Thermal Radiation and Heat Emission

Thermal radiation is the transfer of energy by infrared and other electromagnetic waves emitted by all objects because of their temperature; it needs no medium, and the power emitted by a surface is P = εσAT⁴, where T is the absolute temperature. In brief: hotter objects emit more radiation, with a shorter peak wavelength (Wien’s law: λ_max = 2.898 × 10⁻³ m·K ÷ T). Dark, matt surfaces are good emitters and absorbers, and shiny, light surfaces are good reflectors and poor emitters.

The warmth of the Sun, the glow of a fire and the heat from a hot stove at a distance all come from radiation. This guide explains thermal radiation, the factors that affect emission and absorption, the Stefan-Boltzmann and Wien laws, compares surfaces in a table, works through calculations for the human body and the Sun, and corrects common mistakes.

What is thermal radiation?

Every object with a temperature above absolute zero emits electromagnetic radiation, because its charged particles are in thermal motion. At room temperature the radiation is mostly infrared, which we cannot see but feel as warmth. At about 700 °C an object starts to glow dull red, and at higher temperatures it appears orange, yellow and white. Radiation travels at the speed of light, through a vacuum, which is how the Sun’s energy reaches the Earth. When it hits another object, it can be absorbed (the object warms), reflected or transmitted. An object that absorbs more than it emits warms up, and one that emits more than it absorbs cools down. At equilibrium, they are equal.

How do surfaces affect radiation?

• Dark, matt surfaces are good absorbers and good emitters. A perfect absorber and emitter is called a black body.
• Light, shiny surfaces reflect most of the radiation, and are poor absorbers and poor emitters. This is why emergency blankets and vacuum flasks have shiny linings, and why houses in hot climates are painted white.
• The emissivity ε (between 0 and 1) measures how well a surface emits compared with a black body.

What are the laws of thermal radiation?

• Stefan-Boltzmann law: the total power radiated by a surface of area A at absolute temperature T is P = εσAT⁴, with σ = 5.67 × 10⁻⁸ W/m²·K⁴. Doubling the absolute temperature increases the power 16 times. The net power exchanged with surroundings at T_s is P_net = εσA(T⁴ − T_s⁴).
• Wien’s displacement law: the wavelength of the peak of emission is λ_max = b ÷ T, with b = 2.898 × 10⁻³ m·K. The hotter the object, the shorter the wavelength.

Surfaces compared

Worked example: the human body and the Sun

1. Power emitted by skin. Take a skin area of 1.8 m² at 34 °C (307 K) and assume ε = 1 (a black-body estimate). P = 5.67 × 10⁻⁸ × 1.8 × 307⁴ = 5.67 × 10⁻⁸ × 1.8 × 8.88 × 10⁹ = 906 W.
2. Net power in a room at 20 °C (293 K). P_net = σA(307⁴ − 293⁴) = 5.67 × 10⁻⁸ × 1.8 × (8.88 × 10⁹ − 7.37 × 10⁹) = 154 W. This is an upper estimate (clothes and real emissivity reduce it), but of the same order as the resting metabolic power of about 100 W.
3. Peak wavelength of the body. At 310 K: λ_max = 2.898 × 10⁻³ ÷ 310 = 9.3 × 10⁻⁶ m = 9.3 µm, in the infrared, which is what thermal cameras detect.
4. Peak wavelength of the Sun. The surface temperature is about 5,770 K: λ_max = 2.898 × 10⁻³ ÷ 5,770 = 5.0 × 10⁻⁷ m = 500 nm, in the visible region (green-blue).
5. Doubling temperature. An object heated from 300 K to 600 K emits 2⁴ = 16 times as much power.

How was thermal radiation studied?

William Herschel discovered infrared radiation in 1800 by measuring temperatures beyond the red end of the spectrum. Josef Stefan found the T⁴ law experimentally in 1879, and Ludwig Boltzmann derived it in 1884. Wilhelm Wien published the displacement law in 1893. Max Planck’s explanation of the spectrum of black-body radiation in 1900 started quantum theory.

Which mistakes are common?

Mistake 1: Using Celsius in the T⁴ law

Temperatures must be in kelvins.

Mistake 2: Thinking that only hot objects radiate

All objects above absolute zero radiate. A cold object emits less, but it still emits.

Mistake 3: Saying that dark surfaces always get hotter

They absorb more light, but they also emit more infrared. The final temperature depends on the balance.

Mistake 4: Confusing thermal radiation with nuclear radiation

Thermal radiation is electromagnetic radiation from heat, and is not radioactivity.