Rods A and B have their lengths in the ratio 1: 2 . Their thermal conductivities are K₁ and K₂ respectively. The temperatures at the ends of each rod are T₁ and T₂ . If the rate of flow of heat through the rods is equal, the ratio of area of cross section of A to that of B is

Step-by-step solution

The rate of heat flow H through a rod is given by the formula H = KA(T₁ - T₂) L , where K is the thermal conductivity, A is the area of cross-section, L is the length, and (T₁ - T₂) is the temperature difference across the ends. Given that the rate of heat flow is equal for both rods, we have H_A = H_B . Let L_A = L and L_B = 2L based on the ratio 1:2 . Let A_A and A_B be the areas of cross-section of rods A and B respectively. Equating the heat flow rates: K₁ A_A (T₁ - T₂) L_A = K₂ A_B (T₁ - T₂) L_B Since the temp