How much power does a sphere with a radius of 10 cm radiate into empty space if is has an emissivity of 1.0 and is kept at a temperature of 400 K? (σ = 5.67 × 10^-8 W/m² ∙ K⁴) A)60 W B)70 W C)180 W D)210 W E)360 W

Question

Quizplus · Accepted Answer

The power radiated by a black body (or a body with an emissivity of 1.0) is given by the Stefan-Boltzmann law:

P = σAT^4

where P is the power radiated, A is the surface area of the sphere (4πr^2), σ is the Stefan-Boltzmann constant, and T is the temperature in Kelvin.

Substituting the given values, we get:

P = (5.67 × 10^-8 W/m^2K^4) × (4π(0.1 m)^2) × (400 K)^4 ≈ 180 W

Therefore, the correct answer is C) 180 W.

How Much Power Does a Sphere with a Radius of 10