A heat conducting rod, 1.40 m long, is made of an aluminum section that is 0.50 m long and a copper section that is 0.90 m long. Both sections have cross-sectional areas of of 0.00040 m². The aluminum end and the copper end are maintained at temperatures of 40°C and 280°C, respectively. The thermal conductivity of aluminum is 205 W/m∙K of copper is 385 W/m∙K. The rate at which heat is conducted in the rod is closest to

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Quizplus · Accepted Answer

The rate of heat conduction is given by:Q/t = kA(dT/dx)where Q/t is the rate of heat conduction, k is the thermal conductivity, A is the cross-sectional area, and dT/dx is the temperature gradient.For the aluminum section, we have:Q/t = kA(dT/dx) = (205 W/m∙K)(0.00040 m2)(40°C - 280°C)/0.50 m = -10.25 WFor the copper section, we have:Q/t = kA(dT/dx) = (385 W/m∙K)(0.00040 m2)(280°C - 40°C)/0.90 m = 10.25 WThe total rate of heat conduction is the sum of the rates of heat conduction in the aluminum and copper sections:Q/t = -10.25 W + 10.25 W = 0 WTherefore, the rate at which heat is conducted in the rod is closest to 20 W.

A Heat Conducting Rod, 1