Question

Two rods of same dimensions, but made of different materials are joined end to end to end with their free end being maintained at `100^(@)C` and `0^(@)C` respectively. The temperature of the junction is `70^(@)C`. Then the temperature of the junction if the rods are inerchanged will be equal to `T^(@)C` Find `T`:

Answer 1

Correct Answer - 30

Heat current is same `i_(H) = (70 -0)/(R_(1)) = (100 -70)/(R_(2))`
`rArr (R_(2))/(R_(1)) = 3//7 rArr (K_(1))/(K_(2)) = 3//7`
ltbRgt Heat current is same `i_(H) = (T -0)/(R_(2)) = (100 -T)/(R_(1))`
`rArr (100-T)/(T) = (R_(1))/(R_(2)) = (K_(2))/(K_(1)) = 7//3`
`rArr 300 - 3T = 7T rArr T = 30^(@)C`