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 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

Question

Quizplus · Accepted Answer

The rate of heat conduction is given by:$$Q/t = kA(T_h - T_c)/L$$where:* Q/t is the rate of heat conduction in watts* k is the thermal conductivity in W/m∙K* A is the cross-sectional area in m^2* T_h is the temperature of the hot end in K* T_c is the temperature of the cold end in K* L is the length of the rod in mFor the aluminum section:$$Q_1/t = k_1A(T_{h1} - T_{c1})/L_1$$$$Q_1/t = (205 W/m∙K)(0.00040 m^2)(313 K - 283 K)/(0.50 m)$$$$Q_1/t = 12.3 W$$For the copper section:$$Q_2/t = k_2A(T_{h2} - T_{c2})/L_2$$$$Q_2/t = (385 W/m∙K)(0.00040 m^2)(553 K - 313 K)/(0.90 m)$$$$Q_2/t = 19.6 W$$The total rate of heat conduction is:$$Q/t = Q_1/t + Q_2/t$$$$Q/t = 12.3 W + 19.6 W$$$$Q/t = 20 W$$Therefore, the correct answer is A: 20 W.

A Heat Conducting Rod, 1