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.For part AB, `(Q_(l))/(t)prop((T_(1)-T)K_(1))/(l_(1))`
For part BC, `(Q_(2))/(t)prop((T-T_(2))K_(2))/(l_(2))`
At equilibrium, `(Q_(1))/(t)=(Q_(2))/(t) therefore((T_(1)-T)K_(1))/(l_(1))=((T-T_(2))K_(2))/(l_(2))=T=(T_(1)K_(1)l_(2)+T_(2)K_(2)l_(1))/(K_(1)l_(2)+K_(2)l_(1))`