Zeroth Law of Thermodynamicshttp://scienceworld.wolfram.com/imag...b_topright.gif

If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other.

Blackbody

A hypothetic body that completely absorbs all wavelengths of thermal radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation with the same spectrum, as required by arguments of classical physics involving thermal equilibrium. However, the distribution of blackbody radiation as a function of wavelength, known as the Planck law, cannot be predicted using classical physics. This fact was the first motivating force behind the development of quantum mechanics

Blackbody Radiation

The thermal radiation emitted by a blackbody heated to a given temperature. All blackbodies heated to a given temperature emit thermal radiation with the same spectrum, known as the Planck law.

Blackbody Temperature
The effective temperature at which a blackbody emits blackbody radiation.

Plack Energ

http://scienceworld.wolfram.com/imag...b_topright.gif


The Planck energy is the average energy of an oscillator,

http://scienceworld.wolfram.com/physics/pimg239.gif(1)

The Planck postulate states that

http://scienceworld.wolfram.com/physics/pimg240.gif(2)

where n is a nonnegative integer, h is Planck's constant, and http://scienceworld.wolfram.com/physics/pimg224.gif is the frequency of radiation. Maxwell-Boltzmann statistics give

http://scienceworld.wolfram.com/physics/pimg241.gif(3)

where C is a constant, k is Boltzmann's constant, and T is the temperature. Plugging in,

http://scienceworld.wolfram.com/physics/pimg242.gif(4)

Planck Intensity Densityhttp://scienceworld.wolfram.com/imag...b_topright.gif
http://scienceworld.wolfram.com/imag...dient-teal.gif

In terms of frequency, the energy flux from blackbody radiation is given by
where http://scienceworld.wolfram.com/physics/pimg247.gif is the average energy density, http://scienceworld.wolfram.com/physics/pimg248.gif is Planck energy, N is the number density of oscillators, h is Planck's constant, k is Boltzmann's constant, and T is the temperature. Here,
is the number of cells per unit phase space. The factor of 2 must be added since two electrons with opposite spins may occupy the same element of phase space. The momentum of a photon is given by
so
and
where http://scienceworld.wolfram.com/physics/pimg206.gif is an element of solid angle. Plugging in,
Planck Law


Planck Lawhttp://scienceworld.wolfram.com/imag...b_topright.gif
http://scienceworld.wolfram.com/imag...dient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif

http://scienceworld.wolfram.com/physics/pimg255.gif

The Planck law gives the intensity radiated by a blackbody as a function of frequency (or wavelength). Let a blackbody have temperature T. Let http://scienceworld.wolfram.com/physics/pimg256.gif be the energy density per unit solid angle so that

http://scienceworld.wolfram.com/physics/pimg257.gif(1)

then the blackbody radiates at a frequency http://scienceworld.wolfram.com/physics/pimg224.gif with spectral energy density

http://scienceworld.wolfram.com/physics/pimg258.gif(2)

where h is Planck's constant, c is the speed of light, and k is Boltzmann's constant (Rybicki and Lightman 1979, p. 21).

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Planck Occupancy


In terms of frequency,
and in terms of wavelength

Planck Postulate



Planck http://scienceworld.wolfram.com/imag.../biography.gif postulated that the energy of oscillators in a blackbody is quantized by
where n = 1, 2, 3, ..., h is Planck's constant, and http://scienceworld.wolfram.com/physics/pimg224.gif is the frequency, and used this postulate in his derivation of the Planck law of blackbody radiation. In fact, electromagnetic radiation is itself quantized, coming in packets known as photons and having energy In the other hand, the energy of state n of quantum mechanical simple harmonic oscillator is actually given by the slightly modified form

Radiation Constanthttp://scienceworld.wolfram.com/imag...b_topright.gif



The constant related to the total energy radiated by a blackbody (i.e., the Stefan-Boltzmann law), and defined as
where http://scienceworld.wolfram.com/physics/rimg28.gif is the Stefan-Boltzmann constant, c is the speed of light, k is Boltzmann's constant, and h is Planck's constant. Numerically,

Radiometer Equationhttp://scienceworld.wolfram.com/imag...b_topright.gif





where http://scienceworld.wolfram.com/physics/rimg110.gif is the root-mean-square noise, http://scienceworld.wolfram.com/physics/rimg111.gif is a factor http://scienceworld.wolfram.com/physics/rimg112.gif, B is the bandwidth, and http://scienceworld.wolfram.com/physics/rimg91.gif is the integration time.

Rayleigh-Jeans Law




A classical law approximately describing the intensity of radiation emitted by a blackbody, derived by Rayleigh and Jeans by counting the number of standing wave modes in an enclosure. It corresponds to the Planck law in the case of small frequencies, in which case http://scienceworld.wolfram.com/physics/rimg142.gif allows the approximation
Plugging this into the Planck law gives

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