Radiation
Thermal radiation is heat carried by electromagnetic waves — it needs no medium. Learn the Stefan–Boltzmann law, emissivity, black and grey bodies, Wien's law, view factors, and radiation shields.
Sunlight warms your face across 150 million km of vacuum. A campfire warms you even when the air is cold. That's thermal radiation — every object above absolute zero emits it, and hot objects emit enormously more (∝ T⁴).
Radiation dominates at high temperatures (furnaces, re-entry vehicles, combustion) and in vacuum (spacecraft), and matters even at room temperature for buildings and electronics.
An analogy
A glowing electric heater: you feel warm on the side facing it but not behind a sheet of foil — radiation travels in straight lines and can be blocked or reflected.
Everything radiates
Emission grows with the fourth power of absolute temperature: doubling T (in K) multiplies emission by 16. At room temperature the radiation is infrared; at ~800 K objects start glowing red.
Emissivity and surface finish
A black body (ε = 1) is the ideal emitter/absorber. Real surfaces: polished aluminium ≈ 0.05, oxidised steel ≈ 0.8, paint ≈ 0.9, human skin ≈ 0.98. Kirchhoff's law: at the same wavelength, emissivity = absorptivity. Low-ε coatings (low-e glass, foil) cut radiative loss.
Spectral selectivity
The Sun (≈ 5800 K) peaks at 0.5 µm (visible); room-temperature objects peak near 10 µm. Solar collectors use surfaces that absorb visible but emit little infrared; white roofs reflect sunlight but emit infrared well — staying cool.
View factors and enclosures
Exchange between surfaces depends on how much each 'sees' of the other (view factor) and on their emissivities — solved with radiosity networks. Radiation shields (multi-layer insulation on spacecraft) add resistances in series. Participating gases (CO₂, H₂O) absorb and emit in furnaces and the atmosphere.
Formulas
- Black-body emission:
E_b = σ T⁴ - Small body in large surroundings:
Q̇ = ε σ A (T_s⁴ − T_sur⁴) - Wien's displacement law:
λ_max · T = 2898 µm·K - Linearised radiation coefficient:
h_r ≈ 4 ε σ T_m³
Worked example: Radiation from a hot plate
Given: A = 1 m², ε = 0.9; T_s = 500 K, surroundings 300 K
Find: Net radiative loss.
- Q̇ = 0.9 × 5.67 × 10⁻⁸ × (500⁴ − 300⁴)
- = 0.9 × 5.67 × 10⁻⁸ × 5.44 × 10¹⁰ = 2776 W
Answer: ≈ 2.8 kW
Worked example: Wien's law
Given: Sun ≈ 5800 K, human ≈ 310 K
Find: Peak wavelengths.
- Sun: 2898/5800 = 0.50 µm (green-visible)
- Human: 2898/310 = 9.3 µm (infrared)
Answer: 0.5 µm and 9.3 µm — why thermal cameras work in 8–14 µm
Common mistakes
- Wrong: Using °C in T⁴. — Right: Always kelvin — (227 °C)⁴ is meaningless.
- Wrong: Ignoring radiation at moderate temperatures. — Right: At 100 °C, radiation from a painted surface is comparable to natural convection.
Applications
- Furnaces & boilers: Radiant sections transfer most of the heat from flames to tubes.
- Spacecraft thermal control: Radiators, MLI blankets and coatings balance heat in vacuum.
- Buildings: Low-e glazing, cool roofs and radiant heating panels.
Key takeaways
- E = εσT⁴ with T in kelvin.
- Emissivity depends on surface finish.
- Wien: λ_max T = 2898 µm·K.
- Dominant at high T and in vacuum.
Going further
- Radiosity networks: Surface and space resistances form circuits for multi-surface enclosures.
- Greenhouse effect: Glass and CO₂ transmit short-wave solar radiation but absorb long-wave infrared.
- Radiative sky cooling: Surfaces emitting in the 8–13 µm atmospheric window can cool below ambient even in sunlight.