Three rods of copper, brass and steel are welded together to form a Y – shaped structure. Area of cross section of each rod is $4 c m^{2}$ . End of copper rod is maintained at $100^{0} C$ , where as ends of brass, steel are kept at $0^{0} C$ . Length of the copper, brass and steel rods are 46, 13 and 12 cm respectively. The rods are thermally insulated from surrounding except at ends. Thermal conductivity of copper, brass and steel are 0.92, 0.26 and 0.12 C.G.S units. Rate of heat flow through copper rod is

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3 cal / sec

4.8 cal/sec

6 cal/sec

5.8 cal/sec

answer is B.

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Detailed Solution

${(\frac{Q}{t})}_{Cu} = {(\frac{Q}{t})}_{brass} + {(\frac{Q}{t})}_{steel}$ $\frac{K_{cu} A (100 - θ)}{l_{cu}} = \frac{K_{b} A (θ - 0)}{l_{Br}} + \frac{K_{steel} A (θ - 0)}{l_{s}}$

$\frac{0 .92 \times A (100 - θ)}{46} = \frac{0 .26 \times A (θ - 0)}{13} + \frac{0 .12 \times A (θ - 0)}{12}$ $θ = 40^{0} C$

${(\frac{Q}{t})}_{Cu} = \frac{K_{Cu} A (100 - θ)}{l_{cu}} = 4 .8 cal / \sec$

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