Planck's Law

Planck's Law

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T when there is no net flow of matter or energy between the body and the environment.

In the late 19th century, physicists could not explain why the observed spectrum of black body radiation, then accurately measured at that time, declined dramatically at higher frequencies. then the existing theories expected. In 1900, Max Planck formally found a formula for the observed spectrum by assuming that a speculative oscillator with electricity in a cavity containing black body radiation could only change its energy in a small increase, E, which was proportional to the frequency of its associated electromagnetic wave. This solved the problem of the expected ultraviolet crash of classical physics. This discovery was an advanced view of modern physics and is of great importance for quantum theory.

The law:

All bodily bodies emit electromagnetic radiation and body spectral radiance, B, accounting for the spectral emissive power per unit area, each solid angle unit for specific radiation frequencies. The relationship provided by Planck's law of radiation, given below, shows that with increasing temperature, the total radiation energy of the body increases, and the peak of the spectrum is released moving into shorter waves. According to this, body spectrum radiance for frequency ν at total temperature T.,

where kolt is Boltzmann's constant, h is Planck's constant, and c is the speed of light in the center, whether it is material or vacuum. Spectrum radiance can also be expressed for each unit wavelength λ instead of the frequency per unit. By selecting an appropriate system of units of measurement.

Equalizes the spectral radiance in each unit of waves relative to the frequency per unit where the second essential part binds in because forward integration in frequency space interweaves back in place of a waveform. (Wavelength increases as frequency decreases so Since this equation holds for any limits

shows how the energy of radiation emitted at shorter waves increases more rapidly with temperature than the energy emitted at longer waves. The energy density is a measure of radiation. The SI units of Bν are W • sr - 1 • m - 2 • Hz - 1, and W • sr - 1 • m − 3. I am in the limits of Bλ (ie long waves), Planck's law subject to Rayleigh-Jeans law, although at high frequency (ie small waves) it is subject to Wien speculation.

Max Planck developed the law in 1900 with only empirically proven positions and later showed that expressed as energy circulation, it is the specific stable emission for radiation in thermodynamic equilibrium.  As an energy circuit, it is one of a family of thermal equilibrium distributions that include the Bose-Einstein cycle, the Fermi - Dirac rotation, and the Maxwell - Boltzmann rotation.

Black body radiation:

A black body is a very suitable object that absorbs and emits all frequencies of radiation. It is dependent on temperature, Planck radiation is said to be thermal radiation, hence the higher the body temperature, the more radiation it emits at each wave.

Planck radiation has the greatest intensity at a wave that is dependent on body temperature. For example, at room temperature (300300 K), the body emits thermal radiation that is mostly infrared and invisible. At higher temperatures, the number of infrared radiation increases and can be felt as heat, and more visible radiation is released so that the body shines red. At higher temperatures, the body is light yellow or blue-white and emits large amounts of short-wave radiation, including ultraviolet and even x-rays. The surface of the sun (~ 6000 K) emits large amounts of infrared and ultraviolet radiation; its emissions are high in the visible spectrum. This movement is called the law of movement of Vienna due to temperature.

 The movement of radiation across an interface between media can be characterized by the emissivity of the interface (the ratio of true radiance to Planck's theoretical radiance), usually denoted by the symbol ε.  Natural interface isolation is always between ε = 0 and 1.

A body is said to be a black body that interacts with another medium that contains both ε = 1 and contains all the radiation events on it. The surface of a black body can be modeled by a small hole in a large circulating wall maintained at equal temperatures by opaque walls that, at all waves, do not reflect perfectly. In equilibrium, the radiation inside this fort is defined by Planck's law, as the radiation leaves the small hole.

Just as the Maxwell - Boltzmann rotation is the maximum entropy energy circulation for gas of material grains at thermal equilibrium, so is the Planck rotation for gas of photons. Compared to a material gas where the mass and number of grains play a role, the spectral radiance, weight, and energy density of a photon gas at thermal equilibrium are completely determined by temperature.

If the Planckian photon gas is not present, the second law of thermodynamics guarantees that interactions (between photons and other particles or even, at a sufficiently high temperature, between the photons themselves) cause the photon energy circulation to change. and comes to Planck circulation. In such an approach to thermodynamic equilibrium, photons are formed or ejected in the right numbers and with the right energies to fill the cavity with Planck rotation until they reach the equilibrium temperature. . It is as if the gas is a mixture of sub-gases, one for each band of waves, and eventually each sub-gas reaches the common temperature.

The measure Bν (ν, T) is the spectral radiance as an action of temperature and frequency. The SI system contains units W • m - 2 • sr - 1 • Hz - 1. The magnitude of infinite power Bν (ν, T) cos θ dA dΩ dν is radiated in the direction defined by the angle θ from the normal surface from the infinite surface area dA into a solid angle or -finite dΩ in an infinite frequency band of width dν based on frequency ν. The total power is radiated to any solid angle as an integral part of Bν (ν, T) over these three dimensions, and is provided by the law of Stefan - Boltzmann. The black body is said to be a Lambertian radiator.

Different forms:

Forms on the left are usually found in experimental fields and are usually found on the right in theoretical fields.

Correspondence between spectral variable forms:

Different spectrum variables require different modes of expression compatible with the law. In general, one may not switch between the different forms of Planck's law simply by substituting one variable for another, as this would not imply that the different forms have different units. Waves and frequency units are congruent.

The corresponding sensory modalities are related to the fact that they express one physical reality: for a specific physical increase of a spectrum, a specific physical energy increase is corresponding to its radiation.

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