Three rods of material $X$ and three rods of material $Y$ are connected as shown in the figure. All the rods are of identical length and cross-sectional area. The end $A$ is maintained at $60^{\circ} C$ and the junction $E$ at $10^{\circ} C$ . The thermal conductivity of $X$ is $0.92 c a l / s e c ‐ c m ‐^{\circ} C$ and that of $Y$ is $0.46 c a l / s e c ‐ c m ‐^{\circ} C$ . Choose the correct option(s).

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The temperature of the junction $B$ is $40^{\circ} C$

The temperature of the junction $C$ is $20^{\circ} C$

The temperature of the junction $D$ is $20^{\circ} C$

The temperature of the junction $B$ is $30^{\circ} C$

answer is B, C, D.

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Detailed Solution

$K_{x} = K_{y}$ , so $R_{x} = \frac{R_{y}}{2} = \frac{R}{2}$

The equivalent circuit is shown in figure.

$\frac{60 - T_{B}}{R} = \frac{T_{B} - 10}{2 R / 3} T_{B} = 30^{\circ} C$

Also $T_{C} = T_{D}$

and $\frac{30 - T_{C}}{R / 2} = \frac{T_{C} - 10}{R / 2} T_{C} = 20^{\circ} C$

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