3) when the temperature of a blackbody increases from 900 k to 2300 k, by what factor does the total power of the electromagnetic radiation per-unit- area increase?

The electromagnetic radiation per-unit- area increase by 42.65 times.

Explanation:

The radiation per-unit- area (P) is directly proportional to the fourth power of the temperature. Thus,

P ∝ T⁴

For, when the temperature is raised from T₀ to T₁ , the radiation per-unit- area is related to as:

T₀ =  900 K

T₁ = 2300 K

So,

P₁ = 42.65 P₀

The electromagnetic radiation per-unit- area increase by 42.65 times.