Blackbody Radiation Characteristics

Blackbody radiation exhibits several fundamental characteristics that are universal for all perfect absorbers and emitters. These properties depend only on temperature and are independent of the material composition of the blackbody.

1. Perfect Absorption and Emission

Perfect Absorber

  • Absorbs 100% of incident electromagnetic radiation at all wavelengths
  • No reflection or transmission occurs
  • Absorptivity α = 1 for all wavelengths and angles
  • Independent of the angle of incidence

Perfect Emitter

  • Emits the maximum possible radiation at each wavelength for a given temperature
  • Emissivity ε = 1 for all wavelengths
  • Follows Kirchhoff's law: α = ε at thermal equilibrium

2. Temperature-Dependent Spectral Distribution

Planck Distribution

The spectral energy distribution follows Planck's law exactly:

Bλ(T)=2hc2λ51ehcλkBT−1B_\lambda(T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k_B T}} - 1}

Key Spectral Properties

  • Continuous spectrum: Radiation at all wavelengths
  • Single peak: Maximum intensity at one specific wavelength
  • Asymmetric curve: Steep drop-off at short wavelengths, gradual tail at long wavelengths
  • Temperature scaling: Higher temperatures shift entire curve to shorter wavelengths

Blackbody spectra for different temperatures showing Wien's displacement

3. Wien's Displacement Law

The wavelength of peak emission is inversely proportional to temperature:

λmax=bT\lambda_{max} = \frac{b}{T}

where b = 2.898 × 10⁻³ m·K (Wien's displacement constant)

Physical Implications

  • Hot objects appear blue-white: Peak in UV/blue region
  • Cool objects appear red: Peak in infrared/red region
  • Room temperature objects: Peak in far infrared (~10 μm)
  • Solar radiation: Peak at ~500 nm (green), appears white due to broad spectrum

Temperature Examples

  • 3000K (incandescent bulb): λ_max = 966 nm (near infrared)
  • 5800K (Sun's surface): λ_max = 500 nm (green)
  • 7000K (hot star): λ_max = 414 nm (violet)
  • 300K (room temperature): λ_max = 9.66 μm (far infrared)

4. Stefan-Boltzmann Law

The total power radiated is proportional to the fourth power of absolute temperature:

P=σAT4P = \sigma A T^4

where σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴ (Stefan-Boltzmann constant)

Energy Density

The total energy density of blackbody radiation:

u=4σT4c=aT4u = \frac{4\sigma T^4}{c} = aT^4

where a = 7.57 × 10⁻¹⁶ J·m⁻³·K⁻⁴ (radiation constant)

Practical Applications

  • Stellar luminosity: L = 4πR²σT⁴
  • Earth's energy balance: Solar input vs. thermal radiation
  • Pyrometry: Non-contact temperature measurement
  • Thermal design: Heat transfer calculations

5. Lambertian Emission Pattern

Blackbodies exhibit perfect Lambertian emission characteristics:

Angular Distribution

I(θ)=I0cos⁡(θ)I(\theta) = I_0 \cos(\theta)

where θ is the angle from the surface normal

Properties of Lambertian Emission

  • Maximum intensity: Normal to the surface (θ = 0°)
  • Uniform radiance: Appears equally bright from all viewing angles
  • Cosine law: Intensity decreases as cosine of emission angle
  • Hemispherical emission: No radiation below the surface plane

6. Thermodynamic Properties

Thermal Equilibrium

  • Detailed balance: Rate of absorption equals rate of emission
  • Temperature uniformity: Same temperature throughout
  • Reversibility: No net energy flow in equilibrium

Radiation Pressure

Blackbody radiation exerts pressure on surfaces:

Prad=u3=4σT43cP_{rad} = \frac{u}{3} = \frac{4\sigma T^4}{3c}

Entropy and Information

Blackbody radiation has maximum entropy for given energy, representing thermal equilibrium with no information content.

7. Quantum Characteristics

Photon Statistics

Blackbody radiation follows Bose-Einstein statistics for photons:

⟨nν⟩=1ehνkBT−1\langle n_\nu \rangle = \frac{1}{e^{\frac{h\nu}{k_B T}} - 1}

Average number of photons per mode at frequency ν

Energy Quantization

  • Discrete energy levels: E = nhν for each mode
  • Zero-point energy: Minimum energy per mode is ½hν
  • Thermal fluctuations: Statistical variations in photon number

Coherence Properties

  • Incoherent radiation: Random phases between different modes
  • Short coherence time: τ_c ~ h/(k_BT)
  • Thermal statistics: Super-Poissonian photon number fluctuations

8. Real-World Approximations

Near-Blackbody Objects

  • Cavity radiators: Small hole in heated cavity (ε ≈ 0.999)
  • Carbon surfaces: Graphite, carbon black (ε ≈ 0.97)
  • Human skin: Infrared emissivity ε ≈ 0.98
  • Earth's atmosphere: Good blackbody in far infrared

Deviations from Ideal Behavior

  • Wavelength-dependent emissivity: ε(λ) varies with λ
  • Temperature gradients: Non-uniform temperature distribution
  • Reflection and scattering: Non-zero reflectivity
  • Semi-transparency: Partial transmission of radiation

Summary of Key Characteristics

  1. Perfect absorption and emission at all wavelengths
  2. Temperature-dependent spectrum following Planck's law
  3. Wien's displacement - peak shifts with temperature
  4. Stefan-Boltzmann scaling - total power ∝ T⁴
  5. Lambertian emission - uniform radiance
  6. Thermal equilibrium - maximum entropy
  7. Quantum nature - photon statistics and energy quantization
  8. Universal behavior - independent of material properties

Related Topics

← Back to Introduction to Blackbody Radiation