Three rods of copper, brass and steel are welded together to form a Y -shaped structure. The cross-sectional area of each rod is `4 cm^2`. The end of copper rod is maintained at `100^@C` and the ends of the brass and steel rods at `80^@C` and `60^@C` respectively. Assume that there is no loss of heat from the surfaces of the rods. The lengths of rods are : copper 46 cm, brass 13 cm and steel 12 cm.
(a) What is the temperature of the junction point?
(b) What is the heat current in the copper rod?
K(copper) = 0.92, K (steel) = 0.12 and K(brass) = 0.26 `cal//cm-s^@C` .

Answer

A, B, C, D

Explanation

Let `theta` be the temperature of junction. Then,

`H_1 + H_2 = H_3`
`:. (100-theta )/((46//0.92A)) + (80-theta)/((13//0.26A)) = (theta - 60)/((12//0.12A))`
Solving this equation we have,
`theta = 84^@C`
(b) Heat current in copper rod,
`H_1 = (100-theta)/((46//0.92 xx 4))`
`= 1.28 cal//s`