T). - Equation: - E_bλ = C_1 / [ λ^5 * (exp(C_2 / λT) - 1) ] - Where C_1 and C_2 are radiation constants. --- ## Planck's Law: Spectral Distribution - Plotting Planck's law shows bell-shaped curves for different temperatures. - Key observations: - - Emitted radiation varies continuously with wavelength. - - At any wavelength, magnitude increases with increasing temperature. - - The peak of the curve shifts to shorter wavelengths at higher temperatures. --- ## 2. Wien's Displacement Law - Derived from Planck's Law by finding the maximum of the curve. - States that the wavelength at which maximum emission occurs (λ_max) is inversely proportional to absolute temperature (T). - Equation: λ_max * T = 2898 μm·K - This explains why hotter objects change color (red to yellow to blue-white). --- ## 3. Stefan-Boltzmann Law - Provides the TOTAL emissive power of a black body. - Obtained by integrating Planck's Law from λ=0 to ∞. - Equation for Black Body: E_b = σ * T^4 - σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/(m²·K⁴) - T must be in Kelvin! --- ## Stefan-Boltzmann for Real Surfaces - Real surfaces emit less than a black body. - We incorporate Emissivity (ε) into the Stefan-Boltzmann law. - Equation for Real Surface: E = ε * σ * T^4 - For a Grey Body, ε is a constant independent of wavelength. --- ## 4. Kirchhoff's Law - Relates emission and absorption properties. - States that at thermal equilibrium, the emissivity of a surface equals its absorptivity. - Equation: ε = α - Conditions: Strict equilibrium is required, but it is broadly applied to grey bodies as an engineering approximation. --- ## Implications of Kirchhoff's Law - Since ε = α, and for opaque bodies α + ρ = 1: - We can substitute: ε + ρ = 1 - Therefore, Emissivity = 1 - Reflectivity (ε = 1 - ρ) - Highly reflective surfaces (like aluminum foil) have very low emissivity. --- ## 5. Lambert's Cosine Law - Describes directional characteristics of diffuse emission. - States that the radiation intensity emitted by a diffuse surface is directly proportional to the cosine of the angle between the observer's line of sight and the surface normal. - Equation: I_θ = I_n * cos(θ) - Where I_n is intensity in the normal direction. --- ## Lambert's Law: Diffuse Emitters - A surface that obeys Lambert's Cosine Law is called a Lambertian surface or perfectly diffuse surface. - Interestingly, while intensity varies with cos(θ), the apparent area viewed by the observer also varies by cos(θ). - Result: A Lambertian surface appears equally bright from any viewing angle! (e.g., the Sun, matte paper). --- ## Summary of Laws - Planck: E_bλ vs λ distribution curve. - Wien: Peak wavelength λ_max ∝ 1/T. - Stefan-Boltzmann: Total E_b = σT⁴. - Kirchhoff: Emissivity ε = Absorptivity α. - Lambert: Intensity I_θ = I_n cos(θ). --- ## Next Lecture Preview - Topic: Concept of Shape Factor and Radiation Shields - Key questions to ponder: - - When two surfaces exchange heat, how much of surface 1's radiation actually hits surface 2? - - How can we use reflective materials to drastically reduce radiation heat transfer?