Three bars of equal lengths and equal area of cross-section are connected in series fig. their thermal conducitives are in the ratio `2:3:4`. If at the steady state the open ends of the first and the last bars are at temperature `200^(@)C` and `20^(@)C` respectively, find the temperature of both the junctions.
.

Explanation

Let `theta_(1)` and `theta_(2)` be the temperature of the junctions B and C respectively.
At the steady state, the rate of flow of heat through each bar will be same.
`(Delta Q)/(Delta t) = (2K xx A xx (200-theta_(1)))/(l)`
`=(3KA(theta_(1)-theta_(2)))/(l)` = `(4KA(theta_(2)-20))/(l)`
or `2(200-theta_(1)) = 3(theta_(1)-theta_(2)) = 4 (theta_(2)-20)`
On solving we get, `theta_(1) = 116.9^(@)C, theta_(2) = 61.5^(@)C`.