A certain blackbody radiates 100 W at a temperature of 2000 K.How much power would this body radiate at 3000 K?
A)150 W
B)225 W
C)338 W
D)506 W
E)759 W

Question

Quizplus · Accepted Answer

According to Stefan-Boltzmann Law, the power radiated by a black body is proportional to the fourth power of its temperature. Mathematically, P ∝ T⁴.

So, P₁/P₂ = (T₁/T₂)⁴

where P₁ is the power radiated at temperature T₁ and P₂ is the power radiated at temperature T₂.

Using this formula, we can find that:

P₂ = P₁ x (T₂/T₁)⁴

P₂ = 100 x (3000/2000)⁴ = 506W

Therefore, the answer is D (506 W).

A Certain Blackbody Radiates 100 W at a Temperature of 2000