A heat conducting rod, 1.60 m long, is made of an aluminum section, .9 m long, a

Question

A heat conducting rod, 1.60 m long, is made of an aluminum section, .9 m long, and a copper section, .7 m long. both sections have a cross-sectional area of .0004 m2. the aluminum end and the copper end are maintained at temperatures of 30 degrees celcius and 170 degrees celcius, respectively. the thermal conductivity of aluminum and copper are 205 and 385 W/m*K, respectively. the rate at which heat is conducted in the rod is closest to:

11W

12W

9W

7.9W

10W

Please show the steps how to get to the answer. i really want to learn this.

Explanation / Answer

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A heat conducting rod, 0.90 m long, is made of an aluminum section, 0.20 m long, and a copper section, 0.70 m long. Both sections have a cross-sectional area of 0.0004 m^2. The aluminum end and the copper end are maintained at temperatures of 30*C and 230*C respectively. The thermal conductivities of aluminum and copper are 205 and 385 W/m ? K, respectively. The temperature of the aluminum-copper junction in the rod, in *C, is closest to:

Answer

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 is the temp at the junction

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