شرح قوانين thermodynamic

[عاطف خليفة]

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

Plack Energ




The Planck energy is the average energy of an oscillator,

(1)

The Planck postulate states that

(2)

where n is a nonnegative integer, h is Planck's constant, and is the frequency of radiation. Maxwell-Boltzmann statistics give

(3)

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

(4)

Planck Intensity Density


In terms of frequency, the energy flux from blackbody radiation is given by

(1)

where is the average energy density, 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,

(2)

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

(3)

so

(4)

and

(5)

where is an element of solid angle. Plugging in,

Planck Law


Planck Law

The Planck law gives the intensity radiated by a blackbody as a function of frequency (or wavelength). Let a blackbody have temperature T. Let be the energy density per unit solid angle so that

(1)

then the blackbody radiates at a frequency with spectral energy density

(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).