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_(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))`