# Variable thermal conductivity!

**Classical Mechanics**Level 4

A rod of length \(l\) with thermally insulated lateral surface is made of a material whose thermal conductivity varies as \(K =\dfrac C T\), where \(C\) is a constant. The ends are kept at temperatures \(T_1\) and \(T_2\). The temperature at a distance \(x\) from the first end varies as \( T= T_1 \large(\frac{T_2}{T_1})^{\frac{ax}{2l}} \). Find the value of '\(a\)'.