Physics

Physics

Problem

A spherical ember with radius 2.0 cm glows steadily at 1.2 × 10³ K for 5.0 min before fading. Assuming it behaves as a perfect blackbody, determine how many kilowatt-hours of energy it radiates during this interval. Use σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
Intuitive explanation

This problem combines the Stefan–Boltzmann law for blackbody radiation with basic energy and unit conversion. The key is to find the total power radiated from the sphere's surface using P=σAT4P = \sigma A T^4, then multiply by time to get total energy—being careful to convert your final answer to kilowatt-hours. Think of it as: hotter objects radiate much more power (that T4T^4 dependence is dramatic), and a larger surface area means more total radiation escaping.

Intuitive explanation

This problem combines the Stefan–Boltzmann law for blackbody radiation with basic energy and unit conversion. The key is to find the total power radiated from the sphere's surface using P=σAT4P = \sigma A T^4, then multiply by time to get total energy—being careful to convert your final answer to kilowatt-hours. Think of it as: hotter objects radiate much more power (that T4T^4 dependence is dramatic), and a larger surface area means more total radiation escaping.

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