How much power does a sphere with a radius of 10 cm radiate if is has an emissivity e = 1.0 and is kept at a temperature of 400 K? The Stefan-Boltzmann constant is 5.67 x 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 blackbody is given by the Stefan-Boltzmann law:

P = σeA(T^4),

where σ is the Stefan-Boltzmann constant, e is the emissivity, A is the surface area, and T is the temperature in Kelvin.

For a sphere, the surface area is given by 4πr^2, where r is the radius. Substituting the given values into the formula, we get:

P = (5.67×10^-8 W/(m^2·K^4))×1×4π(0.1 m)^2(400 K)^4

P = 5.67×10^-8 ×4π×4×10^-4×64×10^8

P = 180 W

Therefore, the power radiated by the sphere is 180 W. The correct choice is C).

How Much Power Does a Sphere with a Radius of 10