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(D) The system can be modeled as an equivalent thermal circuit. Each rod has a thermal resistance $R$.Between points $B$ and $C$,there are two paralle

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$40$

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(D) The system can be modeled as an equivalent thermal circuit. Each rod has a thermal resistance $R$.Between points $B$ and $C$,there are two parallel paths,each consisting of two rods in series. The resistance of each path is $R + R = 2R$.The equivalent resistance $R_{BC}$ of these two parallel paths is given by $\frac{1}{R_{BC}} = \frac{1}{2R} + \frac{1}{2R} = \frac{2}{2R} = \frac{1}{R}$,so $R_{BC} = R$.The total thermal resistance of the circuit from $A$ to $D$ is $R_{AD} = R_{AB} + R_{BC} + R_{CD} = R + R + R = 3R$.The steady-state heat current $H$ flowing through the circuit is $H = \frac{\Delta T}{R_{total}} = \frac{100 - 10}{3R} = \frac{90}{3R} = \frac{30}{R}$.The temperature at junction $C$ can be found using the heat current through the rod $CD$:$H = \frac{T_C - 10}{R}$$\frac{30}{R} = \frac{T_C - 10}{R}$$30 = T_C - 10$$T_C = 40^{\circ} C$.

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at $100^{\circ} C$ and $10^{\circ} C$ respectively. The temperature of junction $C$ will be $.... ^{\circ} C$.

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