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 × 10^-8 W/(m²∙K⁴).

Question

Quizplus · Accepted Answer

The power radiated by a sphere is given by the Stefan-Boltzmann law: P = eσAT⁴. Here, e = 1, σ = 5.67 × 10⁻⁸ W/(m²∙K⁴), A = 4πr² (surface area of the sphere), and T = 400 K. Converting radius to meters (0.1 m), A = 4π(0.1)² = 0.1256 m². Thus, P = 1 × 5.67 × 10⁻⁸ × 0.1256 × 400⁴ = 180 W.

How Much Power Does a Sphere with a Radius of 10