Black-body radiation

The term black body was introduced by Gustav Kirchhoff in 1860. Black-body

radiation is also called thermal radiation, cavity radiation, complete

radiation or temperature radiation.

Black-body radiation is the thermal electromagnetic radiation within or

surrounding a body in thermodynamic equilibrium with its environment, emitted

by a black body (an idealized opaque, non-reflective body). It has a specific

spectrum of wavelengths, inversely related to intensity that depends only on the

body's temperature, which is assumed for the sake of calculations and theory to be

uniform and constant.

The thermal radiation spontaneously emitted by many ordinary objects can be

approximated as black-body radiation. A perfectly insulated enclosure that is in

thermal equilibrium internally contains black-body radiation and will emit it

through a hole made in its wall, provided the hole is small enough to have

negligible effect upon the equilibrium.

A black body at room temperature appears black, as most of the energy it radiates

is in the infrared spectrum and cannot be observed by the human eye. Since the

human eye cannot identify light waves below the visible frequency, a black body,

viewed in the dark at the lowest just slightly visible temperature, subjectively
appears grey, even though its objective physical spectrum peak is in the infrared

range. When it becomes a little hotter, it appears dull red. As its temperature

increases further it becomes yellow, white, and ultimately blue-white.

Although planets and stars are neither in thermal equilibrium with their

surroundings nor perfect black bodies, black-body radiation is used as a first

approximation for the energy they emit. Black holes are near-perfect black bodies,

in the sense that they absorb all the radiation that falls on them. It has been

proposed that they emit black-body radiation (called Hawking radiation), with a

temperature that depends on the mass of the black hole.

Black-body radiation has a characteristic, continuous frequency spectrum that

depends only on the body's temperature, called the Planck. The spectrum is peaked

at a characteristic frequency that shifts to higher frequencies with increasing

temperature, and at room temperature most of the emission is in the infrared region

of the electromagnetic spectrum. As the temperature increases past about 500

degrees Celsius, black bodies start to emit significant amounts of visible light.

Viewed in the dark by the human eye, the first faint glow appears as a "ghostly"

grey (the visible light is actually red, but low intensity light activates only the eye's

grey-level sensors). With rising temperature, the glow becomes visible even when

there is some background surrounding light: first as a dull red, then yellow, and

eventually a "dazzling bluish-white" as the temperature rises. When the body

radiation. The Sun, with an effective temperature of approximately 5800 K, is an

approximate black body with an emission spectrum peaked in the central, yellow-

green part of the visible spectrum, but with significant power in the ultraviolet as

well. Black-body radiation provides understanding into the thermodynamic

equilibrium state of cavity radiation.

An object that absorbs all radiation falling on it, at all wavelengths, is called a

black body. When a black body is at a uniform temperature, its emission has a

characteristic frequency distribution that depends on the temperature. Its emission

is called black-body radiation.

A black body radiates energy at all frequencies, but its intensity rapidly tends to

zero at high frequencies (short wavelengths). For example, a black body at room

temperature (300 K) with one square meter of surface area will emit a photon in

the visible range (390–750 nm) at an average rate of one photon every 41 seconds,

meaning that for most practical purposes, such a black body does not emit in the

visible range.

The black-body law may be used to estimate the temperature of a planet orbiting

the Sun.

The temperature of a planet depends on several factors:

 Incident radiation from its star

 The albedo effect causing a fraction of light to be reflected by the planet

 The greenhouse effect for planets with an atmosphere

 Energy generated internally by a planet itself due to radioactive decay, tidal

heating, and adiabatic contraction due by cooling.

Planck's law of black-body radiation

( )

Bν(T) is the spectral radiance (the power per unit solid angle and per unit of

area normal to the propagation) density of frequency ν radiation per

unit frequency at thermal equilibrium at temperature T.

h is the Planck constant;

c is the speed of light in a vacuum;

k is the Boltzmann constant;

ν is the frequency of the electromagnetic radiation;

T is the absolute temperature of the body.

Wien's displacement law shows how the spectrum of black-body radiation at any

temperature is related to the spectrum at any other temperature. If we know the

shape of the spectrum at one temperature, we can calculate the shape at any other

temperature. Spectral intensity can be expressed as a function of wavelength or of

frequency.

A consequence of Wien's displacement law is that the wavelength at which the

intensity per unit wavelength of the radiation produced by a black body has a local

maximum or peak, , is a function only of the temperature:

where, the constant b, known as Wien's displacement constant, is equal

to 2.897771955×10−3 m K. At a typical room temperature of 293 K (20 °C), the

maximum intensity is at 9.9 μm.