Two rods with identical geometrical dimensions are placed between...

Let $R_1$ and $R_2$ be the thermal resistances of the two rods.

In the initial arrangement, the heat current through both rods is the same. Therefore,

$\dfrac{100 - 70}{R_1} = \dfrac{70 - 0}{R_2}$

$\Rightarrow \dfrac{30}{R_1} = \dfrac{70}{R_2}$

$\Rightarrow \dfrac{R_1}{R_2} = \dfrac{3}{7}$

When the rods are interchanged, let the new junction temperature be $T$. The heat current remains the same through both rods in the new series combination:

$\dfrac{100 - T}{R_2} = \dfrac{T - 0}{R_1}$

$\Rightarrow \dfrac{100 - T}{T} = \dfrac{R_2}{R_1}$

Substituting $\dfrac{R_2}{R_1} = \dfrac{7}{3}$, we get:

$\dfrac{100 - T}{T} = \dfrac{7}{3}$

$\Rightarrow 300 - 3T = 7T$

$\Rightarrow 10T = 300$

\Rightarrow T = 30^{}^{{}^{\circ}} C