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Question

Power radiated by a black body at temperature T1 is P and it radiates maximum energy at a wavelength λ1. If the temperature of the black body is changed from T1 to T2, it radiates maximum energy at a wavelength λ12. The power radiated at T2 is:

A
2P
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B
4P
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C
8P
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D
16P
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Solution

The correct option is D 16P
We know, by Wein's displacement law,

Tλmax=b

Thus, T1λ1=T2λ2=T2λ12

T2=2T1

Also, from Stephan-Boltzmann law, radiative power:

P=σAT4

So, P2P1=T24T14=16

Hence, P2=16P

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