Radiation

Radiation is the transfer of thermal energy through electromagnetic waves — no medium is required. Unlike conduction (energy passing through direct contact) or convection (energy carried by moving fluids), radiation can travel through the vacuum of space at the speed of light. This is how the Sun's energy reaches Earth across 150 million kilometres of nearly empty space, and it is why you feel warmth from a campfire even when the air between you is cold and still. Every object with a temperature above absolute zero emits radiation. The hotter the object, the more energy it radiates and the shorter the peak wavelength of that radiation. A metal poker glowing red, a human body emitting infrared, and the Sun radiating visible and ultraviolet light are all examples of the same physical process at different temperatures. The relationship between temperature and radiated power is described by the Stefan–Boltzmann law, one of the most important quantitative results in thermal physics. The concept of a blackbody — an idealised object that perfectly absorbs and emits all radiation — sits at the heart of radiation theory. Real objects behave somewhat like blackbodies, with a dimensionless factor called emissivity (ε) scaling their emission relative to an ideal blackbody. Understanding radiation is essential not only for engineering (thermal insulation, spacecraft design, industrial furnaces) but also for global topics like Earth's energy balance and the greenhouse effect.

Key takeaways
  • Origin of Thermal Radiation
  • The Blackbody Ideal
  • The Stefan–Boltzmann Law
  • Net Radiation and Cooling
  • Wien's Displacement Law

Origin of Thermal Radiation

Thermal radiation originates from the accelerated motion of charged particles — primarily electrons — inside matter. When atoms vibrate due to thermal energy, their charged components accelerate and, by Maxwell's laws, emit electromagnetic waves. These waves span a spectrum of frequencies, but the distribution of intensities across wavelengths depends on temperature alone (for a blackbody). This emission is continuous and spontaneous; no external trigger is needed.

The Blackbody Ideal

A blackbody is defined as an object that absorbs 100% of all incident electromagnetic radiation, regardless of wavelength or angle. Because it reflects or transmits nothing, it is a 'perfect absorber'. By Kirchhoff's law of thermal radiation, a perfect absorber is also a perfect emitter: at any given temperature it radiates more power per unit area than any real object at the same temperature. A cavity with a tiny hole (like a kiln peephole) closely approximates a blackbody — radiation that enters bounces around inside and is almost never reflected back out.

The Stefan–Boltzmann Law

The total power radiated per unit surface area by a blackbody is proportional to the fourth power of its absolute temperature (in kelvin). Doubling the temperature increases radiated power by a factor of 2⁴ = 16. For real objects, the power is reduced by the emissivity ε (a number between 0 and 1), where ε = 1 for a perfect blackbody, roughly 0.95 for human skin, about 0.05 for polished aluminium, and near 0 for a perfect mirror. Shiny metallic surfaces are poor emitters (and poor absorbers) of thermal radiation, which is why emergency 'space blankets' are made from reflective foil.

Net Radiation and Cooling

Any object simultaneously emits radiation to its surroundings and absorbs radiation from them. The net power exchanged depends on both the object's temperature (T) and the surrounding temperature (T_s). If T > T_s the object has a net loss of energy and cools; if T < T_s it has a net gain and warms. At thermal equilibrium (T = T_s) emission and absorption are exactly balanced. This net exchange is expressed as P_net = εσA(T⁴ − T_s⁴), making radiation a self-regulating mechanism that drives systems toward thermal equilibrium with their environment.

Wien's Displacement Law

While the Stefan–Boltzmann law gives total power, Wien's displacement law describes the peak wavelength: λ_max = b/T, where b ≈ 2.898 × 10⁻³ m·K. At room temperature (~300 K), λ_max ≈ 10 μm — deep infrared, invisible to the eye. The Sun's surface (~5778 K) peaks near 500 nm — yellow-green visible light. Night-vision cameras and thermal imaging systems detect the infrared radiation emitted by warm bodies using exactly this principle.

The Key Equation

P=εσAT4P = \varepsilon \sigma A T^{4}
  • P — Radiated power (W (watts)): Total electromagnetic energy emitted per second by the surface.
  • \varepsilon — Emissivity (dimensionless (0 to 1)): A measure of how closely the object behaves like a perfect blackbody; ε = 1 for an ideal blackbody.
  • \sigma — Stefan–Boltzmann constant (W m⁻² K⁻⁴): Universal constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
  • A — Surface area (m²): The total area of the emitting surface.
  • T — Absolute temperature (K (kelvin)): Temperature measured from absolute zero; must be in kelvin, not Celsius.

Worked Example

Problem. A spherical asteroid of radius 500 m is in deep space with a surface temperature of 400 K. Its emissivity is 0.85. (a) Calculate the total power radiated. (b) If the asteroid then absorbs solar radiation and its temperature rises to 800 K, by what factor does the radiated power increase?

P≈3.9×109 W;P2P1=(800400)4=16P \approx 3.9 \times 10^{9}\,\text{W};\quad \frac{P_2}{P_1} = \left(\frac{800}{400}\right)^4 = 16

Answer. Part (a): approximately 3.9 × 10⁹ W (3.9 GW). Part (b): the radiated power increases by a factor of 16.

Figure
Diagram
Blackbody Radiation SpectrumWavelength λIntensity0λ→λ_maxλ_maxλ_maxT = 3000 KT = 4500 KT = 5500 K↑ Higher T →more power,shorter λ_max
Origins · 1 minJosef Stefan and how this was discovered
JS
Josef Stefan
1835–1893 · Austrian

Stefan experimentally established in 1879 that the total power radiated by a hot body is proportional to the fourth power of its absolute temperature. His student Ludwig Boltzmann derived this result theoretically from thermodynamic principles in 1884, yielding what we now call the Stefan–Boltzmann law. Stefan used the law to make the first credible scientific estimate of the surface temperature of the Sun (~5430 K), remarkably close to the modern accepted value. Stefan grew up speaking Slovene as his first language in a village near Klagenfurt (then part of the Austrian Empire). Despite this modest rural background, he became director of the Physical Institute in Vienna at only 31 years old.

  • Conduction — Conduction is one of the three heat-transfer mechanisms alongside radiation; comparing the two clarifies when each dominates.
  • Convection — Convection completes the trio of heat-transfer modes; in many real systems (e.g., building insulation) radiation and convection act simultaneously.
  • The Electromagnetic Spectrum — Thermal radiation is electromagnetic in nature; understanding the spectrum (infrared, visible, UV) is essential for interpreting Wien's law and thermal imaging.
  • Absolute Temperature & the Kelvin Scale — The Stefan–Boltzmann law requires temperature in kelvin; using Celsius gives completely wrong answers, making this prerequisite concept critical.