Three rods made of same material and having same cross-section have been joined as shown in Fig. 7(e).18. Each rod is of the same length. The left and the right ends are kept at `0^(@)C` and `60^(@)C` respectively. What is the temperature of the junction of the three rods.

Answer

`[40^(@)C]`

Explanation

Let `T^(@)C` be the temperature of the junction. At steady state, the sum of the rate of flow of heat through rods 2 and 3 = the rate of flow of heat through rod , i.e.,`((dQ)/(dt))_(2)+((dQ)/(dt))_(3)=((dQ)/(dt))_(1) `
or ` (KA(60^(@)-T))/(l)+(KA(60^(@)-T))/(l)=(KA(t-0^(@)))/(l)`
or `2(60^(@)-T)=T` or `T=40^(@)C`