Illustrated Physics
physics, drawn
Concept

Emissivity — where it appears

How well a surface radiates compared with a perfect blackbody at the same temperature, between zero and one and generally different at every wavelength. Kirchhoff's law forces it to equal the absorptivity at each wavelength, which is why a surface can absorb sunlight well and radiate infrared badly and run hot.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

What a thermal camera reads off a shiny surface. The temperature a camera calibrated for a black body reports, against the emissivity of the surface it is pointed at, for surfaces truly at 323 K, 373 K, 473 K in a room at 293 K. Every curve begins at the true temperature when the emissivity is one and ends at the room's temperature when it is zero, because a surface that emits nothing reflects everything and the camera is then looking at the room. polished aluminium at 0.05 reads 312 K; stainless steel, oxidised at 0.8 reads 451 K; matt black paint at 0.95 reads 468 K; human skin at 0.98 reads 471 K for a surface truly at 473 K. That is not a fault in the instrument. It follows from Kirchhoff's law — a poor emitter is a poor absorber and therefore a good reflector — so the shortfall in a shiny surface's own glow is made up almost exactly by whatever is reflected in it, and no measurement of the light leaving a surface can separate the two without knowing the emissivity in advance.

The glow that says nothing about the surface

A thermal camera pointed at a saucepan of boiling water reads a hundred degrees. Pointed at a polished aluminium block at the same temperature it reads about twenty-five, and the instrument is working perfectly. What it is measuring is emissivity as much as temperature — and a surface's emissivity is forced to equal its absorptivity, at every wavelength and every angle, by an argument with no physics of matter in it at all.

thermodynamics · Blackbody The temperature a planet ought to be. Each body's measured surface temperature against the temperature at which it would radiate away exactly the sunlight it absorbs — computed from two numbers, the sunlight reaching it and the fraction it reflects, with no other property of the body used. Points on the diagonal are bodies the one-line argument gets right. the Moon: balance 270 K, surface 250 K, −20 K with no atmosphere; Mercury: balance 433 K, surface 340 K, −93 K with no atmosphere; Mars: balance 210 K, surface 210 K, +0 K; Earth: balance 255 K, surface 288 K, +33 K; Venus: balance 227 K, surface 737 K, +510 K. The airless bodies fall below the line rather than on it, and the reason is the fourth power: a surface running from noon heat to night cold radiates like its hottest parts and averages like its coldest, so a mean thermometer reading is lower than the temperature that matches the emitted flux. Mars, whose atmosphere is thin and whose surface is nearly isothermal by comparison, sits on the line. Everything with a substantial atmosphere sits above it, by tens of kelvin on Earth and hundreds on Venus, and always in the same direction. Nothing here explains why. What the figure fixes is the size and the sign of what has to be explained.

The height a planet is seen from

A body in sunlight settles where it radiates away what it absorbs, and that takes two numbers and one line of arithmetic. It gets the Moon right and Earth wrong by thirty-three kelvin. The correction is not that the atmosphere traps heat but that it moves the level space sees the planet from, and the rest is done by a lapse rate that is not a radiative quantity at all.

thermodynamics · Blackbody The heat two surfaces exchange when they almost touch. The radiative heat-transfer coefficient between two parallel half-spaces at 300 K, in W/m²K on a logarithmic axis, against the width of the vacuum gap between them, also logarithmic, from fluctuational electrodynamics: silicon carbide (solid) and gold (dashed), with two perfect black bodies, 4σT³ = 6.12 W/m²K, for comparison (dotted). Far apart, silicon carbide exchanges 3.3 W/m²K — less than black — and gold, a good mirror, only 0.024. Closer than the thermal wavelength, about 17 µm, waves that cannot leave either surface begin to tunnel across the gap. At 100 nm silicon carbide exchanges 137 W/m²K, at 10 nm 9338, at 1 nm 9.3·10⁵ — rising as the inverse square of the gap, 1.5·10⁵ times the black-body value at 1 nm. Gold exceeds black only below a few hundred nanometres and then grows much more slowly: 1284 at 10 nm, 2561 at 1 nm.

The heat that crosses a gap too narrow for light

Stefan and Boltzmann's law is usually read as a ceiling: no surface can radiate more heat than a perfect black body at the same temperature, 6.1 watts per square metre for every degree of difference at room temperature. It is a ceiling only for surfaces that are far apart. Bring two of them closer than the wavelength of their thermal glow and they begin to exchange waves that never leave either surface — waves that cling to it and die away within a wavelength — and those waves tunnel across the gap. Two plates of silicon carbide ten nanometres apart exchange fifteen hundred times what two black bodies can, almost all of it in a single colour, and the colour is the one in which silicon carbide is too shiny to glow at all.

quantum · Blackbody How far below the air a surface facing the sky falls. How much colder than the air a surface facing the night sky becomes, when insulated from below and with air at 5 °C, against how strongly the air can warm it, measured by the convection coefficient (3 to 5 W/m²K in still air, 20 or more in a breeze), for sky emissivities of 0.72, 0.82, 0.97 — clear and dry, clear and humid, and overcast. Under a clear dry sky in still air the surface sits 12.3 °C below the air; a breeze of 20 W/m²K halves that and more; under cloud the drop is 1.3 °C. The surface is radiating to something colder than the air: the upper atmosphere and, through the window near ten micrometres, space.

The cold reservoir overhead

On a clear, still night a car roof can grow frost while the air around it is several degrees above freezing. Nothing in the air is cold enough to freeze water. The roof is radiating its heat upward to a sky whose radiation back is that of something twenty degrees colder than the air — part of it the cold upper atmosphere, part of it space itself, seen through a window in the infrared where the air is transparent. The clear sky is a cold reservoir available everywhere, and it can be used: to make frost, to cool buildings below the air temperature even in sunshine, and in principle to run an engine at night.

thermodynamics · Heat engines Each foil divides the heat by one more. The radiant heat flowing from a wall at 293 K to one at 77 K — room temperature to liquid nitrogen — in watts per square metre on a logarithmic axis, against the number of thin shields placed between them, for walls and shields all black-painted, dull metal and aluminised film. With nothing between them, black walls exchange 340 W/m²; aluminised walls 6.3. Each shield adds one more equal resistance in series, so N shields divide the flux by N + 1: thirty aluminised foils bring it to 204 milliwatts per square metre. Between black walls a single aluminised foil passes 6.2 W/m², less than thirty black shields do, 11.0 W/m², because a shield's resistance is 2/ε − 1 and a shiny one is worth 54 black.

The thin foils that stop radiant heat

In a vacuum, heat can cross a gap only as radiation, and a single sheet of foil a few hundredths of a millimetre thick, hung in the gap and touching nothing, halves it. Two sheets cut it to a third, thirty to a thirty-first. The foil does not need to be thick or cold or clever; it needs only to be shiny, because a sheet that absorbs little also emits little, and each one becomes a radiator in its own right, floating at a temperature between its neighbours. The golden blankets on spacecraft and the silvering inside a vacuum flask are the same arithmetic of resistances in series.

thermodynamics · Blackbody

Named alongside it

The objects these essays reach for when they reach for this one.

BlackbodyAbsorptionStefan boltzmannStefan boltzmann lawThermal radiationAlbedoAtmosphereAtmospheric windowCarnot efficiencyCavityConvectionDetailed balance

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