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Question

A heated body maintained at T K emits thermal radiation of total energy E with a maximum intensity at frequency ν. The emissivity of the material is 0.5. If the temperature of the body be increased to and maintained at temperature 3T K, then

A
The maximum intensity of the emitted radiation will occur at frequency ν/3
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B
The maximum intensity of the emitted radiation will occur at frequency 3ν
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C
The total energy of emitted radiation will become 81E
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D
The total energy of emitted radiation will become 27E
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Solution

The correct options are
B The maximum intensity of the emitted radiation will occur at frequency 3ν
C The total energy of emitted radiation will become 81E
According to Wien's Displacement Law, λmax=bT
νmax=bcT
Thus, the new frequency at which maximum intensity occurs is v3.
Also the power of emitted radiation can be written as P=ϵσAT4.
Thus, the power becomes (31)4=81 times the previous power.
Thus, the total energy of emitted radiation will be 81E.

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