Wien approximation

Wien approximation

Wien's approximation (also sometimes called "Wien's law" or the "Wien distribution law") is a law of physics used to describe the spectrum of thermal radiation (frequently called the blackbody function). This law was first derived by Wilhelm Wien in 1896.cite book
author=J. Mehra, H. Rechenberg
title=The Historical Development of Quantum Theory
location=New York
id=ISBN 0-387-90642-8
] cite book
author=R. Bowley, M. Sánchez
title=Introductory Statistical Mechanics
edition=2nd edition
publisher=Clarendon Press
id=ISBN 0-19-850576-0
] The equation does accurately describe the short wavelength (high frequency) spectrum of thermal emission from objects, but it fails to accurately fit the experimental data for long wavelengths (low frequency) emission.

The law may be written as

I( u, T) = frac{2 h u^3}{c^2} e^{-frac{h u}{kT cite book
author=G. B. Rybicki, A. P. Lightman
title=Radiative Processes in Astrophysics
publisher=John Wiley & Sons
location=New York
id=ISBN 0-471-82759-2


:*I( u, T) is the amount of energy per unit surface area per unit time per unit solid angle per unit frequency emitted at a frequency ν.:*T is the temperature of the black body.:*h is Planck's constant.:*c is the speed of light.:*k is Boltzmann's constant.

This equation may also be written as

I(lambda, T) = frac{2 h c^2} {lambda^5} e^{-frac{hc}{lambda kT Equation derived using u=4π/c; see Rybicki, Lightman (1979) reference.]

where I(lambda, T) is the amount of energy per unit surface area per unit time per unit solid angle per unit wavelength emitted at a wavelength λ.

Relation to Planck's law

The Wien approximation was originally proposed as a description of the complete spectrum of thermal radiation, although it failed to accurately describe long wavelength (low frequency) emission. However, it was soon superseded by Planck's law, developed by Max Planck. Unlike the Wien approximation, Planck's law accurately describes the complete spectrum of thermal radiation. Planck's law may be given as

I( u, T) = frac{2 h u^3}{c^2} frac{1}{e^{frac{h u}{kT-1}

The Wien approximation may be derived from Planck's law by assuming h u gg kT. When this is true, then

frac{1}{e^{frac{h u}{kT-1} approx e^{-frac{h u}{kT

and so Planck's law approximately equals the Wien approximation at high frequencies.

Other approximations of thermal radiation

The Rayleigh-Jeans law developed by Lord Rayleigh may be used to accurately describe the long wavelength spectrum of thermal radiation but fails to describe the short wavelength spectrum of thermal emission.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Wien's law — or Wien law may refer to:* Wien approximation, an equation used to describe the short wavelength (high frequency) spectrum of thermal radiation. * Wien s displacement law, an equation that describes the relationship between the temperature of an… …   Wikipedia

  • Wien's displacement law — Wien s Law redirects here. For the historical distribution law, see Wien s Distribution Law. Black body thermal emission intensity as a function of wavelength for various absolute temperatures. Wien s law is not obvious in the picture, because… …   Wikipedia

  • Планк, Макс — Эта статья  о немецком физике. Другие значения термина в заглавии статьи см. на Планк (значения). Макс Планк Max Planck …   Википедия

  • Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… …   Wikipedia

  • Zeta constant — In mathematics, a zeta constant is a number obtained by plugging an integer into the Riemann zeta function. This article provides a number of series identities for the zeta function for integer values.The Riemann zeta function at 0 and 1At zero,… …   Wikipedia

  • Black body — As the temperature decreases, the peak of the blackbody radiation curve moves to lower intensities and longer wavelengths. The blackbody radiation graph is also compared with the classical model of Rayleigh and Jeans …   Wikipedia

  • electromagnetic radiation — Physics. radiation consisting of electromagnetic waves, including radio waves, infrared, visible light, ultraviolet, x rays, and gamma rays. [1950 55] * * * Energy propagated through free space or through a material medium in the form of… …   Universalium

  • Systemtheorie (Ingenieurwissenschaften) — Der Begriff der Systemtheorie wird in verschiedenen wissenschaftlichen Disziplinen angewendet und hat in Bezug auf den Primärbegriff System keine einheitliche Bedeutung. Systeme können sich als physikalische, ökologische, ökonomische, soziale… …   Deutsch Wikipedia

  • Nombre d'or —  Pour l’article homonyme, voir Nombre d or (astronomie).  La proportion définie par a et b est dite d extrême et de moyenne raison lorsque a est à b ce que a + b est à a, so …   Wikipédia en Français

  • Detailed balance — The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions): At equilibrium, each elementary process should be equilibrated by its reverse… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”