Question

A heat conducting rod, 1.60 m long, is made of an aluminum section, 0.90 m long, and a copper section, 0.70 m long. Both sections have a cross-sectional area of 0.0004 m2. The aluminum end and the copper end are maintained at temperatures of 30°C and 170°C, respectively. The thermal conductivities 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:

A) 7.9 W
B) 11 W
C) 9.0 W
D) 10 W

Answer 1

To calculate the rate at which heat is conducted in the rod, you can use the formula Q = k * A * (ΔT / L), where Q is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the section.

Step-by-step explanation:

To calculate the rate at which heat is conducted in the rod, we need to first calculate the temperature difference between the aluminum end and the copper end. We can use the formula:

Q = k * A * (ΔT / L)

Where Q is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the section. We can calculate the rate of heat transfer for each section:

For the aluminum section:

Qaluminum = 205 * 0.0004 * (170 - 30) / 0.90 = 204 W

For the copper section:

Qcopper = 385 * 0.0004 * (170 - 30) / 0.70 = 558 W

The rate at which heat is conducted in the rod is the sum of the rates of heat transfer for each section:

Q = Qaluminum + Qcopper = 204 + 558 = 762 W

Therefore, the closest answer choice is D) 10 W.