4.2 Blackbody radiation and surface properties

Blackbody radiation is the ultimate heat emitter, setting the standard for how surfaces give off energy. It's all about temperature - the hotter something gets, the more radiation it pumps out, following specific patterns that scientists have figured out.

Real surfaces aren't perfect blackbodies, though. They have their own quirks when it comes to emitting, absorbing, and reflecting heat. Understanding these properties helps us predict how things heat up and cool down in the real world.

Blackbody radiation and its properties

Characteristics of blackbody radiation

Top images from around the web for Characteristics of blackbody radiation

• 

  29.1 Quantization of Energy – College Physics View original

  Is this image relevant?

• 

  Planck's equation - Wikiversity View original

  Is this image relevant?

• 

  29.1 Quantization of Energy – College Physics View original

  Is this image relevant?

• 

  Planck's equation - Wikiversity View original

  Is this image relevant?

1 of 2

Top images from around the web for Characteristics of blackbody radiation

• 

  29.1 Quantization of Energy – College Physics View original

  Is this image relevant?

• 

  Planck's equation - Wikiversity View original

  Is this image relevant?

• 

  29.1 Quantization of Energy – College Physics View original

  Is this image relevant?

• 

  Planck's equation - Wikiversity View original

  Is this image relevant?

1 of 2

• Blackbody radiation is the electromagnetic radiation emitted by an idealized physical body that absorbs all incident radiation and emits the maximum possible amount of radiation at any given temperature
• A blackbody is a perfect absorber and emitter of radiation, with an emissivity equal to 1 and reflectivity equal to 0
• The radiation emitted by a blackbody depends only on its temperature and follows a specific spectral distribution described by Planck's law
• The total energy emitted by a blackbody per unit area per unit time is proportional to the fourth power of its absolute temperature, as described by the Stefan-Boltzmann law

Spectral distribution and peak wavelength

• The spectral distribution of blackbody radiation describes the emissive power per unit wavelength as a function of wavelength and temperature
• Planck's law governs the spectral distribution of blackbody radiation, showing that the emissive power peaks at a specific wavelength for a given temperature
• The peak wavelength of the blackbody radiation spectrum is inversely proportional to the absolute temperature, as described by Wien's displacement law
• As the temperature of a blackbody increases, the peak wavelength shifts to shorter wavelengths (visible light at high temperatures, infrared at lower temperatures)

Emissive power and temperature

Definition and units of emissive power

• Emissive power is the rate at which a surface emits thermal radiation per unit area, typically measured in W/m²
• The emissive power of a blackbody is the maximum possible emissive power for any surface at a given temperature
• The emissive power of a real surface is always less than that of a blackbody at the same temperature, and is determined by the surface's emissivity

Relationship between emissive power and temperature

• The emissive power of a surface increases with its absolute temperature, following the Stefan-Boltzmann law
• The Stefan-Boltzmann law states that the total emissive power of a blackbody is proportional to the fourth power of its absolute temperature: $E_b = \sigma T^4$, where $\sigma = 5.67 \times 10^{-8}$ W/(m²·K⁴)
• For real surfaces, the emissive power is modified by the surface's emissivity: $E = \varepsilon \sigma T^4$, where $\varepsilon$ is the emissivity (0 ≤ $\varepsilon$ ≤ 1)
• As the temperature of a surface increases, its emissive power increases rapidly, leading to significant heat transfer by radiation at high temperatures

Applying radiation laws

Planck's law for spectral distribution

• Planck's law describes the spectral distribution of blackbody radiation, giving the emissive power per unit wavelength as a function of wavelength and temperature: $E_{\lambda,b} = \frac{2\pi hc^2}{\lambda^5[\exp(hc/\lambda kT)-1]}$
• To determine the spectral emissive power at a specific wavelength and temperature, substitute the values into Planck's law and solve for $E_{\lambda,b}$
• Planck's law can be used to plot the spectral distribution curves for blackbodies at different temperatures, showing the shift in peak wavelength with temperature

Wien's displacement law for peak wavelength

• Wien's displacement law states that the peak wavelength of the blackbody radiation spectrum is inversely proportional to the absolute temperature: $\lambda_{\max} = \frac{2898 \mu m \cdot K}{T}$
• To find the peak wavelength for a given temperature, substitute the temperature into Wien's displacement law and solve for $\lambda_{\max}$
• Wien's displacement law explains why the color of a blackbody changes with temperature (red at lower temperatures, blue-white at higher temperatures)

Stefan-Boltzmann law for total emissive power

• The Stefan-Boltzmann law relates the total emissive power of a blackbody to its absolute temperature: $E_b = \sigma T^4$, where $\sigma = 5.67 \times 10^{-8}$ W/(m²·K⁴)
• To calculate the total emissive power of a blackbody at a given temperature, substitute the temperature into the Stefan-Boltzmann law and solve for $E_b$
• For real surfaces, modify the Stefan-Boltzmann law using the emissivity of the surface: $E = \varepsilon \sigma T^4$, where $\varepsilon$ is the emissivity (0 ≤ $\varepsilon$ ≤ 1)
• The Stefan-Boltzmann law is used to determine the heat transfer by radiation between surfaces at different temperatures

Radiative properties of real surfaces

Emissivity and absorptivity

• Emissivity is the ratio of a surface's emissive power to that of a blackbody at the same temperature, with values ranging from 0 to 1. It represents the surface's ability to emit thermal radiation
• Absorptivity is the fraction of incident radiation absorbed by a surface, with values ranging from 0 to 1. It depends on the surface material and the wavelength of the incident radiation
• Kirchhoff's law states that, at thermal equilibrium, the emissivity and absorptivity of a surface are equal for a given wavelength and direction
• Surfaces with high emissivity (dark, rough surfaces) are good emitters and absorbers of thermal radiation, while surfaces with low emissivity (shiny, smooth surfaces) are poor emitters and absorbers

Reflectivity and transmissivity

• Reflectivity is the fraction of incident radiation reflected by a surface, with values ranging from 0 to 1. It is related to absorptivity by the conservation of energy principle: $\alpha + \rho = 1$ for opaque surfaces
• Transmissivity is the fraction of incident radiation transmitted through a surface, with values ranging from 0 to 1. It is relevant for transparent or semi-transparent materials
• For transparent materials, the conservation of energy principle includes transmissivity: $\alpha + \rho + \tau = 1$
• The radiative properties of a surface affect its ability to emit, absorb, reflect, and transmit thermal radiation, which in turn influences its temperature and heat transfer characteristics