Question

A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m long and a copper section that is .70m long. Both sections have a cross-sectional area of .000040m2. The aluminum end and the copper end are maintained at temperatures of 30 degrees C and 230 degrees C respectively. The thermal conductivities of aluminum and copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). What is the temperature of the aluminum-copper junction in the rod with steady state heat flow?

These are the answers to select from, I keep getting way off....

A) 100°C

B) 93°C

C) 86°C

D) 80°C

E) 74°C

Answer 1

Resistance of each rod is given by

R = L / kA

so

aluminum: R = 0.20 / 205 * 0.0004 = 2.439

copper: R = 0.70 / 385 * 0.0004 = 4.545

total resistance = 2.439 + 4.545 = 6.9845

total rate of heat flow = total temp diff / total resistance = 200 / 6.9845 = 28.635 Watts

temp diff across aluminum = heat flow * resistance = 28.635 * 2.439 = 69.84 deg C

Since one end of the aluminum is at 30 deg C, the other end is

30 + 69.84 = 99.84 = 100 deg C (Option A) is the temp at the junction