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 length `l_1 and l_2` and thermal conductivities `K_1 and K_2` respectively. The temperature at the interface of the two section is

Options

A. `(k_2l_2T_1 + k_1 l_1 T_2)//(k_1l_1+k_2l_2)`
B. `(k_2l_2T_1 + k_1l_1T_2)//(k_2l_1 + k_1l_2) `
C. `(k_1 l_2T_1 + k_2l_1T_2)//(k_1l_2 + k_2l_1)`
D. `(k_1l_1T_1 + k_2l_2T_2)//(k_1l_1 + k_2l_2) `

Answer

C

Explanation

As both rods are connected in series, the rate of flow of heat is same. Let T be the temperature at the junction of rods,
`A ((T_1 - T)k_1)/(l_1) = A ((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)`