An object is at temp of 400 degree celcius.At what temp would it radiate energy twice as fast?The temp of the surroundings may be as sumed to be negligible

By STefan-Boltzmann law, Rate of heat radiation E is proportional to T⁴ .

Let E = kT⁴.

Also, let the iniotial energy radiated be E₁.

Temperature T = 400 C = 400+273 K = 673 K

So, E₁ = k (673)⁴ .................(1)

Let rate of heat radiation be 2E₁ at temperature T₂.

Then, 2E₁ = k(T₂)⁴

2E₁ = [E₁/(673)⁴] (T₂)⁴ using (1)

(T₂)⁴ = 2 (673)⁴

T₂ = (2)^1/4 * 673 = 1.19 * 673 = 800.33 K