Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1/T_2$ is
Answer: (C) $\dfrac{5}{3}$
Thermal resistance $R_{th} = \dfrac{l}{KA}$. If each outer rod ($2K$) has resistance $R$, the middle rod ($K$) has $2R$. Total: $R + 2R + R = 4R$.
Heat current: $H = \dfrac{3T - T}{4R} = \dfrac{T}{2R}$.
$$T_1 = 3T - HR = 3T - \frac{T}{2} = \frac{5T}{2}$$
$$T_2 = T + HR = T + \frac{T}{2} = \frac{3T}{2}$$
$$\frac{T_1}{T_2} = \frac{5}{3}$$
Solution by Sreeraj P, M.Sc Physics