Two spherical black bodies have radii ' R₁ ' and ' R₂ '. Their surface temperatures are T₁ K and T₂ K respectively. If they radiate the same power, the ratio R ₁ R ₂ is

Step-by-step solution

The power radiated by a spherical black body follows the Stefan-Boltzmann law: P = A T^4 , where is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature. For a sphere, A = 4 R^2 , so P = 4 R^2 T^4 . Given two spheres with different radii and temperatures radiating equal power, set the expressions equal: 4 R₁^2 T₁^4 = 4 R₂^2 T₂^4 Canceling the common factor 4 yields R₁^2 T₁^4 = R₂^2 T₂^4 . Solving for the ratio R₁/R₂ : ( R₁ R₂ )^2 = ( T₂ T₁ )^4 R₁ R₂ = ( T₂ T₁ )^2 The final answer