Two bodies A and B at temperatures ' T ₁ ^ K and ' T ₂ ^ K respectively have the same dimensions. Their emissivities are in the ratio 16: 1 . At T ₁= x T ₂ , they radiate the same amount of heat per unit area per unit time. The value of x is

Step-by-step solution

Stefan–Boltzmann Law: The rate of heat radiated per unit area per unit time is given by P/A = e T^4 , where e is the emissivity, is the Stefan–Boltzmann constant, and T is the absolute temperature. Given equal surface areas and equal radiated heat per unit area per unit time, with emissivities in the ratio 16:1 , let e_A = 16e and e_B = e . From P/A = e T^4 , equating the expressions for bodies A and B yields 16e T₁^4 = e T₂^4 . Canceling e (nonzero) gives 16 T₁^4 = T₂^4 . Substituting T₁ = x T₂ results in 16 x^4 T