Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross – section of each rod = 4 cm². End of the copper rod is maintained at 100^oC where as ends of brass and steel are kept at 0^oC. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings 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 cal/s

2.4 cal/s

4.8 cal/s

6.0 cal/s

Solution

4.8 cal/s

dQ subscript 1 over dt space equals space dQ subscript 2 over dt space equals space dQ subscript 3 over dt rightwards double arrow fraction numerator 0.92 left parenthesis 100 minus straight T right parenthesis over denominator 46 end fraction space equals space fraction numerator 0.26 space left parenthesis straight T minus 0 right parenthesis over denominator 13 end fraction plus fraction numerator 0.12 space left parenthesis straight T minus 0 right parenthesis over denominator 12 end fraction rightwards double arrow straight T space equals space 40 to the power of straight o straight C dQ subscript 1 over dt space equals space fraction numerator 0.92 space straight x space 4 space left parenthesis 100 minus 40 right parenthesis over denominator 40 end fraction space equals space 4.8 space cal divided by straight s

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