Problem

Three rods of copper, brass and steel are welded together to form a Y-shaped structure. The cross-sectional area of each rod is

4 \text{ cm}^2

. The end of copper rod is maintained at

100^{\circ}\text{C}

and the ends of the brass and steel rods at

80^{\circ}\text{C}

and

60^{\circ}\text{C}

respectively. Assume that there is no loss of heat from the surfaces of the rods. The lengths of rods are : copper 46 cm, brass 13 cm and steel 12 cm.

K(\text{copper}) = 0.92, K(\text{steel}) = 0.12 \text{ and } K(\text{brass}) = 0.26 \text{ cal/cm}\cdot\text{s}\cdot^{\circ}\text{C}

(a) What is the temperature of the junction point? (b) What is the heat current in the copper rod?

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