Three rods of Copper, Brass and Steel are welded together to form a Y shaped structure. Area of cross-section of each rod = 4 . End of copper rod is maintained at 100°C whereas ends of brass and steel are kept at 0°C. Lengths of the copper, brass and stee

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 ${cm}^{2}$ . End of copper rod is maintained at 100°C whereas ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cm 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: [2014]

Smart Achievers · Accepted Answer

(3)

Rate of heat flow is given by,

$Q = \frac{K A (θ_{1} - θ_{2})}{l}$

Where, K = coefficient of thermal conductivity

$l$ = length of rod and A = area of cross-section of rod

If the junction temperature is T, then

$Q_{Copper} = Q_{Brass} + Q_{Steel}$

$\frac{0.92 \times 4 (100 - T)}{46} = \frac{0.26 \times 4 (T - 0)}{13} + \frac{0.12 \times 4 (T - 0)}{12}$

$\Rightarrow 200 - 2 T = 2 T + T \Rightarrow T = 40 ° C$

$∴$ $Q_{Copper} = \frac{0.92 \times 4 \times 60}{46} = 4.8 cal/s$

Solution

1 1.2 cal/s

2 2.4 cal/s

3 4.8 cal/s

4 6.0 cal/s

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