A black body emits heat at the rate of 20 W when its temperature is 227oC. Another black body emits heat at the rate of 15W when its temperature is 277oC. Compare the area of the surface of the two bodies if the surrounding is at NTP.

According to the Stefan-Boltzmann law, Power radiated P = eσA(T⁴ - T₀⁴) where e is emmissivity, σ is Stefan's constant, A is surface area of body, T is the temperature of body and T₀ is surrounding temperature. Hence comparing for the two surfaces, P₁/P₂ = A₁(T₁⁴ - T₀⁴)/A₂(T₂⁴ - T₀⁴) Given : P₁ = 20W, P₂ = 15W, T₁ = 227o + 273 = 500K and T₂ = 277o + 273 = 550K Surrounding temperature T₀ = 293K ∴ A₁/A₂ = P₁(T₂⁴ - T₀⁴)/P₂(T₁⁴ - T₀⁴) = 20 × (550⁴ - 293⁴)/15 × (500⁴ - 293⁴) = 12