Question

Three rods are identical geometry but different thermal conductivity are joining as shown. Temperature of three ends are shown. Temperature of junction is​

Answer 1

The temperature at the junction T =  60° C.

Explanation:

The question is incomplete. Please find the complete question below:

Three rods of identical geometry but different materials are welded to form the English alphabet letter Y as shown. If their conductivity are K, 2K and 3K and end temperature are 20°C, 20°C and 100°C. respectively, then their junction temperature T is

(1) 70°C

(2) 60°C

(3) 50°C​

(4) 40°C

Solution:

3K (100-T) / L = K (T-20) / L + 2K (T-20) / L

Dividing both sides by L/K, we get:

3 (100-T) = (T-20) +2 (T-20)

300 - 3T = T - 20 + 2T - 40

300 + 20 + 40 = T + 3T + 2T

360 = 6T

Therefore T = 360 / 6 = 60

The temperature at the junction T =  60° Celcius.

Option 2 is the answer.