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Question

Two spherical black bodies A and B, having radii rA and rB, where rB=2rA emit radiation with peak intensities at wavelength 400 nm and 800 nm respectively. If their temperatures are TA and TB respectively in Kelvin scale, their emissive powers are EA and EB and energies emitted per second are PA and PB respectively, then

A
TATB=2
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B
PAPB=4
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C
EAEB=8
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D
EAEB=16
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Solution

The correct options are
A TATB=2
B PAPB=4
D EAEB=16
Given
rB=2rA

By Wein’s displacement law, wavelength corresponding to maximum intensity is
λA1T
(λm)A(λm)B=TBTA=400800
TATB=2
By Stefan’s law,
E=σeT4
EAEB=T4AT4B=16
PAPB=AAT4AABT4B
PAPB=4πr2AT4A4πr2BT4B=4

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