question_answer

One end of a thermally insulated rod is kept at a temperature \[{{T}_{1}}\] and the other at \[{{l}_{2}}\]. The rod is composed of two sections of length \[{{l}_{2}}\] and\[{{l}_{1}}\] thermal conductivities \[{{\operatorname{K}}_{1}}\] and \[{{K}_{2}}\]respectively. The temperature at the interface of the two section is  

A) \[\frac{\left( {{K}_{1}}{{l}_{1}}{{T}_{1}}+{{K}_{2}}{{l}_{2}}{{T}_{2}} \right)}{\left( {{K}_{1}}{{l}_{1}}+{{K}_{2}}{{l}_{2}} \right)}\]

B) \[\frac{\left( {{K}_{2}}{{l}_{2}}{{T}_{1}}+{{K}_{1}}{{l}_{1}}{{T}_{2}} \right)}{\left( {{K}_{1}}{{l}_{1}}+{{K}_{2}}{{l}_{2}} \right)}\]

C) \[\frac{\left( {{K}_{2}}{{l}_{1}}{{T}_{1}}+{{K}_{1}}{{l}_{2}}{{T}_{2}} \right)}{\left( {{K}_{1}}{{l}_{1}}+{{K}_{2}}{{l}_{2}} \right)}\]

D) \[\frac{\left( {{K}_{1}}{{l}_{2}}{{T}_{1}}+{{K}_{2}}{{l}_{1}}{{T}_{2}} \right)}{\left( {{K}_{1}}{{l}_{1}}+{{K}_{2}}{{l}_{2}} \right)}\]