A 1D planar composite wall, depicted in the Figure below, is made of two layers having different thicknesses and thermal conductivities. Layer I has thickness L and thermal conductivity k_1, while Layer II has thickness 2L and thermal conductivity k_2=k_1/2. The two external boundaries (see Figure below) are kept at 30 C and 80 C, respectively. Consider that there is no heat generation and the two materials are isotropic.

The system is in steady state. Please answer the following questions:

A. Write a symbolic expression for the heat flux.

B. Calculate the temperature at the interface between the two materials.