Question

An iron rod of length 1 meter and cross-sectional area 0.01 square meters is initially at a temperature of 100°C. One end of the rod is placed in contact with a block of ice at 0°C and the other end is maintained at a constant temperature of 60°C. If the thermal conductivity of iron is 80 W/(m·K), calculate the rate of heat transfer through the rod.

Assumptions:

• The rod and the ice remain in thermal equilibrium.
• No heat is lost to the surroundings.

Give your answer in watts.

Solution

To solve this problem, we will use the formula for heat transfer through conduction:

q = k * A * (ΔT / d)

where:

q: rate of heat transfer (in watts) k: thermal conductivity of the material (in W/(m·K)) A: cross-sectional area of the rod (in square meters) ΔT: temperature difference between the ends of the rod (in K) d: length of the rod (in meters)

Given values: k = 80 W/(m·K) A = 0.01 m^2 ΔT = (60°C - 0°C) = 60 K d = 1 m

Substituting the given values into the formula, we have:

q = 80 W/(m·K) * 0.01 m^2 * (60 K / 1 m)

Simplifying the expression, we get:

q = 80 W

Therefore, the rate of heat transfer through the rod is 80 watts.