One end of thermally insulated rod is kept at a temperature `T_(1)` and the other at `T_(2)`. The rod is composed of two section of length `l_(1)` and `l_(2)` thermal conductivities `k_(1)` and `k_(2)` respectively. The temerature at the interface of two section is

Options

A. `(K_(2)l_(2)T_(1) +K_(1) l_(1)T_(2))//)K_(1)l_(1)+K_(2)l_(2))`
B. `(K_(2))l_(1)T_(1)+K_(1)l_(2)T_(2))//(K_(2)l_(1)+K_(1)l_(2))`
C. `(K_(1)l_(2)T_(1)+K_(2)l_(2)T_(2))//(K_(1)l_(2)+K_(2)l_(1))`
D. `(K_(1)l_(1)T_(1)+K_(2)l_(2)T_(2))//(K_(1)l_(1)+K_(2)l_(2))`

Answer

C

Explanation

Let the temperature at the interface be `T`
`(Q_(1))/(t)prop ((T_(1)-T)K_(1))/(l_(1))`
For part `BC, (Q_(2))/(t) prop ((T-T_(2)K_(1)))/(l_(2))`
At equilibrium `(Q_(1))/(t) = (Q_(2))/(t)`
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