Chapter 18 (III)

# Chapter 18 (III) - 18 1.4 Properties of black-body...

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1 18. 1.4. Properties of black-body radiation The energy spectrum is often expressed in terms of wavelength . Since =c/ , . ) / ( 2 d c d Thus, Eq. (18.12) gives the radiation energy in the wavelength range of to +d by . ) 1 ( 8 ) ( / 5 kT hc e d hcV d u (18.13) (1) The energy density (energy per volume) is given by . ) 1 ( 8 0 / 5 kT hc e d hc V U (18.14) Let x=hc/ kT, then =hc/xkT and d = (hc/x 2 kT)dx. Thus, Eq. (18.14) becomes 0 2 5 5 ) 1 ( ) ( ) ( 8 x e x dx x kT hc hc kT hc V U = , ) ( 15 8 15 ) ( ) ( 8 ) 1 ( ) ( ) ( 8 4 4 3 4 5 4 3 4 0 3 3 4 aT T hc k hc kT e dx x hc kT x (18.15) where a= 3 4 5 ) ( 15 8 hc k =7.55x10 -16 J.m -3 K -4 . The photon flux is given by , ) 4 / 1 ( nc h where n=(N/V) is the photon density. By analogy, we have a radiation energy flux : , 4 ) )( 4 1 ( 4 4 T T ac c

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Chapter 18 (III) - 18 1.4 Properties of black-body...

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