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Question

Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T1 and T2 , respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?

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Solution

According to Wein's displacement law
λmT=constant
(λm)ATA=(λm)B(TB)
TATB=(λm)B(λm)A=1500 nm500 nm
TATB=3
According to Stefan Boltzmann law, rate of energy radiated by a black body.
E=σAT4=σ4πR2T4[Here,A=4πR2]
EAEB=(RARB)2(TATB)4=(6 cm18 cm)2(3)4=9

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