شرح قوانين thermodynamic

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Zeroth Law of Thermodynamics

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

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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

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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.

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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).

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وسنكمل ان شاء الله

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[احمد زايد]

جزاك الله كل خير

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Planck Occupancy


In terms of frequency,

(1)

and in terms of wavelength

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Planck Postulate



Planck postulated that the energy of oscillators in a blackbody is quantized by

(1)

where n = 1, 2, 3, ..., h is Planck's constant, and 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

(2)

In the other hand, the energy of state n of quantum mechanical simple harmonic oscillator is actually given by the slightly modified form

(3)

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Radiation Constant



The constant related to the total energy radiated by a blackbody (i.e., the Stefan-Boltzmann law), and defined as

where is the Stefan-Boltzmann constant, c is the speed of light, k is Boltzmann's constant, and h is Planck's constant. Numerically,

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Radiometer Equation

where is the root-mean-square noise, is a factor , B is the bandwidth, and is the integration time.

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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 allows the approximation

(1)

Plugging this into the Planck law gives

(2)

[mohamed*]

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