Consider steady state, one-dimensional heat conduction in an infinite slab of thickness $2L (L = 1\:m)$ as shown in the figure. The conductivity $(k)$ of the material varies with temperature as $\text{k = CT}$, where $T$ is the temperature in $K$, and $C$ is a constant equal to $2\: W \cdot m^{-1} \cdot K^{-2}$. There is a uniform heat generation of $1280\:kW/m^{3}$ in the slab. If both faces of the slab are maintained at $600\: K$, then the temperature at $X = 0$ is _______________ $K$ (in integer).
