Thermal Radiation Laws Quiz

Planck's Law

• Describes the wavelength distribution of thermal radiation emitted by a blackbody
• Spectral emissive power is expressed in W/m²µm
• Planck's law equation involves constants: Planck's constant (ℎ), speed of light in vacuum (𝑐₀), Boltzmann's constant (𝑘_𝐵), and two radiation constants (C₁ and C₂)

Wien's Displacement Law

• Describes the relation between blackbody temperature and the wavelength with maximum spectral emissive power
• The product of maximum wavelength (𝜆_𝑚𝑎𝑥) and absolute temperature (T) is a constant (C₃): 𝜆_𝑚𝑎𝑥 ∙ 𝑇 = 𝐶₃ = 2898 𝜇𝑚 𝐾

Stephan-Boltzmann's Law

• The total emissive power of a blackbody is obtained by integrating Planck's law
• The total emissive power (E_b) is proportional to the fourth power of the absolute temperature (T): 𝐸_𝑏 = 𝜎 ∙ 𝑇⁴
• The Stefan-Boltzmann constant (𝜎) is 5,67·10−8 W∕m2 K4

Blackbody Radiation Tables

• Used to determine absorbed or emitted power in a certain wavelength interval
• 𝐹_0−𝜆 represents the share of thermal radiation energy emitted from a blackbody with absolute temperature T in the wavelength range from 0 to 
• 𝐸_0−𝜆 is the blackbody emissive power in the wavelength range from 0 to 𝜆 and it's calculated with: 𝐸_0−𝜆 = 𝐹_0−𝜆 ∙ 𝜎 ∙ 𝑇⁴
• 𝐸_{𝜆1−𝜆2} represents the blackbody emissive power in the wavelength range from 𝜆₁ to 𝜆₂ and it's calculated with: 𝐸_{𝜆1−𝜆2} = 𝐹_{𝜆1−𝜆2} ∙ 𝜎 ∙ 𝑇⁴
• 𝐹_{𝜆1−𝜆2} is the share of emitted power from a blackbody in the wavelength range from 𝜆₁ to 𝜆₂ and it's calculated with: 𝐹_{𝜆1−𝜆2} = 𝐹_0−𝜆2 − 𝐹_0−𝜆1

Energy Conservation Law

• Energy can neither be created nor destroyed, only transformed from one form of energy to another
• Thermal radiation balance for semitransparent surfaces: 𝛼_𝜆 + 𝜌_𝜆 + 𝜏_𝜆 = 1 and 𝛼+𝜌+𝜏 =1

From Spectral to Total Radiative Properties

• Integral values of radiative properties are preferred in engineering practice
• For solar radiation: 0,3-3 𝜇m
• For longwave radiation: 3-100 𝜇m
• For light: 0,38-0,76 𝜇m
• For atmospheric window: ≈8-13 𝜇m
• Total emissivity (𝜖) can be calculated by integrating spectral emissivity (𝜀𝜆) over the considered wavelength range
• For surfaces with gray surface behavior (𝛼_𝜆 = 𝜖_𝜆), blackbody functions (𝐹_0−𝜆) can be used to calculate total properties
• Caution: Temperature in ·T is different for solar and longwave radiation

Solar Energy Transmissivity

• Example: Determining solar energy transmissivity (𝜏_𝑠) of low Fe oxide glass with a thickness of 6 mm
• Total transmissivity (𝜏_𝑠) can be calculated by multiplying spectral transmissivity (𝜏_𝜆) with blackbody function values in corresponding wavelength ranges

Radiation Characteristics

• Energy balance of a surface exposed to solar radiation includes conduction, convection, and radiation
• Properties that determine the absorption and reflection of radiation affect the surface temperature (𝜃_𝑠𝑒)
• Radiative heat transfer between two parallel plates with narrow gap depends on emissivity values and temperatures of the plates

Solar Collector Absorber

• Should possess high absorptivity for shortwave (solar) radiation (𝛼_𝑠)
• Should have low thermal radiation heat losses (𝜖_𝐼𝑅)
• The selectivity (S) of a solar collector absorber is defined as the ratio of absorptivity to emissivity (𝛼_𝑠/𝜖_𝐼𝑅)

Semi-selective Absorbers

• High absorptivity for shortwave (solar) radiation
• Low thermal radiation heat losses
• The selectivity (S) of semi-selective absorbers is usually around 2 or higher

Cool Coatings

• Reduce heat gains and material expansion
• Reflective paints are not suitable for this application