# Thermal radiation **Thermal radiation** is [[Electromagnetic_radiation|electromagnetic radiation]] emitted by matter simply because it has a [[Temperature|temperature]] above absolute zero. Unlike [[Thermal_conduction|conduction]] and [[Convection|convection]], it needs no medium: it crosses a vacuum, which is how the [[Sun|Sun]] warms the Earth and how a spacecraft rids itself of waste [[Heat|heat]]. Its total emitted flux obeys the Stefan–Boltzmann law, J = ε·σ·T⁴, with σ = 5.67×10⁻⁸ W·m⁻²·K⁻⁴ and the [[Emissivity|emissivity]] ε between 0 and 1, and the wavelength at which it peaks obeys Wien's displacement law, λ_max = b/T with b ≈ 2,900 µm·K.[^ochsner-wien] In the microsim below the reader sets a surface's temperature T, its emissivity ε — with presets taken from Ochsner's table of natural surfaces: snow and ice about 0.99, water 0.98, vegetation 0.95 to 0.98, and soil 0.86 to 0.96, rising with water content — and the temperature of its surroundings.[^ochsner-wien] The readout is the *net* exchange, q = ε·σ·(T⁴ − T_surr⁴), which is what a thermometer or a skin actually feels, and the Wien peak of the emitted spectrum. A side panel sizes a spacecraft radiator from the same law, A = Q/(ε·σ·(T⁴ − T_space⁴)), which is the one heat-rejection problem with no other option available. The Planck curve itself is *not* drawn here: the spectrum belongs to the [[Physics]] flagship's shared C22 sim on [[Black-body_radiation|black-body radiation]], and this page places the concept and links it rather than building a second one. On the [[Energy]] flagship this article is the child of Part VII — Energy transfer, section *Radiation* (row E59), the other half of the shared C15 pair whose first half is [[Thermal_conduction|conduction]]. ## Overview Every surface above absolute zero radiates, and every surface is simultaneously irradiated by everything it can see, so radiative heat transfer is always a *balance* — and the fourth-power law makes that balance behave unlike the others. Conduction and convection are linear in the temperature difference; radiation is not, so a low absolute temperature makes a surface almost invisible radiatively while a high one makes radiation dominate everything else. At 300 K a black surface emits about 459 W/m²; at 600 K, 7,348 W/m², sixteen times more for twice the temperature (derived).[^ochsner-wien] The second structural fact is the separation of spectra. The Sun, at about 5,780 K, peaks near 0.50 µm, in the middle of the visible band; the Earth, at about 287 K, peaks near 10.1 µm, deep in the thermal infrared.[^ochsner-wien] The two distributions barely overlap, which is why the whole of planetary energy accounting can be run as "shortwave in, longwave out", and why a material can be made to behave completely differently toward the two — transparent to sunlight and opaque to room-temperature radiation, which is the [[Greenhouse_effect|greenhouse effect]] and, deliberately engineered, a low-emissivity window. ## History Radiation was the hardest of the three heat-transfer modes to fit into any theory, because it crosses empty space and because its explanation eventually required abandoning classical physics altogether. ### Caloric theory Through the eighteenth century heat was treated as a weightless, conserved fluid called caloric flowing from hot bodies into cold. The model handled conduction and [[Calorimetry|calorimetry]] well enough and radiant heat badly: a fluid crossing a vacuum, and two facing bodies each apparently sending caloric into the other, sat awkwardly with conservation. The picture collapsed when heat was identified as energy in transit, the settlement [[Rudolf_Clausius|Clausius]] completed in his 1865 paper defining [[Entropy|entropy]].[^clausius1865] ### Wave nature of radiation [[James_Clerk_Maxwell|Maxwell]]'s dynamical theory of the electromagnetic field, published in 1865, showed that a changing electric and magnetic field propagates as a wave at a speed computed from purely electrical measurements and equal, within experimental error, to the measured speed of light.[^maxwell1865] That identified light, radiant heat and what would later be called radio as one phenomenon differing only in wavelength, and made thermal radiation a branch of [[Maxwell's_equations|electromagnetism]] rather than a separate species of heat. ### Quantum theory Classical electromagnetism plus classical statistics predicted that a cavity should radiate without limit at short wavelengths. [[Max_Planck|Planck]] escaped the catastrophe in 1901 by assuming that the oscillators exchanging energy with the field could do so only in discrete quanta proportional to frequency, and the distribution he obtained — Planck's law — fits the measured spectrum at every temperature.[^planck1901] [[Albert_Einstein|Einstein]] took the quantisation to be a property of the radiation itself in 1905, explaining the [[Photoelectric_effect|photoelectric effect]], and the [[Photon|photon]] entered physics.[^einstein1905photo] Thermal radiation is thus the phenomenon that began [[Quantum_mechanics|quantum mechanics]]. ## Characteristics Four properties do most of the work in practice: where the radiation sits in the spectrum, how it scales with temperature, what it looks like, and the symmetry between emitting and absorbing. ### Frequency Thermal radiation is broadband, spanning several decades of wavelength with a single broad maximum. A [[Photon|photon]] carries energy E = h·ν = h·c/λ, with h = 6.626×10⁻³⁴ J·s, which in convenient units is E[eV] = 1.24/λ[µm].[^murphy-photon] The Sun's peak photons therefore carry about 2.5 eV and the Earth's about 0.12 eV (derived) — a factor of twenty that matters because chemical bonds and semiconductor gaps sit near the first value and not the second, so sunlight can drive [[Photosynthesis|photosynthesis]] and a [[Solar_cell|photovoltaic cell]] while terrestrial infrared cannot. ### Relationship to temperature Two laws govern the temperature dependence. The Stefan–Boltzmann law fixes the total: J = ε·σ·T⁴, so the emitted power rises steeply and any measurement of it is a sensitive thermometer. Wien's displacement law fixes the location: λ_max = 2,900/T with λ in micrometres and T in kelvin, so a surface at 555 nm peak emission is at 5,225 K (computed).[^ochsner-wien] Emissivity scales the flux but not the peak — a distinction worth keeping, because a low-ε surface is dim, not cold. ### Appearance Below about 800 K almost all the emission is infrared and a body looks black in the dark. Above that a sliver of the curve crosses into the visible and the object glows dull red, then orange, yellow and finally white as the peak slides toward mid-visible — the sequence a blacksmith reads as a temperature gauge. It follows from the shape of the Planck curve and belongs to the [[Black-body_radiation|black-body radiation]] page's sim, which draws the spectrum with a wavelength-to-colour mapping. ### Reciprocity A good emitter at a given wavelength is an equally good absorber at that wavelength: emissivity and absorptivity are equal for a surface in thermal equilibrium with its surroundings. That is why the net exchange in the sim carries a single ε and not two coefficients, and why no surface can absorb sunlight strongly while refusing to emit at the same wavelengths. It can be selective *across* wavelengths — absorbing well at 0.5 µm and poorly at 10 µm — and that loophole is the entire design space of solar-thermal absorbers and radiative coolers. ## Fundamental principles The quantities below are the working vocabulary of radiative transfer, and the sim uses three of them. ### Electromagnetic waves Thermal radiation is an electromagnetic wave field, so it travels in straight lines at the [[Speed_of_light|speed of light]], reflects, refracts and can be polarised. Geometry therefore matters in a way it does not for conduction: two surfaces exchange radiation only insofar as they can see each other, and the fraction of one surface's emission intercepted by another — the view factor — is a purely geometric quantity that must be computed before any temperature enters. ### Irradiation Irradiation is the radiant flux arriving at a surface per unit area, in W/m². For a horizontal surface outdoors it has two parts, shortwave from the [[Sun|Sun]] and longwave from the [[Atmosphere_of_Earth|atmosphere]], and the atmospheric part is computed from an effective sky emissivity that runs from about 0.5 in dry clear air to nearly 1 under thick cloud.[^ochsner-seb] Of the sunlight arriving at the top of the atmosphere only about 53 % reaches the surface, 31 % as direct beam and 22 % as diffuse sky radiation.[^ochsner-wien] ### Radiation intensity Intensity resolves the flux by direction: power per unit area per unit solid angle, integrating over a hemisphere to recover the flux. A perfectly diffuse — Lambertian — emitter has an intensity independent of direction, so its apparent brightness is the same from every angle even though the projected area falls off as the cosine. Most rough natural surfaces are close enough to Lambertian that the sim's single ε suffices; polished metals are not, and their emissivity depends strongly on angle. ### Blackbody radiation A blackbody absorbs everything that falls on it and emits the theoretical maximum at every wavelength for its temperature. Its spectrum is Planck's law, and every other law here is a consequence: integrating it over wavelength gives Stefan–Boltzmann, and differentiating it to find the maximum gives Wien.[^planck1901][^ochsner-wien] **The spectrum itself is not drawn on this page.** The Planck curve, its Wien peak and the colour it implies are the concept of the [[Physics]] flagship's shared C22 sim, which lives on [[Black-body_radiation]]; this page uses only the two integrated laws, and readers who want the curve should follow that link. ### Emission from non-black surfaces Real surfaces emit less than a blackbody, by the factor ε. Ochsner's table is the sim's preset list: sun, snow and ice about 0.99; water 0.98 to 0.99; vegetation 0.95 to 0.98; soil 0.86 to 0.96, rising with water content.[^ochsner-wien] The striking thing about that list is how narrow it is. Natural surfaces differ enormously in [[Albedo|albedo]] — fresh snow reflects up to 0.9 of the sunlight while open water reflects under 0.1 — and hardly at all in longwave emissivity, which is why snow is bright in the visible and nearly black in the infrared, and why it can lose heat freely at midday while absorbing almost nothing.[^ochsner-seb] ## Heat transfer between surfaces This is the sim's own section. A surface at temperature T facing surroundings at T_surr emits ε·σ·T⁴ and absorbs ε·σ·T_surr⁴, so the net loss is q = ε·σ·(T⁴ − T_surr⁴). Everything in the microsim follows from that one line. A wall at 300 K facing a room at 280 K loses 105 W/m² at ε = 0.95; a snowfield at 273 K under a clear sky whose effective radiating temperature is 240 K loses 126 W/m² at ε = 0.99 (derived).[^ochsner-wien] Those are large numbers next to the other terms in an outdoor energy balance, where the measured net radiation over an Iowa field ran from about −50 W/m² at night to +300 W/m² near noon, and the sensible heat flux peaked near 200 W/m².[^ochsner-seb] Two behaviours are worth watching as the sliders move. First, the net flux is not proportional to ΔT even though it vanishes with it: for small differences the law linearises to q ≈ 4·ε·σ·T³·ΔT, so radiation behaves like a heat-transfer coefficient h_r = 4·ε·σ·T³ — about 5.8 W/(m²·K) at 300 K (derived) — which is the same order as still-air natural [[Convection|convection]], and the reason indoor comfort depends on wall temperatures and not only on air temperature. Second, the surroundings' temperature matters as much as the surface's, because both enter to the fourth power. That is the fact the sim's spacecraft panel exploits: with T_space effectively zero, a radiator at 300 K rejecting 1 kW at ε = 0.9 needs 2.4 m², but the same radiator at 250 K needs 5.0 m² (derived). Every 50 K given away doubles the hardware, which is why spacecraft thermal design fights to reject heat hot. ## Applications Because radiation is the only mode that works across a vacuum and the only one that scales as T⁴, it dominates at both the largest and the hottest scales. ### Solar energy All [[Solar_thermal_energy|solar energy]] is thermal radiation that has crossed 1.5×10¹¹ m of vacuum. Taking the Sun as a 5,780 K emitter with ε = 0.990 gives a surface flux of 6.27×10⁷ W/m², a total output of 3.81×10²⁶ W over a radius of 6.96×10⁸ m, and 1,349 W/m² at the Earth's orbit — within a percent of the measured [[Solar_irradiance|solar constant]] (computed).[^ochsner-wien] About 44 % of that arrives as visible light and about 7 % as ultraviolet, of which UVC is wholly absorbed by the atmosphere, UVB mostly, and UVA largely passes.[^patrich-uv] Concentrating that flux for a heat engine is limited by the fact that only the direct beam can be focused: Kerlin's chain gives a net efficiency of roughly 0.51 × 0.30 ≈ 0.15 for a solar-thermal plant.[^kerlin-solar] ### Windows A window is a spectrally selective radiative device. Ordinary [[Glass|glass]] transmits the solar shortwave and is nearly opaque to the 10 µm band the room radiates, so it lets sunlight in and traps the re-emission — the same separation of spectra described above. A low-emissivity coating pushes the trick further by reflecting longwave while still passing visible light, cutting the radiative loss from the warm inner pane to the cold outer one without darkening the room. That loss is a large share of a window's total, so the coating is often worth more than an extra gas fill. ### Spacecraft A spacecraft cannot conduct or convect its waste heat anywhere, so every watt it generates must leave as radiation. Sizing follows directly from the sim's relation, A = Q/(ε·σ·(T⁴ − T_space⁴)), with T_space ≈ 0, and the design levers are the radiator temperature, the area and the emissivity. The same arithmetic governs any thermal machine operating in vacuum — a lunar or asteroid processing plant must carry a radiator sized by this equation, and it is usually the largest single structure on the vehicle.[^ochsner-wien] ## Health and safety Thermal radiation is both how a human body sheds a large share of its heat and, at high intensity, a way to be injured without touching anything. ### Metabolic temperature regulation A resting adult dissipates roughly 100 W — the same figure a 2,000 kcal daily diet implies, 96.85 W spread over 86,400 s — and a substantial fraction of it leaves as longwave radiation from skin and clothing to the surrounding surfaces.[^murphy-photon] Because skin emissivity is near that of water, close to 0.98, the exchange is essentially blackbody, and the relevant environmental variable is the mean temperature of the surfaces in view rather than the air temperature, which is why a cold window makes a warm room feel chilly and why sitting by a fire warms the side facing it. ### Burns At high flux the damage is thermal and rapid. A few kW/m² is painful within seconds, and a large fire or a solar concentrator delivers tens to hundreds of kW/m². The protection is geometric as much as material: because radiation travels in straight lines, a shield that blocks the view blocks the transfer, and a reflective, low-emissivity outer layer both turns away the incoming flux and, being a poor emitter, re-radiates little of what it absorbs to the wearer. ## Near-field radiative heat transfer Everything above assumes the gap between surfaces is much larger than the dominant wavelength — around 10 µm for room-temperature objects. Below that, the assumption fails. Evanescent fields that decay within a wavelength of a surface, and so carry no energy across a large gap, tunnel across a small one, and the heat flux can exceed the blackbody limit by orders of magnitude. The effect is measurable at separations of tens of nanometres and is under investigation for thermophotovoltaic conversion and for heat-assisted magnetic recording, where a [[Nanostructure|nanostructured]] tip must heat a spot far smaller than a wavelength. Nothing here violates the Stefan–Boltzmann law, which is a statement about the far field only. ## See also - [[Black-body_radiation]] - [[Stefan–Boltzmann_law]] - [[Emissivity]] - [[Greenhouse_effect]] - [[Heat_transfer]] - [[Thermal_conduction]] - [[Convection]] - [[Earth's_energy_budget]] ## References [^ochsner-wien]: Ochsner, Tyson (2019). *Rain or Shine*. Chapter 12, "Surface Energy Balance and Evapotranspiration", pp. 275–296: Wien's law as Eq. 12-1, λ_max = b/T with b = 2,900 µm·K (p. 278); the Stefan–Boltzmann law as Eq. 12-2, J = ε·σ·T⁴ with σ = 5.67×10⁻⁸ W·m⁻²·K⁻⁴, the Sun at ≈5,780 K peaking near 0.5 µm and the Earth at ≈287 K near 10 µm, and the emissivity table — Sun, snow and ice ≈0.99, water 0.98–0.99, vegetation 0.95–0.98, soil 0.86–0.96 rising with water content (p. 279); and the surface partition of top-of-atmosphere sunlight, ≈53 % reaching the ground as 31 % direct and 22 % diffuse (p. 280). The book's equation displays were lost in extraction and the standard forms are supplied. Values computed from them and labelled on this page: 2,900/5,780 = 0.502 µm and 2,900/287 = 10.1 µm; σT⁴ = 459 W/m² at 300 K and 7,348 W/m² at 600 K; 5,225 K for a 555 nm peak; the Sun's 6.27×10⁷ W/m², 3.81×10²⁶ W and 1,349 W/m² at 1.50×10¹¹ m (the book's Problem set at p. 283 is unworked); the 105 W/m² wall and 126 W/m² snowfield net exchanges; h_r = 4·ε·σ·T³ = 5.8 W/(m²·K) at 300 K; and the 2.4 m² and 5.0 m² spacecraft radiators. Portal Book 119, https://open.umn.edu/opentextbooks/textbooks/rain-or-shine [^ochsner-seb]: Ochsner (2019), *Rain or Shine*, Chapter 12: net radiation as Eq. 12-3, R_n = (1 − α)·R_s + R_li − R_lo, positive toward the surface (p. 292); the surface balance R_n = LE + H + G (p. 293); albedo values — fresh snow up to ≈0.9, water below 0.1, soils and vegetation 0.1–0.4 (p. 290); atmospheric emissivity from 0.5 to nearly 1, rising with cloud and water vapour (pp. 291–292); and the measured Iowa diurnal cycle over corn residue, R_n from about −50 W/m² at night to +300 W/m² near noon with H peaking near +200 W/m² (p. 295). Portal Book 119. [^murphy-photon]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Chapter 5, "Energy and Fossil Fuels", p. 99 (photon energy E = h·ν = h·c/λ as Eq. 5.4 with h = 6.626×10⁻³⁴ J·s, and E[eV] = 1.24/λ[µm] as Eq. 5.5; visible light at 0.4–0.7 µm carrying 3.1–1.8 eV), p. 98 (1 eV = 1.6×10⁻¹⁹ J) and pp. 94–95 (a 2,000 kcal/day diet as 96.85 W, which the book cautions should not be quoted to four figures). The ≈2.5 eV and ≈0.12 eV peak photon energies for the Sun and the Earth are derived. Portal Book 097, https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^patrich-uv]: Patrich, Jeremy (2020). *Physical Geography, Version 1*, pp. 69 and 71 (about 44 % of sunlight is visible and ≈7 % ultraviolet; UVC is fully blocked by the atmosphere, UVB mostly, and UVA largely passes) and p. 72 (greenhouse-gas comparisons). Portal Book 125, https://open.umn.edu/opentextbooks/textbooks/physical-geography [^kerlin-solar]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, p. 185 — only the unscattered direct beam can be focused, so a solar thermal-electric chain has a net efficiency η_net = f_unscattered × η_thermo ≈ 0.51 × 0.30 ≈ 0.15; the same page gives the land area per quad that follows from it. Portal Book 048, https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^clausius1865]: Clausius, R. (1865). "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie." *Annalen der Physik und Chemie* 125 (7): 353–400. [^maxwell1865]: Maxwell, J. C. (1865). "A Dynamical Theory of the Electromagnetic Field." *Philosophical Transactions of the Royal Society of London* 155: 459–512. [^planck1901]: Planck, M. (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum." *Annalen der Physik* 309 (3): 553–563. https://doi.org/10.1002/andp.19013090310 [^einstein1905photo]: Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." *Annalen der Physik* 322 (6): 132–148. ## Further reading - Ochsner, *Rain or Shine* (2019), Chapter 12 "Surface Energy Balance and Evapotranspiration", pp. 275–296 — Wien, Stefan–Boltzmann, the emissivity and albedo tables and a measured diurnal energy balance. Portal Book 119. - Murphy, *Energy and Human Ambitions on a Finite Planet* (2021), Chapter 5, pp. 87–182 — photon energies and the unit ladder that turns fluxes into human-scale quantities. Portal Book 097. - Kerlin, *Future Energy: Opportunities & Challenges* (2013), pp. 169–191 — solar collectors, concentration and the direct-beam limit. Portal Book 048. - Patrich, *Physical Geography, Version 1* (2020), pp. 68–77 — the solar spectrum at the surface, the ultraviolet bands and the seasons. Portal Book 125. - Yan, *Introduction to Engineering Thermodynamics* (2022), Chapter 6 "Entropy and the Second Law of Thermodynamics", pp. 239–348 — where radiative exchange sits in the second-law accounting. Portal Book 115. ## External links - [Rain or Shine](https://open.umn.edu/opentextbooks/textbooks/rain-or-shine), Tyson Ochsner, open textbook (Portal Book 119) - [Energy and Human Ambitions on a Finite Planet](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet), Thomas Murphy, open textbook (Portal Book 097) - The Wikipedia pair's external links list further open resources <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Thermal_radiation.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Thermal radiation* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Thermal_radiation.html" data-title="Thermal radiation"></div> *Built from `MICROSIM_GUIDE/specs/sims/Thermal_radiation.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Thermal_radiation) : [Wikitube](https://en.wikitube.io/wiki/Thermal_radiation) · pinned revision [1371293319](https://en.wikipedia.org/w/index.php?oldid=1371293319) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E59 · sim pending (matter/Thermal_radiation).*