A composite rod is made of three different materials A, B, and C joined in series. Each material has the same length L and identical uniform cross-sectional area. The steady-state temperature T along the length x of the rod is plotted as a graph. The graph consists of three straight line segments connecting the points (0, 100^ C ) , (L, 70^ C ) , (2L, 50^ C ) , and (3L, 10^ C ) . The ratio of the thermal conductiviti

Step-by-step solution

In steady state, the rate of heat flow (heat current) H is constant across all three materials in series. The heat current is given by H = KA T L . Since the cross-sectional area A and length L are identical for all three parts, the thermal conductivity K is inversely proportional to the temperature drop T across that part. From the given coordinates, the temperature drops are: T_A = 100^ C - 70^ C = 30^ C T_B = 70^ C - 50^ C = 20^ C T_C = 50^ C - 10^ C = 40^ C Therefore, K_A T_A = K_B T_B = K_C T_C 30 K_A = 20 K_B