Illustration of vibrations of a drum.

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Lord Rayleigh on classical limes made an attempt to explain the energy distribution in black body radiation, which was completed by Jeans in 1900. The result obtained by then is known as Rayleigh – Jean’s Law.

Black body emits radiation of continuously variable wavelength right from zero to infinity. This radiation can be imagined as broken up into monochromatic waves. These monochromatic waves originate as a result of a different modes of vibration of the medium, which at that time was supposed to be an electromagnetic sensitive medium called ‘ETHER’ According to well-known result of statistical mechanics, the number of such modes of vibration lying between the wavelength range $ \lambda $ and $ \lambda+d\lambda $ is equal to $ 8\pi{\lambda}^{-4}d\lambda $ per unit volume. And also according to the theorem of equipartition of energy, the total energy of a system for each mode of vibration (or degree of freedom) is equal to $ kT $ , where $ k $ is the Boltzmann constant and $ T $ is the temperature of the system in Kelvin. Hence the total energy of the radiation lying between the wavelength range $ \lambda$ and $ \lambda + d\lambda $ per unit volume is
$ u_{\lambda}d\lambda$ =number of mode of vibration $ \times kT $
or, $ u_{\lambda}d\lambda=8\pi kT{\lambda}^{-4}d\lambda $
This is Rayleigh Jean Law.

Posted by Gaurav Tiwari

A designer by profession, a mathematician by education but a Blogger by hobby. With an experience of over seven years with WordPress, PHP and CSS3, Gaurav is capable of doing almost anything related to these. Beyond that, He is a mathematics graduate & a civil service aspirant.

  1. very nice yours article

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