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Questions and Answers
What does Wien's displacement law relate?
What is the equation for total emissive power derived from Planck's law called?
What is the value of the Stefan-Boltzmann constant?
What represents the share of thermal radiation emitted by a blackbody between 0 to λ?
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Which constant is NOT a component of Planck's law equation?
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What does the term 𝐹0−𝜆 represent in the context of blackbody radiation?
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Which equation correctly defines the blackbody emissive power in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$?
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How is the share of emitted power from a blackbody in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$ calculated?
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In the blackbody radiation context, what does the term $ackslashsigma$ represent?
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If the temperature of a blackbody is raised, what is the expected effect on its emitted thermal radiation energy?
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Study Notes
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 (𝑘𝐵), 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 (𝜆𝑚𝑎𝑥) and absolute temperature (T) is a constant (C3): 𝜆𝑚𝑎𝑥 ∙ 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 (Eb) is proportional to the fourth power of the absolute temperature (T): 𝐸𝑏 = 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
- 𝐹0−𝜆 represents the share of thermal radiation energy emitted from a blackbody with absolute temperature T in the wavelength range from 0 to
- 𝐸0−𝜆 is the blackbody emissive power in the wavelength range from 0 to 𝜆 and it's calculated with: 𝐸0−𝜆 = 𝐹0−𝜆 ∙ 𝜎 ∙ 𝑇4
- 𝐸𝜆1−𝜆2 represents the blackbody emissive power in the wavelength range from 𝜆1 to 𝜆2 and it's calculated with: 𝐸𝜆1−𝜆2 = 𝐹𝜆1−𝜆2 ∙ 𝜎 ∙ 𝑇4
- 𝐹𝜆1−𝜆2 is the share of emitted power from a blackbody in the wavelength range from 𝜆1 to 𝜆2 and it's calculated with: 𝐹𝜆1−𝜆2 = 𝐹0−𝜆2 − 𝐹0−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: 𝛼𝜆 + 𝜌𝜆 + 𝜏𝜆 = 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 (𝛼𝜆 = 𝜖𝜆), blackbody functions (𝐹0−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 (𝜏𝑠) of low Fe oxide glass with a thickness of 6 mm
- Total transmissivity (𝜏𝑠) can be calculated by multiplying spectral transmissivity (𝜏𝜆) 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 (𝜃𝑠𝑒)
- 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 (𝛼𝑠)
- Should have low thermal radiation heat losses (𝜖𝐼𝑅)
- The selectivity (S) of a solar collector absorber is defined as the ratio of absorptivity to emissivity (𝛼𝑠/𝜖𝐼𝑅)
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
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Description
Test your knowledge on Planck's Law, Wien's Displacement Law, and Stefan-Boltzmann's Law. This quiz covers the fundamental principles governing blackbody radiation and their mathematical relationships. Discover how temperature and wavelength interact in thermal radiation phenomena.
