If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' R ₀ ', the same body at 900 K , surrounded by same atmosphere, will have rate of cooling nearly

Step-by-step solution

The rate of cooling for a black body due to radiation follows Stefan-Boltzmann's Law: R = A (T^4 - T_s^4) , where = 1 for a black body. At initial temperature T₁ = 400 K with surroundings at T_s = 300 K, the cooling rate is R₀ = A (400^4 - 300^4) = A 10^8 (256 - 81) = A 10^8 175 . At temperature T₂ = 900 K with the same T_s = 300 K, the cooling rate becomes R = A (900^4 - 300^4) = A 10^8 (6561 - 81) = A 10^8 6480 . The ratio yields R R₀ = 6480 175 = 1296 35 37.03 . Among the given options, this value is closest to