The three rods depicted in the figure have identical geometrical dimensions. In arrangement (a), heat flows from the hot end at a rate of 40 W . The thermal conductivities of aluminium and copper are 200 W m ⁻¹ ^ C ⁻¹ and 400 W m ⁻¹ ^ C ⁻¹ respectively. Determine the rate of heat flow when the rods are joined as in arrangement (c).

Step-by-step solution

Let the length and cross-sectional area of each rod be L and A respectively. The thermal resistance of a rod is given by R = L KA . Let the thermal resistance of the aluminium rod be R_ Al = R . Since K_ Cu = 2K_ Al , the thermal resistance of the copper rod is R_ Cu = R 2 . In arrangement (a), the three rods are connected in series. The equivalent thermal resistance is: R_ a = R_ Al + R_ Cu + R_ Al = R + R 2 + R = 5R 2 The rate of heat flow in arrangement (a) is: H_a = T R_a = 100 5R 2 = 40 R Given H_a = 40 W , we