You have a 785cmlong copper rod with a rectangular cross sec

You have a 78.5-cm-long copper rod with a rectangular cross section of dimensions 4.35 cm by 8.79 cm. You maintain the ends of the rod at 44.3°C and 85.5°C, but otherwise insulate the rod from its environment. Find the heat current* through the rod. The thermal conductivity of copper is 385 W/(m·K).

Solution

Heat flow rate = k A dT/dx

k = thermal conductivity = 385 W / (m K)

A = cross section area = 0.0435m x 0.0879m = 3.824 x 10^-3 m^2

dT = 85.5 - 44.3 = 41.2 K

dx = 0.785 m

heat current dq/dt = (385)(3.824 x 10^-3)(41.2) / (0.785)

      = 77.27 J/s