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Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod = 4 cm². End of copper rod is maintained at 100°C where as ends of brass and steel are at 0°C. Lengths of brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surrounding except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is -

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

Correct answer: 4.8 cal/s

Solution

The rate of heat flow through a rod can be calculated using Fourier's law of heat conduction, which states that the heat transfer rate is proportional to the temperature difference and the thermal conductivity, divided by the length of the rod. Given the thermal conductivity of copper and the temperature difference, the calculated heat flow rate through the copper rod is 4.8 cal/s, making this the correct option.

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