Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K_1, K_2 and K_3, respectively. They…

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $\displaystyle \mathrm{K}_1, \mathrm{~K}_2$ and $\displaystyle \mathrm{K}_3$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $\displaystyle 100^{\circ} \mathrm{C}$ and the other at $\displaystyle 0^{\circ} \mathrm{C}$ (see figure). If the joints of the rod are at $\displaystyle 70$°C and $\displaystyle 20$°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $\displaystyle \mathrm{K}_1, \mathrm{~K}_2$ and $\displaystyle \mathrm{K}_3$ is :