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 100ºC where as ends of brass and steel are kept at 0°C. 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

Engineering

Physics

Conduction of Heat

Question

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 100ºC where as ends of brass and steel are kept at 0°C. 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

4.8 cal/s

1.2 cal/s

2.4 cal/s

6.0 cal/s

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$8 \times \frac{(100 - T)}{\frac{46}{0 .92 \times 4}} = \frac{T - 0}{\frac{13}{0 .26 \times 4}} + \frac{T - 0}{\frac{12}{0 .12 \times 4}}$

0.08 (100 – T) = 0.08T + 0.09T

8 = 0.11T

T = 40

$\frac{dH}{dt}$ = 60 × 0.08 = 4.8 erg/s

Note: The answer is wrong because the answer is 4.8 erg/s.