Three rods of same dimension have thermal conductivities 3k, 2K and K. They are arranged as shown in the figure below. Then in the steady state the temperature of the junction P is

Options

A. `(200)/(3)""^(@)C`
B. `(100)/(3)""^(@)C`
C. `75^(@)C`
D. `(50)/(3)""^(@)C`

Answer

A

Explanation

Amount of heat transmitted from one point to another is
`Q = (kAt (T_(1) - T_(2)))/(d)`
where, k is thermal conductivity, t is time and `T_(1) - T_(2)` is temperature difference. At junction, `Q = Q_(1) + Q_(2)`
`(3kA (100 - T)t)/(d) = (2kA(T - 50)t)/(d) + (kA (T-0)t)/(d)`
`300kA t- 3kA tT = 2kA t T -100 kA t + kATt`
400kAt = 400kAt = 6kAtT
`T = (400)/(6)`
`T= (200^(@))/(3)C`