In: Physics
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.
I have solved this question earlier with different figures. Please
workout using yours figures. If you need any further help just PM
me. If I have helped you please rate me 5 stars first (before you
rate anyone else)
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:
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