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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A heated body radiates energy with a maximum intensity around the frequency ₀ . The emissivity of the material is 0.5 . If the absolute temperature of the body is doubled,

Options

  1. Athe total energy emitted will increase by a factor of 16
  2. Bthe maximum intensity of the radiation will be near the frequency 2 ₀
  3. Cthe maximum intensity of the radiation will be near the frequency ₀/2
  4. Dthe total energy emitted will increase by a factor of 8

Correct answer

B. the maximum intensity of the radiation will be near the frequency 2 ₀

Step-by-step solution

According to the Stefan-Boltzmann law, the total energy radiated per unit area per unit time by a body is given by E = T^4 , where is the emissivity and T is the absolute temperature. When the absolute temperature is doubled ( T' = 2T ), the new total energy emitted is E' = (2T)^4 = 16 T^4 = 16E . Thus, the total energy emitted increases by a factor of 16 . According to Wien's displacement law, the wavelength corresponding to maximum spectral emissive power is inversely proportional to the absolute temperature, _m

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