Black sphere of radius R radiates power P at certain temperature T . If the temperature is doubled, the radius gets doubled. Now the power radiated would be

Step-by-step solution

The power radiated by a black sphere follows the Stefan-Boltzmann Law: P = A T^4 where A = 4 R^2 is the surface area. With initial values P₁ = (4 R^2)T^4 and new conditions R₂ = 2R , T₂ = 2T , the new power becomes: P₂ = (4 (2R)^2)(2T)^4 = (4 4R^2) 16T^4 = 64 (4 R^2)T^4 Recognizing (4 R^2)T^4 = P₁ , we obtain P₂ = 64P₁ . The power increases by a factor of 64 .