Planck's radiation law is given as: 8thv³ I = n(v)ɛ =- c3 hv ekBT –1 8nhc = n(1)ē = 1 25 hc eAkgT – 1 (a) Show that it reduces to the Rayleigh-Jeans law as 2–. (b) Show that it reduces to Wien's law in the short wavelength limit (2 → 0). Evaluate a and b. (c) Derive the constant in the Wien's displacement law.

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Chapter11: Heat Transfer By Radiation
Section: Chapter Questions
Problem 11.33P
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Planck's radiation law is given as:
8thv³
I = n(v)ɛ =-
c3
hv
ekBT – 1
8nhc
1
= n(1)ē =
25
hc
eAkgT – 1
(a) Show that it reduces to the Rayleigh-Jeans law as 2 –∞.
(b) Show that it reduces to Wien's law in the short wavelength limit (1 → 0).
Evaluate a and b.
(c) Derive the constant in the Wien's displacement law.
Transcribed Image Text:Planck's radiation law is given as: 8thv³ I = n(v)ɛ =- c3 hv ekBT – 1 8nhc 1 = n(1)ē = 25 hc eAkgT – 1 (a) Show that it reduces to the Rayleigh-Jeans law as 2 –∞. (b) Show that it reduces to Wien's law in the short wavelength limit (1 → 0). Evaluate a and b. (c) Derive the constant in the Wien's displacement law.
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