A metal rod of length 1.0 m has one end maintained at 100°C and the other end at 0°C. The thermal conductivity of the metal is 400 W/(m·K). If the cross-sectional area of the rod is 0.01 m², what is the rate of heat transfer through the rod?

Core Concept

The rate of heat transfer through a material is given by Fourier's law: Q/t = kA(ΔT/L), where k is thermal conductivity, A is cross-sectional area, ΔT is temperature difference, and L is length. Substituting the values: Q/t = 400 W/(m·K) × 0.01 m² × (100°C - 0°C)/1.0 m = 400 W.