Black Body radiation
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The energy density u of radiation from a black body at temperature T is given by
u = aT^4
where a = ((pi^2)k^4) / (15 (h-bar)^3)c^3)
(here, k is the Boltzmann constant and (h-bar) is the reduced Planck's constant)
Outline the derivation of this result. Derive Stefan's law for the power radiated per unit area by a black body, and obtain an expression for the Stefan-Boltzmann constant which appears in the law.
Obtain an expression for the entropy density of black-body radiation.
Black-body radiation, initially occupying a volume V at temperature Ti, expands adiabatically to a final volume aV where a is a constant. What is its final temperature?
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Solution Summary
A theoretical description for black body radiation is provided in this solution. The first part of the solution is a standard derivation in statistical thermodynamics. The fundamental derivation of energy density, Plank's theorem and the failure of R.J theorem due to ultraviolet catastrophe, etc. are given both in terms of frequency and in terms of wavelength. A historical back ground of the SB law is provided in the second section of this response, along with comments on the T and frequency dependence of a black body. The entropy density is calculated as well. The solution is derived from a basic idea of thermodynamics and the full solution is provided within a pdf attachment.
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