MaxwellBoltzmann distribution law

a description of the statistical distribution of the energies of the molecules of a classical gas. This distribution was first set forth by the Scottish physicist James Clerk Maxwell in 1859, on the basis of probabilistic arguments, and gave the distribution of velocities among the molecules of a gas. Maxwell's finding was generalized (1871) by a German physicist, Ludwig Boltzmann, to express the distribution of energies among the molecules.The distribution function for a gas obeying MaxwellBoltzmann statistics ( f_{M–B}) can be written in terms of the total energy (E) of the system of particles described by the distribution, the absolute temperature (T) of the gas, the Boltzmann constant (k = 1.38 × 10^{16} erg per kelvin), and a normalizing constant (C) chosen so that the sum, or integral, of all probabilities is unity—i.e., f_{M–B} = Ce^{E/kT}, in which e is the base of the natural logarithms. The distribution function implies that the probability dP that any individual molecule has an energy between E and E + dE is given by dP = f_{M–B}dE. The total energy (E) usually is composed of several individual parts, each corresponding to a different degree of freedom of the system. In fact, the total energy is divided equally between these modes. See energy, equipartition of.The law can be derived in several ways, none of which is absolutely rigorous. All systems observed to date appear to obey MaxwellBoltzmann statistics provided that quantummechanical effects are not important.
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MaxwellBoltzmann distribution law — noun (physics) a law expressing the distribution of energy among the molecules of a gas in thermal equilibrium • Syn: ↑Boltzmann distribution law • Topics: ↑physics, ↑natural philosophy • Hypernyms: ↑distribution law … Useful english dictionary
MaxwellBoltzmann distribution law — a method for calculating the relative number of molecules in a given population which possess a given amount of velocity or energy … Medical dictionary
Boltzmann distribution law — noun (physics) a law expressing the distribution of energy among the molecules of a gas in thermal equilibrium • Syn: ↑Maxwell Boltzmann distribution law • Topics: ↑physics, ↑natural philosophy • Hypernyms: ↑distrib … Useful english dictionary
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distribution law — noun (chemistry) the total energy in an assembly of molecules is not distributed equally but is distributed around an average value according to a statistical distribution • Topics: ↑chemistry, ↑chemical science • Hypernyms: ↑law, ↑law of nature… … Useful english dictionary
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Boltzmann, Ludwig Eduard — ▪ Austrian physicist born Feb. 20, 1844, Vienna, Austria died Sept. 5, 1906, Duino, Italy physicist whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as … Universalium
Maxwell, James Clerk — born June 13, 1831, Edinburgh, Scot. died Nov. 5, 1879, Cambridge, Cambridgeshire, Eng. Scottish physicist. He published his first scientific paper at age 14, entered the University of Edinburgh at 16, and graduated from Cambridge University. He… … Universalium
Maxwell , James Clerk — (1831–1879) British physicist Maxwell was born in Edinburgh and studied at the university there (1847–50) and at Cambridge (1850–54), becoming a fellow in 1855. He was professor of natural philosophy at Marishal College, Aberdeen, from 1856 until … Scientists
distribution function — Statistics. (of any random variable) the function that assigns to each number the probability that the random variable takes a value less than or equal to the given number. [1905 10] * * * ▪ mathematics mathematical expression that… … Universalium