Note: Please actually use separation of variables for this solution!

The left (at =0) and right (at =) surfaces of an infinite slab of thickness L are kept at known temperatures T0 and TL (T0 > TL), respectively until steady heat flow is established. The temperature of the left surface only is then suddenly changed to TL and maintained at this temperature. a) Write the initial condition, T(x,0) for this problem. b) Write the boundary conditions for this problem. c) Solve the PDE using the separation of variables technique to develop an expression for the temperature distribution T(x,t) in the slab following the aforementioned change.