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The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4. This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:
This yields Kirchhoff's law: α λ = ε λ {\displaystyle \alpha _{\lambda }=\varepsilon _{\lambda }} By a similar, but more complicated argument, it can be shown that, since black-body radiation is equal in every direction (isotropic), the emissivity and the absorptivity, if they happen to be dependent on direction, must again be equal for any ...
The same phenomena makes the absorptivity of incoming radiation less than 1 and equal to emissivity (Kirchhoff's law). When radiation has not passed far enough through a homogeneous medium for emission and absorption to reach thermodynamic equilibrium or when the medium changes with distance, Planck's Law and the Stefan-Boltzmann equation do ...
The principle was used by Gustav Kirchhoff in his derivation of his law of thermal radiation and by Max Planck in his analysis of his law of thermal radiation. For ray-tracing global illumination algorithms, incoming and outgoing light can be considered as reversals of each other, without affecting the bidirectional reflectance distribution ...
Kirchhoff's laws, named after Gustav Kirchhoff, may refer to: Kirchhoff's circuit laws in electrical engineering; Kirchhoff's law of thermal radiation; Kirchhoff equations in fluid dynamics; Kirchhoff's three laws of spectroscopy; Kirchhoff's law of thermochemistry; Kirchhoff's theorem about the number of spanning trees in a graph
A derivation of the law from theoretical considerations was presented by Ludwig Boltzmann (1844–1906) in 1884, drawing upon the work of Adolfo Bartoli. [17] Bartoli in 1876 had derived the existence of radiation pressure from the principles of thermodynamics.
Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, [3] uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
The variation of the enthalpy of reaction with temperature is given by Kirchhoff's Law of Thermochemistry, which states that the temperature derivative of ΔH for a chemical reaction is given by the difference in heat capacity (at constant pressure) between products and reactants: