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One end of a thermally insulated rod is ...

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

A

`(K_1l_1T_1+K_2l_2T_2)/(K_1l_1+K_2l_2)`

B

`(K_2l_2T_1+K_1l_1T_2)/(K_1l_1+K_2l_2)`

C

`(K_2l_1T_1+K_1l_2T_2)/(K_2l_1+K_1l_2)`

D

`(K_1l_2T_1+K_2l_1T_2)/(K_1l_2+K_2l_1)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d)
`(K_1A(T_1-T))/(l_1)=(K_2A(T-T_2))/(l_2)`
`:. T=(K_1T_1l_2+k_2T_2l_1)/(K_2l_1+K_1l_2)=(K_1l_2T_1+k_2l_1T_2)/(K_1l_2+K_2l_1)`
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