One end of a thermally insulated rod is kept at a temperature `T_(1)` and the other at `T_(2)`. The rod is composed of two sections of lengths `l_(1) and l_(2)` and thermal conductivities `K_(1) and K_(2)` respectively. The temperature at the interface of the two sections 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_(1)L_(1)+K_(1)L_(2)))`
C. `((K_(1)L_(1)T_(1)+K_(2)L_(1)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 temperature of the interface `= T`
`(T_(1)-T)/(((L_(1))/(AK_(1))))=(T-T_(2))/(((L_(2))/(K_(2)A)))`
`rArr T ((L_(1))/(K_(1))+(L_(2))/(K_(2))) =(T_(1)L_(2))/(K_(2))+(T_(2)L_(1))/(K_(1))`
`rArr T = (T_(1)K_(1)L_(2)+T_(2)L_(1)K_(2))/(L_(1)K_(2)+L_(2)K_(1))`