Concept

Stefan boltzmann law — where it appears

The total power a black body radiates per unit area, σT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. The fourth power makes radiation dominate at high temperatures and fade at low ones, and fixes the net exchange between two surfaces at different temperatures.

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

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

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

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.

Emissivity Absorption Albedo Atmosphere Blackbody Convection Energy balance Kirchhoffs law Lapse rate Multilayer insulation Planck law Radiation shield

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