A black rectangular surface of area A emits energy E per unit time at 27^ C. If length and breadth is reduced to ( 1 4 )^ th of initial value and temperature is raised to 327^ C, then energy emitted per unit time becomes

Step-by-step solution

According to Stefan-Boltzmann law, the energy emitted per unit time by a black body is given by E = A T^4 . Initial temperature T₁ = 27^ C = 300 K and initial area A₁ = A . Initial energy emitted per unit time is E₁ = E = A (300)^4 . Final temperature T₂ = 327^ C = 600 K . Since length and breadth are reduced to 1 4 of their initial values, the new area is A₂ = L 4 B 4 = A 16 . Final energy emitted per unit time is E₂ = A₂ T₂^4 . Taking the ratio of E₂ to E₁ : E₂ E₁ = A₂ A₁ ( T₂ T₁ )^4 E₂ E = 1 16 ( 600 300 )^4 E₂