A rectangular black body of temperature 127^ C has surface area 4 ~cm 2 ~cm and rate of radiation is E . If its temperature is increased by 400^ C and surface area is reduced to half of the initial value then the rate of radiation is

Step-by-step solution

Radiation rate from a black body follows Stefan-Boltzmann Law: P = A T^4 . Initial temperature is T₁ = 127^ C = 400 K with surface area A₁ = 8 cm ^2 and radiation rate E = A₁ T₁^4 . Final conditions: T₂ = 127^ C + 400^ C = 527^ C = 800 K , and A₂ = 1 2 A₁ = 4 cm ^2 , giving E' = A₂ T₂^4 . The ratio is E' E = A₂ A₁ ( T₂ T₁ )^4 = 1 2 ( 800 400 )^4 = 1 2 2^4 = 1 2 16 = 8 . New rate is 8E .