A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is R . The rate of cooling of this sphere at 400 K is x 243 . The value of x is (Temperature of surrounding is 300 K)

Step-by-step solution

The rate of cooling of a body is given by Stefan-Boltzmann law: R = dT dt = e A ms (T^4 - T₀^4) This implies R (T^4 - T₀^4) . For the first case, T₁ = 600 K and T₀ = 300 K: R₁ = k (600^4 - 300^4) = R For the second case, T₂ = 400 K and T₀ = 300 K: R₂ = k (400^4 - 300^4) = x 243 Taking the ratio of R₂ to R₁ : R₂ R₁ = 400^4 - 300^4 600^4 - 300^4 R₂ R = 4^4 - 3^4 6^4 - 3^4 R₂ R = 256 - 81 1296 - 81 R₂ R = 175 1215 Dividing the numerator and denominator by 5 : R₂ R = 35 243 R₂ = 35R 243 Comparing this with the given ra