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Question

A heated body emits radiation which has maximum intensity at frequency vm. If the temperature of a body is doubled

A
the maximum intensity radiation will be at frequency 2vm
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B
the maximum intensity radiation will be at frequency 12vm
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C
the total emitted energy will increase by a factor of 16
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D
the total emitted energy will increase by a factor of 2
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Solution

The correct options are
B the maximum intensity radiation will be at frequency 2vm
D the total emitted energy will increase by a factor of 16
We know that from wein"s displacement law.
λmaxT=constant------------(1)
Also, we know that, velocity=frequency×wavelength
So, we can get f1λ[keeping the velocity constant]
By putting in equation (1), we will find Tf=constant, where f=vm
Hence, we can say that T=f, so by increasing the magnitude of temperature twice, simultaneously frequency will also be increased with an equal magnitude.
Also, we know that energy emitted by any body is given as: E=σT4, where σ=StefanBoltzmann Constant
ET4, E=(2T)4=(16T4)

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