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 cm 2 . End of copper rod is maintained at 100 ° C . Where as ends of bras

Question

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 cm 2 . End of copper rod is maintained at 100 ° C . 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 :

TestHub · Accepted Answer

L C u = 46 cm ; L B = 13 cm & L S = 12 cm . K C u = 0 .92 K B = 0 .26 K S = 0 .12 } C G S unit We know that R = L K A R C u = 46 0 .92 × 4 = 12 .5 R B = 13 0 .26 × 4 = 12 .5 R S = 12 0 .12 × 4 = 25 Now, if T is temperature of junction then 100 - T R C u = T - 0 R B + T - 0 R S 100 - T 12 .5 = T 12 .5 + T 25 ∴ 100 - T 12 .5 = 3 T 25 200 = 5 T ∴ T =40 ∘ ⇒ Q C u = 100 - T R C u = 100 - 40 12 .5 = 60 12 .5 ⇒ Q C u = 4 .8 Cal / s

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