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Copper, brass and steel rods are joined at one point to form a Y-shape, each with cross-sectional area 4 cm². The free end of the copper rod is at 100 deg C, while the free ends of the brass and steel rods are at 0 deg C. The lengths are 46 cm (copper), 13 cm (brass) and 12 cm (steel). The rods are insulated except at the ends. Thermal conductivities (CGS): copper 0.92, brass 0.26, steel 0.12 cal/(s.cm.deg C). Find the rate of heat flow through the copper rod.

1. 4.8 cal/s
2. 6.0 cal/s
3. 1.2 cal/s
4. 2.4 cal/s

Correct answer: 4.8 cal/s

Solution

Solving the junction balance gives T = 40 deg C, and the copper heat current is 0.92*4*(100-40)/46 = 4.8 cal/s.

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