“Wien approximation”的意思、由来-开放百科全书

Wien derived his law from thermodynamic arguments, several years before Planck introduced the quantization of radiation. Details are contained in a 2009 paper by J.Crepeau entitled "A Brief History of the T4 Radiation Law".^[4] The law may be written as

where

is the amount of energy per unit surface area per unit time per unit solid angle per unit wavelength emitted at a wavelength λ.

The peak value of this curve, as determined by taking the derivative and solving for zero, occurs at a wavelength λ_max and frequency ν_max of:^[7]

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 However, it was soon superseded by Planck's law, developed by Max Planck.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

The Wien approximation may be derived from Planck's law by assuming

. When this is true, then

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.^[3]^[5]

See also

References

1. ^{{cite journal |last=Wien |first=W. |year=1897 |title=On the division of energy in the emission-spectrum of a black body |journal=Philosophical Magazine |series=Series 5 |volume=43 |issue=262 |pages=214–220 |bibcode= |doi=10.1080/14786449708620983 |ref=harv}}
2. ^{{cite book |last1=Mehra |first1=J. |last2=Rechenberg |first2=H. |year=1982 |title=The Historical Development of Quantum Theory |volume=Vol. 1 |at=Chapter 1 |publisher=Springer-Verlag |isbn=978-0-387-90642-3 |ref=harv}}
3. ^¹²³{{cite book |last1=Bowley |first1=R. |last2=Sánchez |first2=M. |year=1999 |title=Introductory Statistical Mechanics |edition=2nd |publisher=Clarendon Press |isbn=978-0-19-850576-1 |ref=harv}}
4. ^{{cite conference |last=Crepeau |first=J. |year=2009 |title=A Brief History of the T4 Radiation Law |conference=ASME 2009 Heat Transfer Summer Conference |publisher=ASME |volume=Vol. 1 |issue= |pages=59–65 |doi=10.1115/HT2009-88060 |isbn=978-0-7918-4356-7 |ref=harv}}
5. ^¹²³{{cite book |last1=Rybicki |first1=G. B. |last2=Lightman |first2=A. P. |year=1979 |title=Radiative Processes in Astrophysics |publisher=John Wiley & Sons |isbn=978-0-471-82759-7 |ref=harv}}
6. ^{{cite book |last=Modest |first=M. F. |year=2013 |title=Radiative Heat Transfer |publisher=Academic Press |isbn=978-0-12-386944-9 |pages=9, 15}}
7. ^{{cite book |last1=Irwin |first1=J. A. |year=2007 |title=Astrophysics: Decoding the Cosmos |url=https://books.google.com/books?id=7SbN3iyoNf0C&pg=PA130 |page=130 |publisher=John Wiley & Sons |isbn=978-0-470-01306-9 |ref=harv}}