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Question
A heated body emits radiation which has maximum intensity near the frequency v0. The emissivity of the material is 0.5. If the absolute temperature of the body is doubled.
(a) the maximum intensity of radiation will be near the frequency 2v0
(b) the maximum intensity of radiation will be near the frequency v0/2
(c) the total energy emitted will increase by a factor of 16
(d) the total energy emitted will increase by a factor of 8
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Solution
(a) the maximum intensity of radiation will be near the frequency 2v0
(c) the total energy emitted will increase by a factor of 16
From Wein's displacement law,
λmT = b ( a constant )
or `(cT)/(Vm) = b`
Here, T is the absolute temperature of the body.
So, as the temperature is doubled to keep the product on the left hand side constant, frequency is also doubled.
From Stefan's law, we know that the rate of energy emission is proportional to T4
This implies that total energy emitted will increase by a factor of (2)4, which is equal to 16.
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