Illustrated Physics
physics, drawn
Concept

Planck law — where it appears

The formula for the spectrum of radiation in thermal equilibrium at a given temperature, derived by counting light's energy in quanta. It fixes the brightness at every wavelength, so a measured brightness at one wavelength can be turned into a temperature.

Named by 2 essays across 2 fields — 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 wavelength sees from a different height. The weighting functions of 7 infrared channels in a carbon-dioxide band — how much each height contributes to the radiance a satellite measures in that channel — for absorption strengths chosen so that the peaks sit at 3, 8, 14, 20, 27, 35, 43 km. Each is scaled to its own maximum. A channel's peak is where the carbon dioxide above that height amounts to one optical depth: deeper, its emission is absorbed on the way out; higher, there is too little gas to emit. Each function is about 17 km wide at half its peak, the same for every channel, because the absorber's density falls with one scale height, 7 km. The dotted curve is the temperature profile of the standard atmosphere, on its own scale from 180 to 300 K, whose cold tropopause and warm stratosphere the channels between them straddle.

The spectrum that is a thermometer at every height

A satellite looking down at the Earth in the infrared sees, at each wavelength, the glow of whatever layer of air that wavelength escapes from. In the wings of carbon dioxide's great absorption band the air is transparent and the satellite sees the ground; towards the band's centre the gas grows opaque and each wavelength escapes from higher up. A single spectrum is therefore a stack of thermometers at different heights, and weather forecasts are built on reading it. What cannot be read from it is anything much thinner than the ten to twenty kilometres of air each of those thermometers averages over.

quantum · Blackbody

Named alongside it

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

Lapse rateAbsorptionAlbedoAtmosphereBlackbodyBlackbody radiationBrightness temperatureConvectionEmissivityEnergy balanceInverse problemOptical depth

All concepts