|
Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. The law is named after Max Planck, who originally proposed it in 1900. It is a pioneering result of modern physics and quantum theory. The spectral radiance of a body, , describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body at absolute temperature is given by : where the Boltzmann constant, the Planck constant, and the speed of light in the medium, whether material or vacuum. The spectral radiance can also be measured per unit wavelength instead of per unit frequency. In this case, it is given by :. The law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of are , while those of are . In the limit of low frequencies (i.e. long wavelengths), Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies (i.e. small wavelengths) it tends to the Wien approximation. Max Planck developed the law in 1900, originally with only empirically determined constants, and later showed that, expressed as an energy distribution, it is the unique stable distribution for radiation in thermodynamic equilibrium. As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose–Einstein distribution, the Fermi–Dirac distribution and the Maxwell–Boltzmann distribution. ==Introduction== Every physical body spontaneously and continuously emits electromagnetic radiation. Near thermodynamic equilibrium, the emitted radiation is nearly described by Planck's law. Because of its dependence on temperature, Planck radiation is said to be thermal radiation. The higher the temperature of a body the more radiation it emits at every wavelength. Planck radiation has a maximum intensity at a specific wavelength that depends on the temperature. For example, at room temperature (~), a body emits thermal radiation that is mostly infrared and invisible. At higher temperatures the amount of infrared radiation increases and can be felt as heat, and the body glows visibly red. At even higher temperatures, a body is dazzlingly bright yellow or blue-white and emits significant amounts of short wavelength radiation, including ultraviolet and even x-rays. The surface of the sun (~) emits large amounts of both infrared and ultraviolet radiation; its emission is peaked in the visible spectrum. Planck radiation is the greatest amount of radiation that any body at thermal equilibrium can emit from its surface, whatever its chemical composition or surface structure. The passage of radiation across an interface between media can be characterized by the emissivity of the interface (the ratio of the actual radiance to the theoretical Planck radiance), usually denoted by the symbol . It is in general dependent on chemical composition and physical structure, on temperature, on the wavelength, on the angle of passage, and on the polarization. The emissivity of a natural interface is always between and 1. A body that interfaces with another medium which both has and absorbs all the radiation incident upon it, is said to be a black body. The surface of a black body can be modelled by a small hole in the wall of a large enclosure which is maintained at a uniform temperature with opaque walls that are perfectly non-reflective at any wavelength. At equilibrium, the radiation inside this enclosure follows Planck's law, and so will the radiation coming out of the small hole. Just as the Maxwell–Boltzmann distribution is the unique maximum entropy energy distribution for a gas of massive particles at thermal equilibrium, so is Planck's distribution for a gas of photons. By contrast to a real gas where the masses and number of particles play a role, the spectral radiance, pressure and energy density of a photon gas at thermal equilibrium are entirely determined by the temperature. If the photon gas is not initially Planckian, the second law of thermodynamics guarantees that interactions (between photons and other particles or even between the photons themselves) will cause the photon energy distribution to change and approach the Planck distribution. In such an approach to thermodynamic equilibrium, photons are created or annihilated in the right numbers and with the right energies to fill the cavity with a Planck distribution until they reach equilibrium temperature. The quantity is the spectral radiance as a function of temperature and frequency. It has units of W·m−2·sr−1·Hz−1 in the SI system. An infinitesimal amount of power is radiated in the direction described by the angle from the surface normal from infinitesimal surface area into infinitesimal solid angle in an infinitesimal frequency band of width centered on frequency . The total power radiated into any solid angle is the integral of over those three quantities, and is given by the Stefan–Boltzmann law. The spectral radiance of Planckian radiation from a black body has the same value for every direction and angle of polarization, and so the black body is said to be a Lambertian radiator. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Planck's law」の詳細全文を読む スポンサード リンク
|