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Schwarzschild's Equation For Radiative Transfer
In the study of heat transfer, Schwarzschild's equation Those without access to a text discussing Schwarzschild's equation can find a discussion abstracted from these pages at: https://scienceofdoom.com/2011/02/07/understanding-atmospheric-radiation-and-the-“greenhouse”-effect-–-part-six-the-equations/. is used to calculate radiative transfer ( energy transfer via electromagnetic radiation) through a medium in local thermodynamic equilibrium that both absorbs and emits radiation. The incremental change in spectral intensity, (, /sr/m2/μm at a given wavelength as radiation travels an incremental distance () through a non-scattering medium is given by: dI _\lambda = n\sigma_\lambda B_\lambda(T) \, ds - n\sigma_\lambda I_\lambda \, ds = n \sigma_\lambda _\lambda(T) - I_\lambda\, ds where * is the density of absorbing/emitting molecules, * is their absorption cross-section at wavelength , * is the Planck function for temperature and wavelength , * is the spectral intens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weather Forecasting Models
Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the troposphere, just below the stratosphere. Weather refers to day-to-day temperature, precipitation, and other atmospheric conditions, whereas climate is the term for the averaging of atmospheric conditions over longer periods of time. When used without qualification, "weather" is generally understood to mean the weather of Earth. Weather is driven by air pressure, temperature, and moisture differences between one place and another. These differences can occur due to the Sun's angle at any particular spot, which varies with latitude. The strong temperature contrast between polar and tropical air gives rise to the largest scale atmospheric circulations: the Hadley cell, the Ferrel cell, the polar cell, and the jet stream. Weather systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beer–Lambert Law
The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics, for photons, neutrons, or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation. History The law was discovered by Pierre Bouguer before 1729, while looking at red wine, during a brief vacation in Alentejo, Portugal. It is often attributed to Johann Heinrich Lambert, who cited Bouguer's ''Essai d'optique sur la gradation de la lumière'' (Claude Jombert, Paris, 1729) – and even quoted from it – in his '' Photometria'' in 1760. Lambert's law stated that the loss of light intensity when it propagates in a medium is directly proportional to intensity and path length. Much later, the German scientist August ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Scattering
Rayleigh scattering ( ), named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering particle (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength. Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle, therefore, becomes a small radiating dipole whose radiation we see as scattered light. The particles may be individual atoms or molecules; it can occur when light travels through transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering of sunlight in Earth's atmosphere cau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Infrared
Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around 1 millimeter (300 GHz) to the nominal red edge of the visible spectrum, around 700 nanometers (430 THz). Longer IR wavelengths (30 μm-100 μm) are sometimes included as part of the terahertz radiation range. Almost all black-body radiation from objects near room temperature is at infrared wavelengths. As a form of electromagnetic radiation, IR propagates energy and momentum, exerts radiation pressure, and has properties corresponding to both those of a wave and of a particle, the photon. It was long known that fires emit invisible heat; in 1681 the pioneering experimenter Edme Mariotte showed that glass, though transparent to sunlight, obstructed radiant heat. In 1800 the astronomer Sir William Herschel discovered tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collisional Excitation
Collisional excitation is a process in which the kinetic energy of a collision partner is converted into the internal energy of a reactant species. Astronomy In astronomy, collisional excitation gives rise to spectral lines in the spectra of astronomical objects such as planetary nebulae and H II regions. In these objects, most atoms are ionised by photons from hot stars embedded within the nebular gas, stripping away electrons. The emitted electrons, (called photoelectrons), may collide with atoms or ions within the gas, and excite them. When these excited atoms or ions revert to their ground state, they will emit a photon. The spectral lines formed by these photons are called ''collisionally excited lines'' (often abbreviated to CELs). CELs are only seen in gases at very low densities (typically less than a few thousand particles per cm³) for forbidden transitions. For allowed transitions, the gas density can be substantially higher. At higher densities, the reverse process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: :p_i \propto e^ where is the probability of the system being in state , is the energy of that state, and a constant of the distribution is the product of the Boltzmann constant and thermodynamic temperature . The symbol \propto denotes proportionality (see for the proportionality constant). The term ''system'' here has a very wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore the Boltzmann distribution can be used to solve a very wide variety of problems. The distrib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Law Of Thermal Radiation
In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility. A body at temperature radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature ( Stefan–Boltzmann law), universal for all perfect black bodies. Kirchhoff's law states that: Here, the dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium. In slightly different terms, the emissive power of an arbitrary opaque bod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absorptance
Absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power. This should not be confused with absorbance and absorption coefficient. Mathematical definitions Hemispherical absorptance Hemispherical absorptance of a surface, denoted ''A'', is defined as :A = \frac, where *Φea is the radiant flux ''absorbed'' by that surface; *Φei is the radiant flux received by that surface. Spectral hemispherical absorptance Spectral hemispherical absorptance in frequency and spectral hemispherical absorptance in wavelength of a surface, denoted ''A''ν and ''A''λ respectively, are defined as :A_\nu = \frac, :A_\lambda = \frac, where *Φe,νa is the spectral radiant flux in frequency ''absorbed'' by that surface; *Φe,νi is the spectral radiant flux in frequency received by that surface; *Φe,λa is the spectral radiant flux in wavelength ''absorbed'' by that surface; *Φe,λi is the spectral radiant f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emissivity
The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is not visible to human eyes. A portion of the thermal radiation from very hot objects (see photograph) is easily visible to the eye. The emissivity of a surface depends on its chemical composition and geometrical structure. Quantitatively, it is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. The ratio varies from 0 to 1. The surface of a perfect black body (with an emissivity of 1) emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature (, ). All real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates. Emissivities are important in several conte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stefan–Boltzmann Law
The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time j^ (also known as the black-body '' radiant emittance'') is directly proportional to the fourth power of the black body's thermodynamic temperature ''T'': : j^ = \sigma T^. The constant of proportionality ''σ'', called the Stefan–Boltzmann constant, is derived from other known physical constants. Since 2019, the value of the constant is : \sigma=\frac = 5.670374419\times 10^\, \mathrm, where ''k'' is the Boltzmann constant, ''h'' is Planck's constant, and ''c'' is the speed of light in a vacuum. The radiance from a specified angle of view (watts per square metre per steradian) is given by : L = \frac\pi = \frac\sigma\pi T^. A body that does not absorb all incident radiation (sometimes known as a grey body) emits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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