Power radiated by black body at temperature T1 is P and it radiates maximum energy at a wavelength 11. If the temperature of the black body is changed from T1 to T2, it radiates max energy at a wavelength of 11/2. The power radiated at T2 is

Explanation

The information provided in the image states that:The power radiated by a black body at temperature T₁ is P, and it radiates maximum energy at a wavelength λ₁.When the temperature of the black body changes from T₁ to T₂, it starts radiating maximum energy at a wavelength of λ₁/2.We are asked to find the power radiated at temperature T₂.Key concept:Wein's displacement law states that the wavelength (λ) at which a black body radiates the maximum intensity is inversely proportional to its temperature (T). Mathematically, it can be expressed as:λT = constantwhere the constant is approximately 2.897 x 10^-3 m⋅K.Reasoning:Relating λ₁ and T₁ using Wein's displacement law:λ₁T₁ = constantRelating λ₂ and T₂ using Wein's displacement law:λ₂T₂ = constantWe are given:λ₂ = λ₁/2Substituting the second equation into the first equation:λ₁T₁ = (λ₁/2)T₂Solving for T₂:T₂ = 2T₁Relation between power radiated (P) and temperature (T) for a black body:P ∝ T⁴ (Stefan-Boltzmann law)Taking the ratio of the power radiated at T₂ (P₂) to the power radiated at T₁ (P₁):P₂/P₁ = (T₂⁴ / T₁⁴)Substituting T₂ = 2T₁ from step 5:P₂/P₁ = (2T₁⁴ / T₁⁴) = 2⁴ = 16Therefore, the power radiated at temperature T₂ (P₂) is 16 times the power radiated at temperature T₁ (P₁). This translates to 16P as the answer.