Heat is conducted by two cylindrical rods, one carbon and one aluminum, with identical cross-sectional area and length. The temperature difference between the ends of each rod is the same. Carbon has a thermal conductivity of 1100 J/(s . m . C°) and that of aluminum is 240 J/(s . m . C°). What percentage of the total energy transferred by the two rods each second is conducted by the silver rod?

Question

Quizplus · Accepted Answer

Let Qc and Qa be the amounts of heat conducted per second by the carbon and aluminum rods, respectively. Since the temperature difference is the same for both rods, the rate of heat transfer per unit length is proportional to the thermal conductivity:
Qc/Qa = (thermal conductivity of carbon)/(thermal conductivity of aluminum) = (1100 J/(s·m·°C))/(240 J/(s·m·°C)) = 4.58
Therefore, Qc/(Qc + Qa) = 1/(1 + Qa/Qc) = 1/(1 + 1/4.58) = 0.179 or 17.9%, so the percentage of the total energy transferred by the silver (aluminum) rod is 100% - 17.9% = 82.1%, which is closest to choice (B).

Heat Is Conducted by Two Cylindrical Rods, One Carbon and One