Three rods of material X and three rods of material Y are connected as shown in the figure. All the rods are of identical length and cross-sectional area. If the end A is maintained at `60^@C` and the junction E at `10^@C`. Calculate the temperature of the junction B, C and D. The thermal conductivity of X is `0.92cal//sec-cm^@C` and that of Y is `0.46cal//sec-cm-^@C`.

Answer

B, C, D

Explanation

`K_X=0.92 cal//sec-cm-^@C`
`K_Y=0.46 cal//sec-cm-^@C`

The heat flow through AB is divided
into two path Bc and BD. Symmetry shows that no heat will
flow through CD. Therefore
`(K_YA(60-T_B))/l=(K_XA(T_B-10))/2l+(K_YA(T_B-10))/2l`
On solving the above equation, we get
`T_B=30^@C`
As C is a point at the middle of BE therefore temperature at
`C is 20^@C.`
Similarly temperature at D is also `20^@C.`