AP Physics 2 Exam Question:

A metal rod with a length of 0.5 meters and a cross-sectional area of 0.02 square meters is at a uniform temperature of 20°C. The rod is initially placed in thermal contact with a heat source at 100°C. After a certain amount of time, the temperature of the rod rises and reaches a steady-state value of 80°C.

a) Calculate the heat transfer rate through the rod. b) Determine the thermal conductivity of the metal.

Assumptions:

• The metal rod is homogeneous and isotropic.
• The thermal conductivity of the metal remains constant at all temperatures.

Solution:

a) To calculate the heat transfer rate through the rod, we'll use the equation:

Q = k * A * (ΔT / L)

where:

• Q is the heat transfer rate
• k is the thermal conductivity of the metal
• A is the cross-sectional area of the rod
• ΔT is the temperature difference between the two ends of the rod
• L is the length of the rod

Given:

• A = 0.02 m²
• ΔT = 80°C - 20°C = 60°C
• L = 0.5 m

Plugging in the values, we have:

Q = k * 0.02 m² * (60°C / 0.5 m)

Q = k * 0.02 m * 120°C

b) To determine the thermal conductivity of the metal, rearrange the equation:

k = Q / (A * ΔT / L)

Substituting the known values:

k = Q / (0.02 m² * (60°C / 0.5 m))

k = Q / (0.02 m * 120°C)

Answer:

a) The heat transfer rate through the rod is given by Q = k * 0.02 m * 120°C.

b) The thermal conductivity of the metal is determined by k = Q / (0.02 m * 120°C).

Phrasing is improved by using the correct markdown.