Podcast
Questions and Answers
What does Wien's displacement law relate?
What does Wien's displacement law relate?
What is the equation for total emissive power derived from Planck's law called?
What is the equation for total emissive power derived from Planck's law called?
What is the value of the Stefan-Boltzmann constant?
What is the value of the Stefan-Boltzmann constant?
What represents the share of thermal radiation emitted by a blackbody between 0 to λ?
What represents the share of thermal radiation emitted by a blackbody between 0 to λ?
Signup and view all the answers
Which constant is NOT a component of Planck's law equation?
Which constant is NOT a component of Planck's law equation?
Signup and view all the answers
What does the term 𝐹0−𝜆 represent in the context of blackbody radiation?
What does the term 𝐹0−𝜆 represent in the context of blackbody radiation?
Signup and view all the answers
Which equation correctly defines the blackbody emissive power in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$?
Which equation correctly defines the blackbody emissive power in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$?
Signup and view all the answers
How is the share of emitted power from a blackbody in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$ calculated?
How is the share of emitted power from a blackbody in the wavelength range from $ackslashlambda_1$ to $ackslashlambda_2$ calculated?
Signup and view all the answers
In the blackbody radiation context, what does the term $ackslashsigma$ represent?
In the blackbody radiation context, what does the term $ackslashsigma$ represent?
Signup and view all the answers
If the temperature of a blackbody is raised, what is the expected effect on its emitted thermal radiation energy?
If the temperature of a blackbody is raised, what is the expected effect on its emitted thermal radiation energy?
Signup and view all the answers
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
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
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.
